Macroeconomics – Business and Economics, Appunti di Macroeconomia

Scarica Macroeconomics – Business and Economics e più Appunti in PDF di Macroeconomia solo su Docsity! Macroeconomics Paolo Vanin Start punctual, one pause, end class at 17.30/19.30. Office hours: online Wednesday 12.00-13.00. Textbook: Gregory Mankiw, Macroeconomics, 10°Edition, Mcmillan, 2019 (8°or 9°eds. less updated but fine as well) Exam: - mandatory written, computerised, each will have a different set of questions. It can be attended either at the computer lab, or online. 9 multiple choices and 4 open questions. - Completing problem sets (3 for each term) will give an extra grade for the exam. They will not be graded considering quality, just completeness. - The oral exam will give +/-3 points. It is on the whole program. You need it to get honours. - Partial exams: 1st part: November 3. LECTURE 1: The science of Macroeconomics (Ch.1) In Macroeconomics, you forget about individual decision making, and you understand how the economy works as a whole. Macroeconomists collect data on incomes, prices, unemployment, and many other variables from different time periods and different countries. The main topics will will address are: - What causes recession (unemployment)? What is “government stimulus”, why might it help? - What economic response to the pandemic? - What is the government budget deficit? How does it affect workers, consumers, businesses, and taxpayers? Is government debt a problem? - Why are so many countries poor? What policies might help them grow out of poverty? - What determines the cost of living? - What determines youth unemployment? - Brexit or Italexit: good ideas? Economists use many types of data to measure the performance of an economy. Three macroeconomic variables are especially important: real gross domestic product (GDP), the inflation rate, and the unemployment rate. • Real GDP: measures the total income of everyone in the economy (adjusted for the level of prices). Real GDP per Person indicates the average standard of living per capita in a country, i.e. the income of the average person in the economy. • The inflation rate: measures how fast prices are rising. The percentage change in the average level of prices from the year before. When the inflation rate is above zero, prices are rising. When it is below zero, deflation, prices are falling. If the inflation rate declines but remains positive, prices are rising but at a slower rate. • The unemployment rate: measures the fraction of the labor force that is out of work. People who are not searching for a job do not take part in the unemployment rate. 1.1 CASE STUDY: THE HISTORICAL PERFORMANCE OF THE U.S. ECONOMY What determines the steepness in the LR (first part of the course)? What determines the ups and downs in the SR (second part of the course)? Two main features of these data: - Over the long run, clear upward trend in living standards. - In the short run, fluctuations. There are repeated periods during which real GDP falls, the most dramatic instance being the early 1930s. Such periods are called recessions if they are mild and depressions if they are more severe. Italian Unemployment Rate, 1970-2019 (% of labor force) & Unemployment Rates, 1970-2019
 (% of labor force) Unlike inflation, there’s not lots of convergences. The outlier here is Spain, because it has a large number of temporary jobs, which are easy to create and easy to destroy. 1.2 HOW ECONOMISTS THINK Economists often study politically charged issues, but they try to address these issues with a scientist’s objectivity. Like any science, economics has its own set of tools: terminology, data, and a way of thinking. Economic models: there is no single “correct” model that applies to every economic question. Instead, there are many models, each of which is useful for shedding light on a particular facet of the economy. - Are simplified versions of a more complex reality: irrelevant details are stripped away - Are used to: show relationships between variables, explain the economy’s behavior, devise policies to improve economic performance. The slides offer some brief revision of microeconomics concepts. Here are the key/new ones: Exogenous and endogenous - Endogenous variables are those variables that a model explains. - Exogenous variables are those variables that a model takes as given. The purpose of a model is to show how the exogenous variables influence the endogenous variables. Prices: sticky vs flexible: Economists normally presume that the price of a good or a service moves quickly to bring quantity supplied and quantity demanded into balance. In other words, they assume that markets are normally in equilibrium, so the price of any good or service is found where the supply and demand curves intersect. This assumption, is called market clearing: prices are flexible, adjust to equate supply and demand. However, the assumption of continuous market clearing is not entirely realistic. For markets to clear continuously, prices must adjust instantly to changes in supply and demand. In fact, many wages and prices adjust slowly (e.g. wages set by contracts). The economy’s behavior depends partly on whether prices are sticky or flexible: - If prices sticky (short run), demand may not equal supply, which explains unemployment (excess supply of labor), and why firms cannot always sell all the goods they produce. In the real world, some wages and prices are sticky. Better for studying the short term. - If prices are flexible (long run), markets clear and economy behaves very differently. Market clearing models assume that all wages and prices are flexible. Better for studying the long term. 0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 20 12 20 14 20 16 20 18 0,0 5,0 10,0 15,0 20,0 25,0 30,0 19 70 19 73 19 76 19 79 19 82 19 85 19 88 19 91 19 94 19 97 20 00 20 03 20 06 20 09 20 12 20 15 20 18 France Germany Italy Spain UK USA SUMMARY CH.1 • Macroeconomics is the study of the economy as a whole, including: - growth in incomes - changes in the overall level of prices - the unemployment rate • Macroeconomists attempt to explain the economy and to devise policies to improve its performance. • Economists use different models to examine different issues. • Models with flexible prices describe the economy in the long run; models with sticky prices describe the economy in the short run. • Macroeconomic events and performance arise from many microeconomic transactions, so macroeconomics uses many of the tools of microeconomics. LECTURE 2: The Data of Macroeconomics (Ch.2) GROSS DOMESTIC PRODUCT: EXPENDITURE AND INCOME Gross domestic product, or GDP, is often considered the best measure of how well an economy is performing. Two definitions of GDP: • Total expenditure on domestically-produced final goods and services (in a given period of time) • Total income earned by domestically-located factors of production (in a given period of time)* *domestically located factors of production means labour and capital Why does GDP represent both total expenditure and total income? “Expenditure equals income because every dollar spent by a buyer becomes income to the seller.” Thus the value of total expenditure and the value of total income is the same. THE CIRCULAR FLOW The inner loop represents the flows of labor and bread: households sell their labor to firms, and the firms sell the bread they produce to households. The outer loop represents the corresponding flows of dollars: households pay the firms for the bread, and the firms pay wages and profit to the households. GDP measures the flow of dollars in this economy. We can compute it in two ways. GDP is the total income from the production of bread, which equals the sum of wages and profit — the top half of the circular flow of dollars. GDP is also the total expenditure on purchases of bread — the bottom half of the circular flow of dollars. To compute GDP, we can look at either the flow of dollars from firms to households or the flow of dollars from households to firms. The diversity of products in the economy complicates the calculation of GDP because different products have different values. To compute the total value of different goods and services, the national income accounts use market prices because these prices reflect how much people are willing to pay for a good or service. Thus, if apples cost $0.50 each and oranges cost $1.00 each, GDP would be GDP=(Price of Apples×Quantity of Apples)+ (Price of Oranges×Quantity of Oranges)=($0.50×4)+($1.00×3)=$5.00.
 GDP equals $5.00 - that is - the value of all the apples, $2.00, plus the value of all the oranges, $3.00. VALUE ADDED The value of output minus the value of the intermediate goods used to produce that output. One way to compute the value of all final goods and services is to sum the value added at each stage of production. The value added of a firm equals the value of the firm’s output less the value of the intermediate goods that the firm purchases. - A farmer grows a kilo of wheat and sells it to a miller for €1.00. - The miller turns the wheat into flour and sells it to a baker for €3.00. - The baker uses the flour to make a loaf of bread and sells it to an engineer for €6.00. - The engineer eats the bread. Compute value added at each stage of production and GDP. The value added by the farmer is 1, the value added by the miller is 2 (3-1, for him, the intermediate good is wheat), the value added by the baker is 3 (6-3). So 1+2+3 equals 6, the value of the output. Hence, GDP is also the total value added of all firms in the economy. FINAL GOODS, VALUE ADDED, AND GDP (TO REMEMBER BY HEART) • GDP: market value of all final goods and services produced within an economy in a given period of time. = sum of value added at all stages of production. • The value of the final goods already includes the value of the intermediate goods, 
 so including intermediate and final goods in GDP would be double-counting. In order to make these computations, it needs to be about goods that have a monetary value. We do not add up intermediate goods in the calculation of GDP, only final goods, otherwise intermediate goods would be double counted. WHICH TRANSACTIONS ARE INCLUDED IN GDP? • Used goods? No, it’s a transfer of existing wealth • Inventories? Yes, they are production of new wealth • Imputations and housing services. Housing services to home owners are imputed to GDP (but for simplicity services from durable goods are not) INNOVATIONS IN EUROPEAN ACCOUNTING • European system of accounts: ESA 2010 - Consistent with the U.S. SNA 2008 • Main change, since September 2014: - Capitalisation of R&D: from intermediate spending to investment; now included in GDP. • All EU states should also include estimates of consumption of drugs, prostitution, and smuggled alcohol and cigarettes - Principle: include all revenue generating transactions based on mutual agreement AN IGNOBLE IG NOBEL • 2011 Italian GDP is 3.7% higher with ESA 2010 1.3% (20.6 bln €) from capitalisation of R&D 1% (15.5 bln €) from inclusion of illegal markets (drug sales: 10.5 bln €; prostitution: 3.5 bln €; cigarettes smuggling: 0.3 bln €) • ISTAT won the 2014 Ig Nobel Prize for Economics “for proudly taking the lead in fulfilling the EU mandate for each country to increase the official size of its national economy by including revenues from prostitution, illegal drug sales, smuggling, and all other unlawful financial transactions between willing participants” NOW YOU TRY: AN EXPENDITURE-OUTPUT PUZZLE? Suppose a firm: - produces $10 million worth of final goods - only sells $9 million worth Does this violate the expenditure = output identity? No, because the output will simply fall into different categories, both ending up in the same computation for the GDP. Unsold output adds to inventory, and thus counts as inventory investment – whether intentional or unplanned. Thus, it’s as if a firm “purchased” its own inventory accumulation. With inventory investment, that future use is to give the firm the ability in the future to sell more than its output. WHY OUTPUT = EXPENDITURE Unsold output goes into inventory, and is counted as “inventory investment”… …whether or not the inventory buildup was intentional. In effect, we are assuming that firms purchase their unsold output. GDP: AN IMPORTANT AND VERSATILE CONCEPT We have now seen that GDP measures: - total income - total output - total expenditure - the sum of value-added at all stages in the production of final goods This is why economists often use the terms income, output, expenditure, and GDP interchangeably. GNP VS. GDP • Gross National Product (GNP): Total income earned by the nation’s factors of production, regardless of where located (if I have an Italian worker working abroad in the USA, the value of their work goes into USA GDP, but in Italian GNP) • Gross Domestic Product (GDP): Total income earned by domestically-located factors of production, regardless of nationality GNP= GDP + factor payments from abroad - factor payments to abroad Examples of factor payments: wages, profits, rent, interest & dividends on assets. For instance, if a Japanese resident owns an apartment building in New York, the rental income he earns is part of U.S. GDP because it is earned in the United States. But because this rental income is a factor payment to abroad, it is not part of U.S. GNP. In the United States, factor payments from abroad and factor payments to abroad are similar in size — each representing about 4 percent of GDP — so GDP and GNP are quite close. • Net Domestic Product: GDP - depreciation of capital (e.g. a machine becoming obsolete). (Thus, Net National Product will be NNP=GNP−Depreciation.) In the national income accounts, depreciation is called the consumption of fixed capital. Because the depreciation of capital is a cost of producing the output of the economy, subtracting depreciation shows the net result of economic activity. • Net national product is approximately equal to another measure called national income. The two differ by a small correction called the statistical discrepancy, which arises because different data sources may not be completely consistent: National Income=NNP−Statistical Discrepancy. National income measures how much everyone in the economy has earned. • A series of adjustments take us from national income to personal income, the amount of income that households and non-corporate businesses receive. SEASONAL ADJUSTMENT Because real GDP and the other measures of income reflect how well the economy is performing, economists are interested in studying the quarter-to-quarter fluctuations in these variables. Yet when we start to do so, one fact leaps out: all these measures of income exhibit a regular seasonal pattern. The output of the economy rises during the year, reaching a peak in the fourth quarter (October, November, and December) and then falling in the first quarter (January, February, and March) of the next year. It is not surprising that real GDP follows a seasonal cycle. Some of these changes are attributable to changes in our ability to produce: for example, building homes is more difficult during the cold weather of winter than during other seasons. In addition, people have seasonal tastes: they have preferred times for activities like vacations and Christmas shopping. When economists study fluctuations in real GDP and other economic variables, they often want to eliminate the portion of fluctuations due to predictable seasonal changes. You will find that most of the economic statistics reported are seasonally adjusted. NOW YOU TRY: DISCUSSION QUESTION In your country, which would you want to be bigger, GDP or GNP? Why? Ireland has attracted a lot of foreign capital because of the fact that labour taxations are much lower. Bangladesh has a lot of migration from Bangladesh to other countries. In Japan, GNP is 3.2% bigger than GDP. This means that the income earned by all Japanese citizens is 3.2% larger than the value of production occurring within Japan’s borders. In India, GNP is 1.2% smaller than GDP. This means that 1.2% of all the income earned in India leaves the country and is paid to foreigners. In Ireland, 18.3% of the value of domestic production is paid to foreigners. Some students offer this response: It’s better to have GNP > GDP, because it means our nation’s income is greater than the value of what we are producing domestically. If, instead, GDP > GNP, then a portion of the income generated in our country is going to people in other countries, so there’s less income left over for us to enjoy. REAL VS. NOMINAL GDP GDP is the value of all final goods and services produced. • nominal GDP measures these values using current prices. It is easy to see that GDP computed this way is not a good gauge of economic well-being. That is, this measure does not accurately reflect how well the economy can satisfy the demands of households, firms, and the government. If all prices doubled without any change in quantities, nominal GDP would double. Yet it would be misleading to say that the economy’s ability to satisfy demands has doubled because the quantity of every good produced remains the same. • real GDP measure these values using the prices of a base year. Shows what would have happened to expenditure on output if quantities had changed but prices had not. With the prices held constant, real GDP varies from year to year only if the quantities produced vary. Because a society’s ability to provide economic satisfaction for its members ultimately depends on the quantities of goods and services produced, real GDP provides a better measure of economic well-being than does nominal GDP. NOW YOU TRY: REAL & NOMINAL GDP (EXAM EXERCISE) - Compute nominal GDP in each year. - Compute real GDP in each year using 2010 as the base year. • nominal GDP multiply Ps & Qs from same year
 2010: $46,200 = $30 × 900 + $100 × 192 
 2011: $51,400 
 2012: $58,300 • real GDP multiply each year’s Qs by 2010 Ps
 2010: $46,200
 2011: $50,000 
 2012: $52,000 = $30 × 1050 + $100 × 205 REAL GDP CONTROLS FOR INFLATION Changes in nominal GDP can be due to: - changes in prices. - changes in quantities of output produced. Changes in real GDP can only be due to changes in quantities, because real GDP is constructed using constant base-year prices. REAL GDP AND WELFARE
 Real GDP per capita is an imperfect measure of social welfare. It does not consider: • Non-market goods and services: home production, child caring, leisure, volunteering, … • Quality of the physical and social environment • Income distribution But it is still one of the most important measures we have. CHAIN-WEIGHTED REAL GDP Over time, relative prices change, so the base year should be updated periodically. In essence, chain-weighted real GDP updates the base year every year, so it is more accurate than constant-price GDP. Your textbook usually uses constant-price real GDP, because: - the two measures are highly correlated. - constant-price real GDP is easier to compute. The base year changes continuously over time. In essence, average prices in 2017 and 2018 are used to measure real growth from 2017 to 2018, average prices in 2018 and 2019 are used to measure real growth from 2018 to 2019, and so on. These various year-to-year growth rates are then put together to form a “chain” that can be used to compare the output of goods and services between any two dates. Since constant-price GDP is easier to understand and compute, and because the two measures of real GDP are so highly correlated, this textbook emphasises the constant-price version of real GDP. THE SIZE OF THE CPI’S BIAS - In 1995, a U.S. Senate-appointed panel of experts estimated that the CPI overstates inflation by about 1.1% per year. - - So the BLS made adjustments to reduce the bias. - Now, the CPI’s bias is probably under 1% per year. CPI VS. GDP DEFLATOR: DIFFERENCES • Prices of capital goods: The first difference is that the GDP deflator measures the prices of all goods and services produced, whereas the CPI measures the prices of only the goods and services bought by consumers. Thus, an increase in the price of goods bought only by firms or the government will show up in the GDP deflator but not in the CPI. - included in GDP deflator (if produced domestically) - excluded from CPI • Prices of imported consumer goods: - included in CPI - excluded from GDP deflator • The basket of goods: The CPI assigns fixed weights to the prices of different goods, whereas the GDP deflator assigns changing weights. In other words, the CPI is computed using a fixed basket of goods, whereas the GDP deflator allows the basket of goods to change over time as the composition of GDP changes. - CPI: fixed - GDP deflator: changes every year Are both measures of the average price of the economy, but are built a bit different. Economic theorists have studied the properties of these different types of price indexes to determine which is a better measure of the cost of living. The answer, it turns out, is that neither is clearly superior. When prices of different goods are changing by different amounts, a Laspeyres (fixed basket) index tends to overstate the increase in the cost of living because it does not take into account the fact that consumers have the opportunity to substitute less expensive goods for more expensive ones. By contrast, a Paasche (changing basket) index tends to understate the increase in the cost of living. Although it accounts for the substitution of alternative goods, it does not reflect the reduction in consumers’ welfare that result from such substitutions. • PCE: In addition to the CPI and the GDP deflator, another noteworthy measure of inflation is the implicit price deflator for personal consumption expenditures (PCE), or PCE deflator. The PCE deflator is calculated like the GDP deflator but, rather than being based on all of GDP, it is based on just the consumption component. That is, the PCE deflator is the ratio of nominal consumer spending to real consumer spending. Like the GDP deflator, the PCE deflator allows the basket of goods to change over time as the composition of consumer spending changes. Because of this mix of attributes, the Federal Reserve uses the PCE deflator as its preferred gauge of how quickly prices are rising. How the PCE is like the CPI:
 - only includes consumer spending
 - includes imported consumer goods How the PCE is like the GDP deflator:
 - the “basket” changes over time THE BILLION PRICES PROJECT AT MIT • Automatically collect daily price data from online retailers in Argentina or mobile phones in Venezuela ( http://bpp.mit.edu ) • Pro: faster and cheaper data collection - In some cases, more manipulation proof than official data • Con: smaller coverage ONLINE VS. CPI INFLATION IN THE U.S. CATEGORIES OF THE POPULATION • employed: working at a paid job • unemployed: not employed but looking for a job, specifically had tried to find employment during the previous four weeks. It also includes those waiting to be recalled to a job from which they had been laid off. • labor force: the amount of labor available for producing goods and services; Labor Force=Number of Employed+Number of Unemployed • not in the labor force: not employed, not looking for work, e.g. full-time student, retiree. • discouraged worker: Notice that a person who wants a job but has given up looking — a discouraged worker — is counted as not being in the labor force. TWO IMPORTANT LABOR FORCE CONCEPTS • unemployment rate: percentage of the labor force that is unemployed. Unemployed/Labor Force • labor force participation rate: the fraction of the adult population that “participates” in the labor force • Adult population: aged 15-64 (also called “active population”) Cost of basket in that month Cost of basket in base period National Income: Where it Comes From and Where it Goes (Ch.3) THE CIRCULAR FLOW OF THE ECONOMY Let’s look at the flow of dollars from the viewpoints of these actors. Households receive income and use it to pay taxes to the government, to consume goods and services, and to save through the financial markets. Firms receive revenue from the sale of the goods and services they produce and use it to pay for the factors of production. Households and firms borrow in financial markets to buy investment goods, such as houses and factories. The government receives revenue from taxes and uses it to pay for government purchases. Any excess of tax revenue over government spending is called public saving, which can be either positive (a budget surplus) or negative (a budget deficit). OUTLINE OF THE MACROECONOMIC MODEL A closed economy, market-clearing model • Supply side - factor markets (supply, demand, price) - determination of output/income • Demand side - determinants of C, I, and G • Equilibrium - goods market - loanable funds market What determines the total production of goods and services? An economy’s output of goods and services—its GDP—depends on (1) its quantity of inputs, called the factors of production, and (2) its ability to turn inputs into output, as represented by the production function. FACTORS OF PRODUCTION Factors of production are the inputs used to produce goods and services. K = capital: tools, machines, and structures used in production L = labor: the physical and mental efforts of workers, time spent working In this chapter we take the economy’s factors of production as given. In other words, we assume that the economy has fixed amounts of capital and labor. (So K bar and L bar) THE PRODUCTION FUNCTION: Y = F(K,L) • shows how much output Y the economy can produce from K units of capital and L units of labor • reflects the economy’s level of technology: if someone invents a better way to produce a good, the result is more output from the same amounts of capital and labor • exhibits constant returns to scale: increase in input results in a proportional increase in output RETURNS TO SCALE: A REVIEW Initially Y1 = F (K1 , L1 ) Scale all inputs by the same factor z: K2 = zK1 and L2 = zL1 (e.g., if z = 1.2, then all inputs are increased by 20%) What happens to output, Y2 = F (K2, L2 )? - If constant returns to scale, Y2 = z Y1 - If increasing returns to scale, Y2 > z Y1 - If decreasing returns to scale, Y2 < z Y1 The firm’s demand for factors: We now know that our firm will hire labor and rent capital in the quantities that maximise profit. But what are those profit-maximising quantities? DEMAND FOR LABOR - Assume markets are competitive: each firm takes W, R, and P as given. - Basic idea: A firm hires each unit of labor if the cost does not exceed the benefit. Cost: real wage Benefit: marginal product of labor MARGINAL PRODUCT OF LABOR (MPL) - Definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) – F (K, L) - With derivatives: It is the slope of the production function Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor decreases as the amount of labor increases. To see why, consider again the production of bread at a bakery. As a bakery hires more labor, it produces more bread. The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fixed amount of capital, however, the MPL falls. Fewer additional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fixed, each additional worker adds fewer loaves of bread to the bakery’s output. FROM THE MARGINAL PRODUCT OF LABOR TO LABOR DEMAND When the competitive, profit-maximising firm is deciding whether to hire an additional unit of labor, it considers how that decision would affect profits. It therefore compares the extra revenue from increased production with the extra cost from hiring the additional labor. - Because an extra unit of labor produces MPL units of output and each unit of output sells for P dollars, the extra revenue is P*MPL. - The extra cost of hiring one more unit of labor is the wage W. Thus, the change in profit from hiring an additional unit of labor is: Δ Profit=Δ Revenue − Δ Cost=(P×MPL)−W So: the firm’s manager knows that if the extra revenue P×MPL exceeds the wage W, an extra unit of labor increases profit. Therefore, the manager continues to hire labor until the next unit would no longer be profitable—that is, until the MPL falls to the point where the extra revenue equals the wage. To get the answers: - Using calculus: Take the derivative of F( ) with respect to L. The resulting expression is the MPL. Looking at this expression, determine whether MPL falls as L rises. (Or, take derivative of your MPL function w.r.t. L and see whether it’s positive, negative, or zero.) - Using algebra: Plug in any value for K and another value for L. See what happens if you increase L, then increase it again, and again. This may require a calculator. - With a graph: You can sketch the graph of these production functions (Y on the vertical, L on the horizontal, assuming a given value of K). If you know the general shape of the square root function, then it’s easy to tell that (b) and (c) have diminishing marginal returns. To maximise profit, the firm hires up to the point at which the marginal product of labor equals the real wage. For example, again consider a bakery. Suppose the price of bread P is $2 per loaf, and a worker earns a wage W of $20 per hour. The real wage W/P is 10 loaves per hour. In this example, the firm keeps hiring workers as long as the additional worker would produce at least 10 loaves per hour. When the MPL falls to 10 loaves per hour or less, hiring additional workers is no longer profitable. Because the MPL diminishes as the amount of labor increases, this curve slopes downward. For any given real wage, the firm hires up to the point at which the MPL equals the real wage. Hence, the MPL schedule is also the firm’s labor demand curve. THE MARGINAL PRODUCT OF CAPITAL AND CAPITAL DEMAND The firm decides how much capital to rent in the same way it decides how much labor to hire. The marginal product of capital (MPK) is the amount of extra output the firm gets from an extra unit of capital, holding the amount of labor constant: MPK=F(K+1, L)−F(K, L)
 Thus, the marginal product of capital is the difference between the amount of output produced with K+1 units of capital and that produced with only K units of capital. Like labor, capital is subject to diminishing marginal product. The increase in profit from renting an additional machine is the extra revenue from selling the output of that machine minus the machine’s rental price: Δ Profit=Δ Revenue − Δ Cost=(P×MPK)−R.
 To maximise profit, the firm continues to rent more capital until the MPK falls to equal the real rental price: MPK=R/P The real rental price of capital is the rental price measured in units of goods rather than in dollars. Lesson 4 MATHEMATICALLY - Each firm demands L and K to maximise profits, taking technology (F) and prices (W, R and P) as given. - Market demand: aggregate demand of each firm EXPLANATIONS FOR RISING INEQUALITY IN INCOME 1. Rise in capital’s share of income, since capital income is more concentrated than labor income. 2. - Technological progress has increased the demand for skilled relative to unskilled workers. - Due to a slowdown in expansion of education, the supply of skilled workers has not kept up. - Result: Rising gap between wages of skilled and unskilled workers. The Gini coefficient is a popular measure of inequality. A value of 0 would mean perfect equality, while a value of 1 would mean that one person has all the income. OUTLINE OF MODEL A closed economy, market-clearing model We have seen what determines the level of production and how the income from production is distributed to workers and owners of capital. We now continue our tour of the circular flow diagram, and examine how the output from production is used. MPL = ∂F K,L( ) ∂L DEMAND FOR GOODS & SERVICES Components of aggregate demand (i.e. of GDP): C = consumer demand for goods & services I = demand for investment goods G = government demand for goods & services NX = net exports The circular flow diagram contains only the first three components. For now, to simplify the analysis, we assume our economy is a closed economy—a country that does not trade with other countries. Thus, net exports are always zero. Households consume some of the economy’s output, firms and households use some of the output for investment, and the government buys some of the output for public purposes. We want to see how GDP is allocated among these three uses. CONSUMPTION, C - Disposable income is total income minus total taxes (net of transfers): Y – T. - Consumption function: C = c(Y – T) Shows that ↑(Y – T ) ⇒ ↑C (i.e. as disposable income goes up, so does consumption. This equation states that consumption is a function of disposable income. The relationship between consumption and disposable income is called the consumption function. - Marginal propensity to consume (MPC) is the change in C when disposable income increases by one euro. The MPC is between zero and one: an extra dollar of income increases consumption but by less than one dollar. - Mathematically: MPC= dC d(Y-T) The slope of the consumption function tells us how much consumption increases when disposable income increases by one dollar. That is, the slope of the consumption function is the MPC. INVESTMENT, I The quantity of investment goods demanded depends on the interest rate, which measures the cost of the funds used to finance investment. For an investment project to be profitable, its return (the revenue from increased future production of goods and services) must exceed its cost (the payments for borrowed funds). If the interest rate rises, fewer investment projects are profitable, and the quantity of investment goods demanded falls. When studying the role of interest rates in the economy, economists distinguish between the nominal interest rate and the real interest rate. The nominal interest rate is the interest rate as usually reported: it is the rate of interest that investors pay to borrow money. • The investment function is I = I (r ), where r denotes the real interest rate, the nominal interest rate corrected for inflation. E.g. If the nominal interest rate is 8 percent and the inflation rate is 3 percent, then the real interest rate is 5 percent. • The real interest rate is: - the cost of borrowing (e.g. borrowing money from the bank). If cost of borrowing money is very high, and if my investment relies on borrowing money, then “I” will go down. - the opportunity cost of using one’s own funds to finance investment spending. If I am wealthy, and the real interest rate is higher, I can simply lend my money to someone who will pay me the real interest rate instead of investing that money myself. • So, ↑r ⇒ ↓I GOVERNMENT SPENDING, G The basic macroeconomic model takes government spending as exogenously given. • G = govt spending on goods and services. • G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits). Unlike government purchases, transfer payments are not made in exchange for some of the economy’s output of goods and services. Therefore, they are not included in the variable G. • Transfer payments are the opposite of taxes: they increase households’ disposable income, just as taxes reduce disposable income. Thus, an increase in transfer payments financed by an increase in taxes leaves disposable income unchanged. We can now revise our definition of T to equal taxes minus transfer payments. Disposable income, Y – T, includes both the negative impact of taxes and the positive impact of transfer payments. • Assume government spending and total taxes are exogenous: THE MARKET FOR GOODS & SERVICES We have now come full circle in the circular flow diagram, Figure 3-1. We began by examining the supply of goods and services, and we have just discussed the demand for them. How can we be certain that all these flows balance? In other words, what ensures that the sum of consumption, investment, and government purchases equals the amount of output produced? In this classical model, the interest rate is the price that has the crucial role of equilibrating supply and demand. - The demand for the economy’s output comes from consumption, investment, and government purchases. Consumption depends on disposable income, investment depends on the real interest rate, and government purchases and taxes are the exogenous variables set by fiscal policymakers. - We saw that the factors of production and the production function determine the quantity of output supplied to the economy. Now let’s combine these equations describing the supply and demand for output. If we substitute the consumption function and the investment function into the national income accounts identity, we obtain: Because the variables G and T are fixed by policy, and the level of output, Y, is fixed by the factors of production and the production function, we can write (last equation). This equation states that the supply of output equals its demand, which is the sum of consumption, investment, and government purchases. Notice that the interest rate r is the only variable not already determined in the last equation. This is because the interest rate still has a key role to play: it must adjust to ensure that the demand for goods is equals the supply. The higher the interest rate, the lower the level of investment, and thus the lower the demand for goods and services. If the interest rate is too high, then investment is too low, and the demand for output falls short of the supply. If the interest rate is too low, then investment is too high, and the demand exceeds the supply. At the equilibrium interest rate, the demand for goods and services equals the supply. This conclusion may seem mysterious: how does the interest rate get to the level that balances the supply and demand for goods and services? The best way to answer this question is to consider how financial markets fit into the story. early 1980s, corresponding to the beginning of huge and persistent deficits, we see a huge increase in the debt ratio, from 32% in 1981 to 66% in 1995. In the mid 1990s, budget surpluses and rapid growth started to reduce the debt ratio, but it started rising again in 2001 due to the economic slowdown, the Bush tax cuts, and higher spending (Afghanistan and Iraq, war on terrorism, 2002 airline bailout, etc.). The recent financial crisis/recession has increased the debt ratio, as revenues have fallen while outlays (the stimulus package, bailouts) have sharply increased. LOANABLE FUNDS SUPPLY CURVE National saving does not depend on r, so the supply curve is vertical. LOANABLE FUNDS MARKET EQUILIBRIUM THE SPECIAL ROLE OF R “r” adjusts to equilibrate the goods market and the loanable funds market simultaneously: If L.F. market is in equilibrium, then Y – C – G = I Add (C +G ) to both sides to get Y = C + I + G (goods market eq’m) Thus, COMPARATIVE STATICS The equilibrium level endogenous variables change in response to changes in the exogenous variables. • In the loanable funds model, what shifts supply and demand curves? • How does the equilibrium react to changes in the exogenous variables? SHIFTS IN SAVING Things that shift the saving curve • public saving - fiscal policy: changes in G or T • private saving - preferences - tax laws that affect saving (replace income tax with consumption tax; taxes on interests income) To induce investment to fall, the interest rate must rise. Hence, the increase in government purchases causes the interest rate to increase and investment to decrease. Government purchases are said to crowd out investment. To grasp the effects of an increase in government purchases, consider the impact on the market for loanable funds. Because the increase in government purchases is not accompanied by an increase in taxes, the government finances the additional spending by borrowing—that is, by reducing public saving. With private saving unchanged, this government borrowing reduces national saving. As Figure 3-9 shows, a reduction in national saving is represented by a leftward shift in the supply of loanable funds available for investment. At the initial interest rate, the demand for loanable funds exceeds the supply. The equilibrium interest rate rises to the point where the investment schedule crosses the new saving schedule. Thus, an increase in government purchases causes the interest rate to rise from r1 to r2 . Now consider a reduction in taxes of ΔT. The immediate impact of the tax cut is to raise disposable income and thus to raise consumption. Disposable income rises by ΔT, and consumption rises by an amount equal to ΔT times the marginal propensity to consume MPC. The higher the MPC, the greater the impact of the tax cut on consumption. Because the economy’s output is fixed by the factors of production and the level of government purchases is fixed by the government, the increase in consumption must be met by a decrease in investment. For investment to fall, the interest rate must rise. Hence, a reduction in taxes, like an increase in government purchases, crowds out investment and raises the interest rate. SHIFTS IN INVESTMENT DEMAND Things that shift the investment curve: • some technological innovations: to take advantage some innovations, firms must buy new investment goods • tax laws that affect investment: e.g., investment tax credit SAVING AND THE INTEREST RATE • Why might saving depend on r ? • How would the results of an increase in investment demand be different? - Would r rise as much? - Would the equilibrium value of I change? 1. An increase in r makes saving more attractive, increases the reward for postponing consumption. 2. Many consumers finance their spending on big-ticket items like cars and furniture, and an increase in r makes such borrowing more expensive. 3. However, an increase in r might also reduce saving through the income effect: a higher interest rate makes net savers better off, so they purchase more of all “normal” goods. If current consumption is a normal good, then it will rise and saving will fall. It is usually assumed that the substitution effect is at least as great as the income effect, so that an increase in the interest rate will either increase saving or leave saving unchanged. INCREASE IN INVESTMENT DEMAND WHEN SAVING DEPENDS ON R Under our assumptions, the fixed level of saving determines the amount of investment; in other words, there is a fixed supply of loanable funds. An increase in investment demand merely raises the equilibrium interest rate. We would reach a different conclusion, however, if we modified our simple consumption function and allowed consumption (and its flip side, saving) to depend on the interest rate. Because the interest rate is the return to saving (as well as the cost of borrowing), a higher interest rate might reduce consumption and increase saving. In this case, the saving schedule would be upward sloping rather than vertical. With an upward-sloping saving schedule, an increase in investment demand would raise both the equilibrium interest rate and the equilibrium quantity of investment. Figure 3-11 shows such a change. The increase in the interest rate causes households to consume less and save more. The decrease in consumption frees resources for investment. Chapter 4: The monetary system, What it is money and how it works MONEY: DEFINITION Money: is the stock of assets that can be readily used to make transactions. A house is also an asset, so why don’t we consider it money? Because it is so “illiquid” that I couldn’t possibly buy e.g. bread with it, at least not immediately. MONEY: FUNCTIONS • Medium of exchange: we use it to buy goods and services. When you walk into stores, you are confident that the shopkeepers will accept your money in exchange for the items they are selling. The ease with which an asset can be converted into the medium of exchange and used to buy other things (goods, services, or capital assets) is called the asset’s liquidity. Because money is the medium of exchange, it is the economy’s most liquid asset. • Store of value: transfers purchasing power from the present to the future. Money is not a fantastic store of value in periods of inflation, because it loses value. • Unit of account: the common unit by which everyone measures prices and values. Again, it is a measure that changes continuously, so in periods of inflation it is hard to use it to measure. E.g. A car dealer says that a car costs $40,000, not 800 shirts (even though it may amount to the same thing). BANKS’ ROLE IN THE MONETARY SYSTEM To understand the role of banks, we will consider three scenarios: 1. No banks 2. 100-percent-reserve banking 3. Fractional-reserve banking In each scenario, we assume C = $1,000. M=money supply, D=deposits. • SCENARIO 1: No banks With no banks, 
 D = 0 and M = C = $1,000. We begin by imagining a world without banks. In such a world, all money takes the form of currency, and the quantity of money is simply the amount of currency that public holds. • SCENARIO 2: 100-percent-reserve banking Now introduce banks. At first, suppose that banks accept deposits but do not make loans. The only purpose of the banks is to provide a safe place for depositors to keep their money. The deposits that banks have received but have not lent out are called reserves. Initially C = $1000, D = $0, M = $1,000. Now suppose households deposit the $1,000 at “Firstbank.” After the deposit: 
 C = $0, D = $1,000, M = $1,000 LESSON:
 100%-reserve banking has no impact on size of money supply. The bank’s assets are the $1,000 it holds as reserves; the bank’s liabilities are the $1,000 it owes to depositors. Unlike banks in our economy, this bank is not making loans, so it will not earn profit from its assets. The bank presumably charges depositors a small fee to cover its costs. • SCENARIO 3: Fractional-reserve banking Now imagine that banks start lending out some of their deposits—for example, to families buying houses or to firms investing in new plants and equipment. The advantage to banks is that they can charge interest on the loans. The banks must keep some reserves on hand so that reserves are available whenever depositors want to make withdrawals. Suppose banks hold 20% of deposits in reserve, making loans with the rest. - Firstbank will make $800 in loans. The money supply now equals $1,800: Depositor has $1,000 in demand deposits. Borrower holds $800 in currency. Before the loan is made, the money supply is $1,000, equaling the deposits in Firstbank. After the loan is made, the money supply is $1,800: the depositor still has a demand deposit of $1,000, but now the borrower holds $800 in currency. Thus, in a system of fractional-reserve banking, banks create money. The creation of money does not stop with Firstbank. If the borrower deposits the $800 in another bank (or if the borrower uses the $800 to pay someone who then deposits it), the process of money creation continues. - Suppose the borrower deposits the $800 in Secondbank. Initially, Secondbank’s balance sheet is: Secondbank will loan 80% of this deposit. Thus, Secondbank creates $640 of money. If this $640 is eventually deposited in Thirdbank, - Then Thirdbank will keep 20% of it in reserve 
 and loan the rest out. LESSON: in a fractional-reserve banking system, banks create money. This process of money creation can continue forever, but it does not create an infinite amount of money. FINDING THE TOTAL AMOUNT OF MONEY: Original deposit = $1000 + Firstbank lending = $ 800 + Secondbank lending = $ 640 + Thirdbank lending = $ 512 + other lending… Total money supply = (1/rr ) × $1,000 
 where rr = ratio of reserves to deposits In our example, rr = 0.2, so M = $5,000 Each $1 of reserves generates $(1/rr) of money. In our example, rr = 0.2, so the original $1,000 generates $5,000 of money. The banking system’s ability to create money is the main difference between banks and other financial institutions. As we first discussed in Chapter 3, financial markets have the important function of transferring the economy’s resources from those households that wish to save some of their income for the future to those households and firms that wish to borrow to buy investment goods to be used in future production. The process of transferring funds from savers to borrowers is called financial intermediation. MONEY CREATION IN THE BANKING SYSTEM A fractional-reserve banking system creates money, but it doesn’t create wealth: bank loans give borrowers some new money and an equal amount of new debt. In other words, the creation of money by the banking system increases the economy’s liquidity, not its wealth. The more banks lend money, the better off they are. BANK CAPITAL, LEVERAGE, AND CAPITAL REQUIREMENTS Opening a bank requires some capital. That is, the bank owners must start with some financial resources to get the business going. • Bank capital: the resources a bank’s owners have put into the bank, the equity (i.e. share capital) of the bank’s owner. A more realistic balance sheet: The bank obtains resources from its owners who provide capital, from customers by taking in deposits, and from investors by issuing debt. It uses these resources in three ways. Some funds are held as reserves; some are used to make bank loans; and some are used to buy financial securities, such as government or corporate bonds. The bank allocates its resources among these asset classes, considering the risk and return that each offers and any regulations that restrict its choices. The reserves, loans, and securities on the left side of the balance sheet must equal, in total, the deposits, debt, and capital on the right side of the balance sheet. • Leverage: the use of borrowed money to supplement existing funds for purposes of investment • Leverage ratio = assets/capital = $(200 + 500 + 300)/$50 = 20 This means that for every dollar of capital that the bank owners have contributed, the bank has $20 of assets and, thus, $19 of deposits and debts. • Being highly leveraged makes banks vulnerable, makes it more at risk of bankruptcy in case its assets are subjects to fluctuations. Example: Suppose a recession causes our bank’s assets to fall by 5%, to $950. Then, capital = assets – liabilities = 950 – 950 = 0 If the value of the assets declines by more than 5 percent, assets fall below liabilities, sending bank capital below zero. The bank is said to be insolvent. The fear that bank capital may run out, and thus that depositors might not be repaid in full, is what generates bank runs when there is no deposit insurance. Bank regulators require that banks hold sufficient capital. The goal of a capital requirement is to ensure that banks will be able to pay off their depositors and other creditors. The amount of capital required depends on the kind of assets a bank holds. If the bank holds safe assets such as government bonds, regulators require less capital than if the bank holds risky assets such as loans to borrowers whose credit is of dubious quality. Capital requirement: • minimum amount of capital mandated by regulators • intended to ensure banks will be able to pay off depositors • higher for banks that hold more risky assets 2008-2009 financial crisis: • Losses on mortgages shrank bank capital, slowed lending, exacerbated the recession. • Governments injected $ billions of capital into banks to ease the crisis and encourage more lending. A MODEL OF THE MONEY SUPPLY If the Federal Reserve adds a dollar to the economy and that dollar is held as currency, the money supply increases by exactly one dollar. But as we have seen, if that dollar is deposited in a bank, and banks hold only a fraction of their deposits in reserve, the money supply increases by more than one dollar. As a result, to understand what determines the money supply under fractional- reserve banking, we need to take account of the interactions among (1) the Fed’s decision about how many dollars to create, (2) banks’ decisions about whether to hold deposits as reserves or to lend them out, and (3) households’ decisions about whether to hold their money in the form of currency or demand deposits. Exogenous variables, we take the monetary base as exogenously given and controlled by the Central Bank, just like all the following variables, all are given, the first two are also controlled by the Central Bank: • Monetary base, B = C + R controlled by the central bank. Is the total number of dollars held by the public as currency C and by the banks as reserves R. • Reserve-deposit ratio, rr = R/D depends on regulations & bank policies. Is the fraction of deposits that banks hold in reserve. It is determined by the business policies of banks and the laws regulating banks. • Currency-deposit ratio, cr = C/D. Is the amount of currency C people hold as a fraction of their holdings of demand deposits D. It reflects the preferences of households about the form of money they wish to hold. - So then one of the things you may do is: you realise that some assets pay a zero interest rate, but you have assets with longer maturity whose interest late is still positive, so you can lower the interest rate of those. So what the Central Bank usually does is purchase long term assets and purchase government bonds. - OR it may lend directly to the private sector to stimulate money supply. This of course it totally non standard, but these solutions, called quantitative easing, have become popular since 2008. CASE STUDY: QUANTITATIVE EASING IN THE U.S. From 1960 to 2007, the monetary base grew gradually over time. But then from 2007 to 2014 it spiked up substantially, increasing about 5-fold over just a few years. This huge increase in the monetary base is attributable to actions the Federal Reserve took during the financial crisis and economic downturn of this period. With the financial markets in turmoil, the Fed pursued its job as a lender of last resort with historic vigour. It began by buying large quantities of mortgage-backed securities. Its goal was to restore order to the mortgage market so that would-be homeowners could borrow. These quantitative easing significantly changed the accounting sheets of Central Banks, who before only owned short-term govt bonds. • Quantitative easing: the Fed bought long-term govt bonds instead of T-bills (short term Treasury Bills) to keep their prices up and long-term interest rates down. These open-market purchases led to the substantial increase in the monetary base. • The huge expansion in the monetary base, however, did not lead to a similar increase in broader measures of the money supply. While the monetary base increased about 400 percent from 2007 to 2014, M1 increased by only 100 percent and M2 by only 55 percent. These figures show that the tremendous expansion in the monetary base was accompanied by a large decline in the money multiplier. Why did this decline occur? From 2007 to 2014, the reserve ratio increased substantially because banks chose to hold substantial quantities of excess reserves. That is, rather than making loans, the banks kept much of their available funds in reserve. (Excess reserves rose from about $1.5 billion in 2007 to about $2.5 trillion in 2014.) This decision prevented the normal process of money creation that occurs in a system of fractional- reserve banking. • Why did banks choose to hold so much in excess reserves? Part of the reason is that banks had made many bad loans leading up to the financial crisis; when this fact became apparent, bankers tried to tighten their credit standards and make loans only to those they were confident could repay. In addition, interest rates had fallen to such low levels that making loans was not as profitable as it normally is. Banks did not lose much by leaving their financial resources idle as excess reserves. • The Fed also bought mortgage-backed securities to help the housing market. • But after losses on bad loans, banks tightened lending standards and increased excess reserves, causing money multiplier to fall. • If banks start lending more as the economy recovers, rapid money growth may cause inflation. To prevent this, the Fed started “tapering” (reducing asset purchases) in 2014. CASE STUDY, PROBLEMS IN MONETARY CONTROL: BANK FAILURES IN THE 1930S The Fed has substantial power to influence the money supply, but it cannot control the money supply perfectly. Banks’ discretion in how they conduct their businesses, as well as households’ decisions about their personal financial affairs, can cause the money supply to change in ways the Fed did not anticipate. For example, if banks choose to hold more excess reserves, the reserve–deposit ratio increases and the money supply falls. Similarly, if households decide to hold more of their money in the form of currency, the currency–deposit ratio increases and the money supply falls. Hence, the money supply sometimes moves in ways the Fed does not intend. • From 1929 to 1933: - over 9,000 banks closed - money supply fell 28% • This drop in the money supply may not have caused the Great Depression, but certainly contributed to its severity. You can see that the fall in the money supply cannot be attributed to a fall in the monetary base: in fact, the monetary base rose 18 percent over this period. Instead, the money supply fell because the money multiplier fell 38 percent. The money multiplier fell because the currency– deposit and reserve–deposit ratios both rose substantially. • Loss of confidence in banks: ↑cr ⇒ ↓m • Banks became more cautious: ↑rr ⇒ ↓m The public confidence in the banking system diminished because of bank failures, and consequently it's raised the currency-deposit ratio (people withdrew their deposits). When they withdrew their deposits, they drained the banks of reserves, to which banks responded by reducing their reserve deposit ratio well above the legal minimum. To summarise: just as households responded to the banking crisis by holding more currency relative to deposits, bankers responded by holding more reserves relative to loans. Together these changes caused a large fall in the money multiplier. Chapter 5: Inflation, its causes, effects, and social costs What is inflation? We know inflation is a change in money value, the rate at which money loses value. Over the short run, the inflation rate can be volatile. In later chapters, we will learn about the forces that affect inflation in the short-run. In this chapter, we focus on the long-run trend behavior of inflation. We will learn a simple theory of inflation over the long run and see that its predictions are very consistent with U.S. and international data. In this chapter we examine the classical theory of the causes, effects, and social costs of inflation. The theory is “classical” in the sense that it assumes that prices are flexible. The quantity theory of money • A simple theory linking the inflation rate to the growth rate of the money supply. • Money demand for transactions begins with the concept of velocity… The starting point of the quantity theory of money is the insight that people hold money to buy goods and services. The more money they need for such transactions, the more money they hold. Thus, the quantity of money in the economy is related to the number of dollars exchanged in transactions. The link between transactions and money is expressed in the following equation, called the quantity equation: Money × Velocity = Price × Transactions M × V = P × T Let’s examine each of the four variables in this equation. RHS: PT, equals the number of dollars exchanged in a year. • T represents the total number of transactions during some period of time, say, a year. In other words, T is the number of times in a year that goods or services are exchanged for money. • P is the price of a typical transaction—the number of dollars exchanged. LHS: the money used to make the transactions. • M is the quantity of money. • V, called the transactions velocity of money, measures the rate at which money circulates in the economy. VELOCITY • Velocity: the rate at which money circulates. It is the number of times the average euro coin changes hands in a given time period • example: In 2018, - €500 billion in transactions - money supply = €100 billion - The average euro is used in five transactions in 2018 - So, velocity = 5 In order for €500 billion in transactions to occur when the money supply is only €100B, each euro must be used, on average, in five transactions. This suggests the following definition: V= T M where V = velocity T = value of all transactions M = money supply When studying the role of money in the economy, economists usually use a slightly different version of the quantity equation than the one just introduced. The problem with the first equation is that the number of transactions is difficult to measure. To solve this problem, the number of transactions T is replaced by the total output of the economy Y. Use nominal GDP as a proxy for total transactions. Then, V= PxY M where P = price of output (GDP deflator) Y = quantity of output (real GDP) P × Y = value of output (nominal GDP) (To make this easier to understand, we can write it in terms of percentages: %ΔM+%ΔV=%ΔP+%ΔY) • π (Greek letter pi ) denotes the inflation rate: • The result from the preceding slide: • Solve this result for π: - Economic growth requires a certain amount of money supply growth to facilitate the growth in transactions. - Money growth in excess of this amount leads to inflation. - Simplified classical theory: Y is given (it depends on F, K and L, which are given), so Example: Suppose real GDP is growing by 3% per year over the long run. Thus, production, income, and spending are all growing by 3%. This means that the volume of transactions will be growing as well. The central bank can achieve zero inflation (on average over the long run) simply by setting the growth rate of the money supply at 3%, in which case exactly enough new money is being supplied to facilitate the growth in transactions. Thus, the quantity theory of money states that the central bank, which controls the money supply, has ultimate control over the rate of inflation. If the central bank keeps the money supply stable, the price level will be stable. If the central bank increases the money supply rapidly, the price level will rise rapidly. Note: the theory doesn’t predict that the inflation rate will equal the money growth rate. It predicts that a change in the money growth rate will cause an equal change in the inflation rate. CONFRONTING THE QUANTITY THEORY WITH DATA The quantity theory of money implies: 1. Countries with higher money growth rates should have higher inflation rates. 2. The long-run trend in a country’s inflation rate should be similar to the long-run trend in the country’s money growth rate. Are the data consistent with these implications? Whenever money supply grows faster, the inflation rate is higher. The quantity theory of money is intended to explain the long-run relation of inflation and money growth, not the short-run relation. In the long run, inflation and money growth are positively related, as the theory predicts. In the short run, however, inflation and money growth appear highly negatively correlated! One possible reason is that the causality is reversed in the short run: When inflation rises—or is expected to rise—the Fed cuts back on money growth. If the economy slumps and inflation falls, the Fed increases money growth. So why should the state print money so fast as to generate inflation? Inflation has a social cost for the economy, we would like not to have it! So why is the state doing this? P P Δ =π M P Y M P Y Δ Δ Δ = + π Δ Δ = − M Y M Y The answer is that: think of the government, you have to finance some public spending. You collect taxes, or alternatively you can borrow money by issuing government bonds. But there is another way: if you control monetary policy you can just print the money you need. 
 The government is clearly getting some purchasing power. The Central Bank prints new money, but it’s not creating new wealth, because it creates a debt, since the government will then have to pay back that loan to the Central Bank. Where are those resources coming from? By printing new money, the central bank creates inflation, which acts exactly like a tax. The only difference in this case is that it acts as a tax on money holding. By creating inflation, you are taxing every money holder, because you are reducing their purchasing power. Thus, the central bank provides new resources to the government by printing money, but by doing so, it is just like it was taxing money holders. SEIGNIORAGE • To spend more without raising taxes or selling bonds, the govt can print money. • The “revenue” raised from printing money is called seigniorage (pronounced SEEN-your-idge). • The inflation tax: printing money to raise revenue causes inflation. Inflation is like a tax on people who hold money. As prices rise, the real value of the money in your wallet falls. Therefore, when the government prints new money for its use, it makes the old money in the hands of the public less valuable. In essence, inflation is a tax on holding money. If you overexploit seigniorage you create too much inflation. INFLATION AND INTEREST RATES: REAL AND NOMINAL Suppose you deposit your savings in a bank account that pays 8 percent interest annually. Next year, you withdraw your savings and the accumulated interest. Are you 8 percent richer than you were when you made the deposit a year earlier? The answer depends on what “richer” means. To be sure, you have 8 percent more dollars than you had before. But if prices have risen, each dollar buys less, and your purchasing power has not risen by 8 percent. If the inflation rate was 5 percent over the year, then the amount of goods you can buy has increased by only 3 percent. And if the inflation rate was 10 percent, then your purchasing power has fallen by 2 percent. • Nominal interest rate, i not adjusted for inflation • Real interest rate, r adjusted for inflation: r = i − π • π: rate of inflation THE FISHER EFFECT • The Fisher equation: i = r + π • Chap. 3: S = I determines r. • Hence, an increase in π causes an equal increase in i. • This one-for-one relationship is called the Fisher effect. Once we separate the nominal interest rate into these two parts, we can use this equation to develop a theory that explains the nominal interest rate. Chapter 3 showed that the real interest rate adjusts to equilibrate saving and investment. The quantity theory of money shows that the rate of money growth determines the rate of inflation. The Fisher equation then tells us to add the real interest rate and the inflation rate together to determine the nominal interest rate. The quantity theory and the Fisher equation together tell us how money growth affects the nominal interest rate. According to the quantity theory, an increase in the rate of money growth of 1 percent causes a 1 percent increase in the rate of inflation. According to the Fisher equation, a 1 percent increase in the rate of inflation in turn causes a 1 percent increase in the nominal interest rate. The one-for-one relation between the inflation rate and the nominal interest rate is called the Fisher effect. The data are consistent with the Fisher effect: Inflation and the nominal interest rate are very highly correlated. That they are not perfectly correlated does not contradict the Fisher effect. Over time, the saving and investment curves (see Chapter 3) move around, changing the real interest rate, which, in turn, causes the nominal interest rate to change for a given value of inflation. Before the seventies there’s no fisher effect. The interest rate is flat. Why? Back in time, you had no clue about the interest rate. In recent times, the fisher effect is clearly there. Answers, the details: First, we need to find π. Constant velocity implies π = (ΔM/M) - (ΔY/Y) = 5 – 2 = 3. Then, i = r + π = 4 + 3 = 7. b. Changes in the money growth rate do not affect real GDP or its growth rate. So, a two-point increase in money growth causes a two-point increase in inflation. According to the Fisher effect, the nominal interest rate should rise by the increase in inflation: two points (from i = 7 to i = 9). c. π = (ΔM/M) – (ΔY/Y). If (ΔY/Y) falls by 1 point, then π will increase by 1 point; the Fed can prevent this by reducing (ΔM/M) by 1 point. Intuition: With slower growth in the economy, the WHAT DETERMINES WHAT variable how determined (in the long run) M exogenous (Fed/ECB) r adjusts to ensure S = I Y P adjusts to ensure Again, it is very important for students to learn the logical order in which variables are determined. I.e., we do not need to know P in order to determine Y. We do need to know Y in order to determine L, and we need to know L and M in order to determine P. HOW P RESPONDS TO ΔM • For given values of r, Y, and Eπ , a change in M causes P to change by the same percentage —just like in the quantity theory of money. This shows the connection between the money market equilibrium condition and the (simpler) quantity theory of money, presented earlier in this chapter. WHAT ABOUT EXPECTED INFLATION? • Over the long run, people don’t consistently over- or under-forecast inflation, so Eπ = π on average. • In the short run, Eπ may change when people get new information. • EX: CB announces it will increase M next year. People will expect next year’s P to be higher, 
 so Eπ rises. • This affects P now, even though M hasn’t changed yet…. HOW P RESPONDS TO ΔE𝝿 • For given values of r, Y, and M , The expected inflation goes up because of the announcement. (Self fulfilling expectation: prices may go up today just because you expect there will be inflation, and because of that, there is inflation). CBs can affect the interest rate just through announcements: this is a very powerful tool. Credibility is crucial here. THE CAGAN MODEL (NOT IN THE BOOK) • Assume Y and r constant and neglect them in L • Let m = log M and p = log P • Money demand: • Money supply: • Perfect foresight: • Equilibrium: • Current prices depend on the stream of future money supply • The weight on future money is higher, the higher gamma (elasticity of real balances to inflation) • Imperfect foresight: • Central bank’s credibility is crucial! THE LAYMAN’S VIEW AND THE CLASSICAL RESPONSE If you ask the average person why inflation is a social problem, she will probably answer that inflation makes her poorer. “Each year my boss gives me a raise, but prices go up and that takes some of my raise away from me.” The implicit assumption in this statement is that if there were no inflation, she would get the same raise and be able to buy more goods. This complaint about inflation is a common fallacy. As we know from Chapter 3, the purchasing power of labor—the real wage—depends on the marginal productivity of labor, not on how much money the government prints. If the central bank reduces inflation by slowing the rate of money growth, workers will not see their real wages increasing more rapidly. Instead, when inflation slows, firms will increase the prices of their products less each year and, as a result, will give their workers smaller raises. According to the classical theory of money, a change in the price level is like a change in the units of measurement. It is as if we switched from measuring distances in feet to measuring them in inches: numbers get larger, but nothing really changes. Imagine that tomorrow morning you wake up and find that, for some reason, all dollar figures in the economy have been multiplied by ten. The price of everything you buy has increased 10-fold, but so have your wage and the value of your savings. What difference would such a price increase make to your life? All numbers would have an extra zero at the end, but nothing else would change. Your economic well-being depends on relative prices, not the overall price level. Why, then, is a persistent increase in the price level a social problem? It turns out that the costs of inflation are subtle. Indeed, economists disagree about the size of the social costs. To the surprise of many laymen, some economists argue that the costs of inflation are small—at least for the moderate rates of inflation that most countries have experienced in recent years. The CPI has risen tremendously over the past 45 years. However, nominal wages have risen by a roughly similar magnitude. If the common misperception were true, then the real wage should show exactly the opposite behavior as the CPI. It doesn’t. While the real wage is not constant, it exhibits no downward long-term trend. (We wouldn’t expect the real wage to be constant over the long run – we would expect it to change in response to shifts in the labor supply and MPL curves.) THE CLASSICAL VIEW OF INFLATION (RECAP) The classical view: 
 A change in the price level is merely a change in the units of measurement. Then, why is inflation a social problem? THE SOCIAL COSTS OF INFLATION …fall into two categories: 1. costs when inflation is expected. 2. costs when inflation is different than people had expected. The costs of expected inflation: Consider first the case of expected inflation. Suppose that every month the price level rose by 1/2 percent. What would be the social costs of such a steady and predictable 6 percent annual inflation? 1. SHOELEATHER COST One cost is the distorting effect of the inflation tax on the amount of money people hold. As we have already discussed, a higher inflation rate leads to a higher nominal interest rate, which in turn leads to lower real money balances. But for people to hold lower money balances and spend the same amount, they must make more frequent trips to the bank to withdraw money. • Shoeleather cost: the costs and inconveniences of reducing money balances to avoid the inflation tax. (Walking to the bank more often causes one’s shoes to wear out more quickly) • ↑π ⇒ ↑i ⇒ ↓ real money balances • Remember: In long run, inflation does not affect real income or real spending. • So, same monthly spending but lower average money holdings means more frequent trips to the bank to withdraw smaller amounts of cash. Thanks to ATMs and internet banking, the shoeleather cost is likely to be very small. 
2. MENU COSTS A second cost of inflation arises because high inflation induces firms to change their posted prices more often. Changing prices is sometimes costly; for example, it may require printing and distributing a new catalog. • Menu costs: The costs of changing prices. • Examples: - cost of printing new menus - cost of printing & mailing new catalogs • The higher is inflation, the more frequently firms must change their prices and incur these costs. 
3. RELATIVE PRICE DISTORTIONS A third cost of inflation arises because firms facing menu costs change prices infrequently; therefore, the higher the rate of inflation, the greater the variability in relative prices. For example, suppose a firm issues a new catalog every January. If there is no inflation, then the firm’s prices relative to the overall price level are constant over the year. Yet if inflation is 1/2 percent per month, then from the beginning to the end of the year the firm’s relative prices fall by 6 percent. Sales from this catalog will tend to be low early in the year (when its prices are relatively high) and high later in the year (when its prices are relatively low). Hence, when inflation induces variability in relative prices, it leads to microeconomic inefficiencies in the allocation of resources. • Firms facing menu costs change prices infrequently. • Example: A firm issues new catalog each January. As the general price level rises throughout the year, the firm’s relative price will fall. • Different firms change their prices at different times, leading to relative price distortions… causing microeconomic inefficiencies in the allocation of resources. finance this budget deficit by issuing debt, it may find itself unable to borrow, often because lenders view the government as a bad credit risk. To cover the deficit, the government turns to the printing press. The result is rapid money growth and hyperinflation. • Once the hyperinflation is under way, the fiscal problems become even more severe. Because of the delay in collecting tax payments, real tax revenue falls as inflation rises. Thus, the govt’s need to rely on seigniorage is self-reinforcing. Rapid money creation leads to hyperinflation, which leads to a larger budget deficit, which leads to even more rapid money creation. • In theory, the solution to hyperinflation is simple: stop printing money. • In the real world, to find a solution, this requires drastic and painful fiscal reforms. Once the magnitude of the problem becomes apparent, the government musters the political will to reduce government spending and increase taxes. These fiscal reforms reduce the need for seigniorage, which allows a reduction in money growth. One particular case of hyperinflation happened in Germany between the two wars. This is why Germans are so averse to inflation nowadays, After World War I, Germany experienced one of history’s most spectacular examples of hyperinflation. At the war’s end, the Allies demanded that Germany pay substantial reparations. These payments led to fiscal deficits in Germany, which the German government eventually financed by printing large quantities of money. Panel (b) shows inflation and real money balances: as inflation rose, real money balances fell. When the inflation ended at the end of 1923, real money balances rose. HYPERINFLATION IN ZIMBABWE • Ineffective land reform, corruption, war • Estimated π , 2008: almost 250 million % per year in June, almost 80 billion % per month in November “If you don’t get a bill collected in 48 hours, it isn’t worth collecting, because it is worthless. Whenever we get money, we must immediately spend it, just go and buy what we can. Our pension was destroyed ages ago. None of us have any savings left.” The Zimbabwe hyperinflation finally ended in March 2009, when the government abandoned its own money. The U.S. dollar became the nation’s official currency. Inflation quickly stabilised and remained low in the years that followed. HYPERINFLATION IN VENEZUELA • CPI yearly π , 2018: almost 1 Ml % • Exponential increase in M2 since 2018 - New currency (Bolívar soberano, Aug 2018) • IMF π forecasts - 10 Ml % in 2019 (Oct. 2019) - 15 K % in 2020 (Oct. 2020) - 5 K % in 2021 (Oct. 2021) THE CLASSICAL DICHOTOMY Let’s now step back and examine a key assumption that has been implicit in our discussion about the impact of money supply on inflation. Real variables: measured in physical units (rather than a monetary) — quantities and relative prices, for example: - GDP: quantity of output produced - real wage: output earned per hour of work - real interest rate: output earned in the future by lending one unit of output today Nominal variables: measured in money units, e.g. price level, the inflation rate, and the dollar wage a person earns. - nominal wage: dollars per hour of work. - nominal interest rate: dollars earned in future by lending one dollar today. - the price level: the amount of dollars needed to buy a representative basket of goods. • Note: Real variables were explained in Chap. 3, nominal ones in Chap. 5. • Classical dichotomy: the theoretical separation of real and nominal variables in the classical model, which implies nominal variables do not affect real variables. It allows us to examine real variables, as we have done, while ignoring nominal variables. • Neutrality of money: changes in the money supply do not affect real variables. In the real world, money is approximately neutral in the long run. Irrelevance of money in the determination of real variables. Chapter 6: The Open Economy Does there exist any close economy? We know that even North Korea trades with other countries. The answer is: the world is a closed economy. GLOBALISATION, 1970-2010 The evolution of World Real GDP. World output has increased a lot. But if you see the increase of Real Exports, you see that it has grown even faster, in comparison to the past. This means that nowadays we trade goods and services a lot more. IMPORTS AND EXPORTS OF SELECTED COUNTRIES, 2013 Germany is a net exporter.
 The US imports more than it exports. Why does Germany export more than the US? Because trades between US states are not considered international trades. So big countries trade, but also inside themselves, but those are considered local trades. IN AN OPEN ECONOMY • The key macroeconomic difference between open and closed economies is that, in an open economy, a country’s spending in any given year need not equal its output of goods and services. • A country can spend more than it produces by borrowing from abroad, or it can spend less than it produces and lend the difference to foreigners. • Saving need not equal investment: if individuals in an open economy want to save more than domestic firms want to borrow, no problem. The savers simply send their extra funds abroad to buy foreign assets. Similarly, if domestic firms want to borrow more than individuals are willing to save, then the firms simply borrow from abroad (i.e. sell bonds to foreigners). THE NATIONAL INCOME IDENTITY IN AN OPEN ECONOMY Consider the expenditure on an economy’s output of goods and services, again denoted as Y. • In a closed economy, all output is sold domestically, and expenditure is divided into three components: consumption C, investment I, and government purchases G. • In an open economy, some output is sold domestically and some is exported to be sold abroad. In addition, some of the goods and services included in consumption, investment, and government purchases are produced abroad and imported. GDP excludes import because: spending on imports is included in domestic spending (C+I+G), and because goods and services imported from abroad are not part of a country’s output. This equation states that expenditure on domestic output is the sum of consumption, investment, government purchases, and net exports. This form of the national income accounts identity should be familiar from Chapter 2. The national income accounts identity shows how domestic output, domestic spending, and net exports are related. TRADE SURPLUSES AND DEFICITS • trade surplus: 
 output > spending and exports > imports 
 Size of the trade surplus = NX (net exports are positive) • trade deficit: 
 spending > output and imports > exports 
 Size of the trade deficit = –NX (net exports are negative) INTERNATIONAL CAPITAL FLOWS • Net capital outflow = S – I = net outflow of “loanable funds” = net purchases of foreign assets, the country’s purchases of foreign assets minus foreign purchases of domestic assets • When S > I, country is a net lender • When S < I, country is a net borrower THE LINK BETWEEN TRADE & CAPITAL FLOWS In an open economy, as in the closed economy we discussed in Chapter 3, financial markets and goods markets are closely related. To see the relationship, we must rewrite the national income accounts identity in terms of saving and investment. Begin with the identity: Y=C+I+G+NX
 Subtract C and G from both sides to obtain Y−C−G=I+NX Recall that Y−C−G is national saving S, which equals the sum of private saving, Y−T−C, and public saving, T−G where T stands for taxes. Therefore, S=I+NX.
 Subtracting I from both sides, we can write the national income accounts identity as: S-I=NX. This form of the national income accounts identity shows that an economy’s net exports must always equal the difference between its saving and its investment. S-I=NX Net exports: exports-imports NX = X - IM - r*: world interest rate - rc: interest rate if the economy were closed NEXT, THREE EXPERIMENTS: 1. Fiscal policy at home 2. Fiscal policy abroad 3. An increase in investment demand (exercise) In the textbook, NX = 0 in the economy’s initial equilibrium for each of these three experiments. In these slides, NX > 0 in the initial equilibrium. For completeness, you might have your students repeat the three experiments for the case of NX < 0 in the initial equilibrium. This would be a good homework or in-class exercise. 1. FISCAL POLICY AT HOME Consider first what happens to the small open economy if the government expands domestic spending by increasing government purchases. The increase in G reduces national saving, because S=Y−C−G.
 With an unchanged world real interest rate, investment remains the same. Therefore, saving falls below investment, and some investment must now be financed by borrowing from abroad. The fall in S implies a fall in NX. The same logic applies to a decrease in taxes. A tax cut lowers T, raises disposable income Y−T, stimulates consumption, and reduces national Our model generates a prediction: the government’s budget deficit and the country’s trade balance should be negatively related. Does this prediction come true in the real world? Let’s look at the data… Our model implies a negative relationship between NX and the budget deficit. We observe this negative relationship during most periods. There are some exceptions. For example, from 1991 to 2001, NX and the budget deficit fell, due to a long expansion: rising incomes increased imports and tax revenues. 2. FISCAL POLICY ABROAD Consider now what happens to a small open economy when foreign governments increase their government purchases. The result of this is an increase in Net Exports. Why? It might be worth taking a moment to explain that the world interest rate r* is determined by saving and investment in the world loanable funds market. S* is the sum of all countries’ saving; I* the sum of all countries’ investment. r* adjusts to equate I* with S*, just like in Chapter 3, because the world as a whole is a closed economy. A fiscal expansion in other countries would reduce S* and raise r* (same results as in Chapter 3). Because the policy change occurs abroad, the domestic saving (i.e. supply for loanable funds) and investment schedules remain the same. The only change is an increase in the world interest rate from r1* to r2*. The trade balance is the difference between the saving and investment schedules; because saving exceeds investment at r2*, there is a trade surplus, there’s an increase in the amount of funds flowing abroad. 3. AN INCREASE IN INVESTMENT DEMAND Consider what happens to a small open economy if its investment schedule shifts outward so there is greater demand for investment goods at every interest rate. This shift would occur if, for example, the government changed the tax laws to encourage investment by providing an investment tax credit. At a given world interest rate, investment is now higher. Because saving is unchanged, some investment must now be financed by borrowing from abroad. Because capital flows into the economy to finance the increased investment, the net capital outflow is negative. In contrast to a closed economy, investment is not constrained by the fixed (domestic) supply of loanable funds. Hence, the increase in firm’s demand for loanable funds can be satisfied by borrowing abroad, which reduces net outflow of financial capital. And since net capital outflow = NX, we see a fall in NX equal to the increase in investment. Put differently, because NX=S−I, the increase in I implies a decrease in NX. EVALUATING ECONOMIC POLICY (BOOK) Our model of the open economy shows that the flow of goods and services measured by the trade balance is inextricably connected to the international flow of funds for capital accumulation. The net capital outflow is the difference between domestic saving and domestic investment. Thus, the impact of economic policies on the trade balance can always be found by examining their impact on domestic saving and domestic investment. Policies that increase investment or decrease saving tend to cause a trade deficit, and policies that decrease investment or increase saving tend to cause a trade surplus. Our analysis of the open economy has been positive, not normative. It has shown how various policies influence the international flows of capital and goods but not whether these policies and outcomes are desirable. Evaluating economic policies and their impact on the open economy is a frequent topic of debate among economists and policymakers. When a country runs a trade deficit, policymakers must confront the question of whether it represents a national problem. Most economists view a trade deficit not as a problem in itself, but perhaps as a symptom of a problem. A trade deficit could reflect low saving. In a closed economy, low saving leads to low investment and a smaller future capital stock. In an open economy, low saving leads to a trade deficit and a growing foreign debt, which eventually must be repaid. In both cases, high current consumption leads to lower future consumption, implying that future generations will bear the burden of low national saving. 6.3 Exchange Rates Having examined the international flows of capital and of goods and services, we now extend the analysis by considering the prices that apply to these transactions. The exchange rate between two countries is the price at which residents of those countries trade with each other. THE NOMINAL EXCHANGE RATE • ”e”, nominal exchange rate: the relative price of domestic currency in terms of foreign currency (e.g. dollars per euro). When people refer to “the exchange rate” between two countries, they usually mean the nominal exchange rate. How many units of foreign currency can we buy with one unit of domestic currency? How many dollars I can buy with one euro? With one euro I can buy 1.17 dollars. Some textbooks and newspapers define the exchange rate as the reciprocal of the one here (e.g., dollars per yen instead of yen per dollar). This book always expresses the exchange rate in units of foreign currency per dollar. With this convention, a rise in the exchange rate—say, from 100 to 110 yen per dollar—is called an appreciation of the dollar; a fall in the exchange rate is called a depreciation. When the domestic currency appreciates, it buys more of the foreign currency; when it depreciates, it buys less. An appreciation is sometimes called a strengthening of the currency, and a depreciation is sometimes called a weakening of the currency. THE REAL EXCHANGE RATE • ε = real exchange rate, the relative price of domestic goods in terms of foreign goods (e.g. U.S. Big Macs per Italian Big Mac). At which we can trade the goods of one country for the goods of another. The real exchange rate is sometimes called the terms of trade. Students often have trouble understanding the units of the real exchange rate. Note: The examples here and in the text are in terms of one good, i.e. Big Macs. But P and P* are the overall price levels of the domestic & foreign countries. Thus, they each measure the price of a basket of goods. Supply: (vertical line) Represents the net capital outflow and thus the supply of dollars to be exchanged into foreign currency and invested abroad. Demand: (downward-sloping line) Represents the net demand for dollars coming from foreigners who want dollars to buy goods from this country. At the equilibrium real exchange rate, the supply of dollars available from the net capital outflow balances the demand for dollars by foreigners buying this country’s net exports. How Policies Influence the Real Exchange Rate We can use this model to show how the changes in economic policy we discussed earlier affect the real exchange rate. NEXT, FOUR EXPERIMENTS: 1. Fiscal policy at home 2. Fiscal policy abroad 3. An increase in investment demand (exercise) 4. Trade policy to restrict imports 1. FISCAL POLICY AT HOME A fiscal expansion reduces national saving, by increasing government purchases or cutting taxes, net capital outflow, and the supply of domestic currency in the foreign exchange market… …causing the real exchange rate to rise and NX to fall. Makes domestic goods more expensive and harder to export. That is, the dollar becomes more valuable. 2. FISCAL POLICY ABROAD What happens to the real exchange rate if foreign governments increase government purchases or cut taxes? Either change in fiscal policy reduces world saving and raises the world interest rate r*. The increase in the world interest rate reduces domestic investment I, increasing net capital outflow and the supply of domestic currency in the foreign exchange market… …causing the real exchange rate to fall and NX to rise. Makes domestic currency go up, and it loses value. The country experiences a real depreciation, which makes domestic goods cheaper and easier to export, and foreign goods more expensive and harder to import. 3. AN INCREASE IN INVESTMENT DEMAND (EXERCISE) 4. TRADE POLICY TO RESTRICT IMPORTS (PROTECTIONISTIC POLICY) Trade policies, broadly defined, are policies designed to directly influence the amount of goods and services exported or imported. Most often, trade policies take the form of protecting domestic industries from foreign competition—either by placing a tax on foreign imports (a tariff) or restricting the amount of goods and services that can be imported (a quota). For an example of a protectionist trade policy, consider what would happen if the government prohibited the import of foreign cars. For any given real exchange rate, imports would now be lower, implying that net exports (exports minus imports) would be higher. Thus, the net-exports schedule would shift outward, as in Figure 6-12. To see the effects of the policy, we compare the old equilibrium and the new equilibrium. In the new equilibrium, the real exchange rate is higher, and net exports are unchanged. Despite the shift in the net-exports schedule, the equilibrium level of net exports remains the same, because the protectionist policy does not alter either saving or investment. At any given value of ε, an import quota ⇒ ↓IM ⇒ ↑NX ⇒ demand for domestic currency shifts right Trade policy doesn’t affect S or I , so capital flows and the supply of domestic currency remain fixed. The analysis here applies for import restrictions (tariffs, quotas) as well as export subsidies. It also applies for exogenous changes in preferences regarding domestic vs. foreign goods. This analysis shows that protectionist trade policies do not affect the trade balance. Because a trade deficit reflects an excess of imports over exports, one might guess that reducing imports— such as by prohibiting the import of foreign cars—would reduce a trade deficit. Yet our model shows that protectionist policies lead only to an appreciation of the real exchange rate. Results: Δε > 0 (demand increase) ΔNX = 0 (supply fixed) ΔIM < 0 (policy) ΔEX < 0 (rise in ε) Balance between imports and exports stays the same, but the volume of trades with the rest of the world is reduced. The country therefore exports less in the new equilibrium. Because net exports are unchanged, it must import less as well. THE DETERMINANTS OF THE NOMINAL EXCHANGE RATE • Start with the expression for the real exchange rate: • Solve for the nominal exchange rate: • So e depends on the real exchange rate and the price levels at home and abroad… …and we know how each 
 of them is determined: It’s important here for students to learn the (logical, not necessarily chronological) order in which the variables are determined. I.e., what causes what. It is instructive to consider changes in exchange rates over time. The exchange rate equation can be written: % Change in e = % Change in ε + % Change in P*− % Change in P. The percentage change in ε is the change in the real exchange rate. The percentage change in P is the domestic inflation rate π, and the percentage change in P* is the foreign country’s inflation rate π*. Thus, the percentage change in the nominal exchange rate is: % Change in e = % Change in ε + (π*−π) Pct change in Nom Exchange Rate=Pct change in Real Exchange Rate+Difference in Inflation Rates THE DETERMINANTS OF THE NOMINAL EXCHANGE RATE e = ε x P* P • Rewrite this equation in growth rates 
 (see “arithmetic tricks for working with percentage changes,” Chapter 2 ): Δe = Δε + ΔP* - ΔP = Δε + π* - π e ε P* P ε • For a given value of ε, 
 the growth rate of e equals the difference between foreign and domestic inflation rates. e = ε x P* P • The results from large open economy analysis are a mixture of the results for the closed & small open economy cases. • For example… A FISCAL EXPANSION IN THREE MODELS A fiscal expansion causes national saving to fall. 
 The effects of this depend on openness & size: In the table, there’s a cell for NX in the closed economy column. Instead of putting “N.A.” in this cell, I put “no change.” Why? In a closed economy, EX = IM = NX = 0. After a change in saving, NX = 0 still. Hence, it is not incorrect to say “no change”. More importantly we are trying to show students how the results for a large open economy are in between the results for the closed & small open cases. Looking at the items in the last row of the table, “falls, but not as much as in small open economy” seems to be in between “no change” and “falls,” but does not seem to be in between “N.A.” and “falls”. It would be completely understandable if you still feel that “N.A.” should be in the closed economy NX cell of the table, so please feel free to edit that cell. Chapter 7: Unemployment NATURAL RATE OF UNEMPLOYMENT Natural rate of unemployment: the average rate of unemployment around which the economy fluctuates. It is the rate of unemployment toward which the economy gravitates in the long run, given all the labor-market imperfections that impede workers from instantly finding jobs. - In a recession, the actual unemployment rate rises above the natural rate. - In a boom, the actual unemployment rate falls below the natural rate. The natural rate of unemployment is the “normal” unemployment rate the economy experiences when it is neither in a recession nor a boom. The actual unemployment rate fluctuates considerably over the short run. These fluctuations are the focus of Part IV of the book. For this chapter, though, our goal is to understand the behavior of the natural rate of unemployment, essentially the long-run trend in the unemployment rate. Unemployment data are based on seasonally-adjusted, monthly unemployment rates for the civilian non- institutional population of the U.S. The actual u-rate for each quarter is an average of the three monthly unemployment rates in that quarter. The natural u-rate in a given quarter is estimated by averaging all unemployment rates from 10 years earlier to 10 years later; future unemployment rates are set at 5.5%. (Therefore, estimates of the natural rate may become less accurate toward the end of the sample period.) A FIRST MODEL OF THE NATURAL RATE Notation: L = # of workers in labor force, so E+U E = # of employed workers U = # of unemployed U/L = unemployment rate ASSUMPTIONS: 1. To see what determine the unemployment rate, we assume that the labor force L is fixed and focus on the transition of individuals in the labor force between employment E and unemployment U. 2. During any given month, - s: rate of job separations, fraction of employed workers that become separated from their jobs i.e. lose or leave their jobs each month. - f: rate of job finding, fraction of unemployed workers that find a job each month Together, the rate of job separation s and the rate of job finding f determine the rate of unemployment. s and f are exogenous THE STEADY STATE CONDITION • Steady state: the labor market is in steady state, or long-run equilibrium, if the unemployment rate is constant, i.e. if the unemployment rate is neither rising nor falling, then the number of people finding jobs fU must equal the number of people losing jobs sE. • The steady-state condition is: In order for the unemployment rate to be constant, the number of people who become unemployed in each month must equal the number of formerly unemployed people who find jobs. FINDING THE “EQUILIBRIUM” U RATE f × U = s × E f × U = s × (L - U) substitute L-U for E f × U = s × L - s × U divide both sides of this equation by L L L f × U = s (1 - U) L L Solve for the unemployment rate U/L to find: U = s s L (s + f ) so, - if f goes up, then unemployment rate goes down - if s goes up, then unemployment rate goes up (in proportion, the numerator goes up faster than the denominator). • Example: (exam) Each month, - 1% of employed workers lose their jobs (s = 0.01) - 19% of unemployed workers find jobs (f = 0.19) Find the natural rate of unemployment: U = 0.01 = 0.05 = the rate of unemployment in this example is about 5% L (0.01+0.19) POLICY IMPLICATION This simple model of the natural rate of unemployment has an important implication for public policy. • A policy will reduce the natural rate of unemployment only if it lowers s or increases f. • In case it affects both, it reduces the natural rate of unemployment if it increases f/s. Answers given in class: - A good way to reduce s is to make it costly to fire employees. - A good way to increase f is to give incentives to firms who hire. - Another way is to create demand for jobs by investing. WHY IS THERE UNEMPLOYMENT? • If job finding were instantaneous (f = 1), 
 then all spells of unemployment would be brief, and the natural rate of unemployment would be near zero. However, job finding is not instantaneous. • There are two reasons why f < 1: 1. job search 2. wage rigidity • 2010 Nobel Prize in Economics: to Diamond, Mortensen and Pissarides for their analysis of markets with search frictions 1. JOB SEARCH & FRICTIONAL UNEMPLOYMENT One reason for unemployment is that it takes time to match workers and jobs. The equilibrium model of the aggregate labor market discussed in Chapter 3 assumes that all workers and all jobs are identical and, therefore, that all workers are equally well suited to all jobs. If this were true and the labor market were in equilibrium, a job loss would not cause unemployment: a laid-off worker would immediately find a new job at the market wage. • Frictional unemployment: is the unemployment caused by the time it takes workers to search for a job. • Occurs even when wages are flexible and there are enough jobs to go around • Occurs because: - workers have different abilities, preferences - jobs have different skill requirements - geographic mobility of workers not instantaneous - flow of information about vacancies and job candidates is imperfect For all these reasons, searching for a job takes time and effort, and this tends to reduce the rate of job finding. SECTORAL SHIFTS Some frictional unemployment is inevitable in a changing economy. For many reasons, the types of goods that firms and households demand vary over time. As the demand for goods shifts, so does the demand for the labor that produces those goods. • Sectorial shifts: changes in the composition of demand among industries or regions. Because sectoral shifts are always occurring, and because it takes time for workers to change sectors, there is always frictional unemployment. Example: Technological change 
 - more jobs repairing computers, fewer jobs repairing typewriters Example: A new international trade agreement 
 - labor demand increases in export sectors, decreases in import-competing sectors These scenarios result in frictional unemployment. Sometimes the unemployment caused by sectoral shifts is severe. Example: due to increasing imports of cheaper foreign-made textiles (particularly since the expiration in 2005 of long-standing quotas on textiles from China), the U.S. textile industry has been in decline for years. Tens of thousands of workers in this industry have lost jobs. Many of these workers are in their 50s and have worked in this industry for decades. Such workers are unlikely to have the skills necessary to get jobs available in newly booming industries, and they are less likely to invest in the acquisition of the necessary skills for these jobs. Hence, such workers are at greater risk for becoming “discouraged workers.” Sectoral shifts are not the only cause of job separation and frictional unemployment. In addition, workers find themselves out of work when their firms fail, when their job performance is deemed The equilibrium wages of teenagers tend to be low for two reasons. First, because teenagers are among the least skilled and least experienced members of the labor force, they tend to have low marginal productivity. Second, teenagers often take some “compensation” in the form of on-the-job training rather than direct pay. An internship is a classic example of training offered in place of wages. For both reasons, the wage at which the supply of teenage workers equals the demand is low. The minimum wage is therefore more often binding for teenagers than for others in the labor force. Empirical studies typically find that a 10 percent increase in the minimum wage reduces teenage employment by 1 to 3 percent. • Cannot explain the natural rate of unemployment. (it is lower than most workers’ actual wages). But this is in general, and it doesn’t apply to all sectors and to unskilled workers. - Evidence of a negligible employment effect in the U.S. non- tradable sector • Raises poor families’ income (Dube 2019: U.S.) Advocates of a higher minimum wage view it as a way to raise the income of the working poor. Certainly, the minimum wage provides only a meager standard of living. Although minimum-wage advocates often admit that the policy causes unemployment for some workers, they argue that this cost is worth bearing to raise others out of poverty. • Notice that there is no minimum wage in Italy. 2. LABOR UNIONS A second cause of wage rigidity is the market power of unions. • Unions exercise monopoly power to secure higher wages for their members. The wages of unionised workers are determined not by the equilibrium of supply and demand but by bargaining between union leaders and firm management. • When the union wage exceeds the eq’m wage, unemployment results. • Insiders: Employed union workers whose interest is to keep wages high. • Outsiders: Unemployed non-union workers who prefer eq’m wages, so there would be enough jobs for them. Often, the final agreement raises the wage above the equilibrium level and allows the firm to decide how many workers to employ. The result is a reduction in the number of workers hired, a lower rate of job finding, and an increase in structural unemployment. Even in countries like Italy with high unemployment rate, it is about 10%. So unions obviously try to negotiate higher wage to protect the 90%, accepting as a collateral damage the higher unemployment for the 10%. Labor unions represent the employed workers. The theory has two implications we can confront with data: 1) Union members’ average earnings should be higher than non-union members’ average earnings. 2) The difference between union and non-union wages should be higher in industries that are more heavily unionised (and hence, in which unions have more market power) than in less heavily unionised industries. Unions can also influence the wages paid by firms whose workforces are not unionised because the threat of unionisation can keep wages above the equilibrium level. Most firms dislike unions. 3. EFFICIENCY WAGES Efficiency-wage theories propose a third cause of wage rigidity • Theories in which higher wages increase worker productivity by: - attracting higher quality job applicants - increasing worker effort, reducing “shirking” - reducing turnover, which is costly to firms - improving health of workers (in developing countries) • Firms willingly pay above-equilibrium wages to raise productivity: Even though a wage reduction would lower a firm’s wage bill, it would also—if these theories are correct—lower worker productivity and the firm’s profits. • Result: structural unemployment. HENRY FORD AND EFFICIENCY WAGES - 1908-1913: from 450 to 14,000 workers - 1913: 370% turnover, 10% absenteism - 1914: from 9 to 8 hours/day, doubling the wage (from 2.34 to 5 dollars a day) - Turnover fell to 16% in 1915! - Absenteism to 2.5% - Productivity increased between 40% and 70% - And profits increased Possible answers: 1. Stop raising the (nominal) minimum wage, so that its real value will gradually erode to zero. 2. Regulate unions (just like other monopolies are regulated) to reduce unions’ impact on wages. 3. Reduce the generosity of unemployment insurance benefits. 3. Implement government employment agencies to increase the accessibility of information about job vacancies and available workers. 4. Increase public funding to help retrain workers displaced from jobs in declining industries. THE DURATION OF UNEMPLOYMENT When a person becomes unemployed, is the spell of unemployment likely to be short or long? • The data: - More spells of unemployment are short-term than medium-term or long-term. - Yet, most of the total time spent unemployed is attributable to the long-term unemployed. • Long-term unemployment cannot easily be attributed to the time it takes to match jobs and workers: we would not expect this matching process to take many months. Long-term unemployment is more likely to be structural unemployment and/or due to sectoral shifts among vastly different industries. • Knowing this is important because it can help us craft policies that are more likely to work. The figure shows that the duration of unemployment typically rises during recessions. The huge increase during the recession of 2008– 2009, however, is without precedent in modern history. WHY UNEMPLOYMENT ROSE IN EUROPE BUT NOT THE U.S. Shock 
 Technological progress has shifted labor demand from unskilled to skilled workers in recent decades. Effect in United States
 An increase in the “skill premium” – the wage gap between skilled and unskilled workers. Led to a gap between skilled and unskilled workers. Effect in Europe
 Higher unemployment, due to generous govt benefits for unemployed workers and strong union presence. In the seventies: the US has a way more flexible labor market, while Europe has a more rigid labor market. … UNTIL THE 2008 CRISIS • With the 2008 crisis, more flexible countries have witnessed higher layoffs, bringing U.S. and European unemployment rates to converge. • Since 2010, job creation was faster in the U.S. than in Europe - Europe went through the sovereign debt crisis, the U.S. did not - Unemployment increased in Europe and decreased in the U.S. - It only decreased in Europe since 2014 SOCIAL AND POLITICAL EQUILIBRIA • Job protection and family values - If parents have stable jobs and income, but children do not (and have low job finding rates), they will stay longer at home with parents • If insiders are the majority (or are powerful enough), they will block any attempt to remove their rent. Insiders won’t agree with attempts to introduce more flexibility. - If protections are removed to outsiders but not to insiders, non protected groups may revolt LABOR MARKET REFORMS IN EUROPE • Many European countries have increased flexibility for new employed in the Nineties - Flexibilisation at the margin (more flexible contracts only for the newly employed, only for the new entrants) • Objectives - Increase productivity - Reduce youth (and overall?) unemployment - Reduce the shadow economy - Without touching insiders’ rents • Risks: - Delayed independence, insecurity, difficulty to make long run plans - Intergenerational clash - Discouraging firms’ investment in employees and workers’ investment in firm-specific human capital (if a worker won’t stay in my firm for so long I have no interest in providing learning opportunities for him). • Incentive to the shadow economy - Tax evasion, fake unemployment, black temporary jobs, fake autonomous jobs • Higher asymmetries - Redistribution from young to elderly - Higher debt and social contribution to finance early retirement - Smart working for skilled workers, not for blue collars - Gender gap - Burden of lockdown disproportionately on women Chapter 8: Economics Growth I: Capital Accumulation and Population Growth WHY GROWTH MATTERS Anything that effects the long-run rate of economic growth – even by a tiny amount – will have huge effects on living standards in the long run. THE SOLOW MODEL (1956) • Due to Robert Solow, won Nobel Prize for contributions to the study of economic growth • A major paradigm: - widely used in policy making - benchmark against which most recent growth theories are compared • Looks at the determinants of economic growth and the standard of living in the long run HOW SOLOW MODEL IS DIFFERENT FROM CHAPTER 3’S MODEL 1. K is no longer fixed: investment causes it to grow, depreciation causes it to shrink 2. L is no longer fixed: population growth causes it to grow 3. the consumption function is simpler 4. no G or T (only to simplify presentation; we can still do fiscal policy experiments) 5. cosmetic differences As in Chapter 3, closed economy (NX = 0) Start with fixed L and then consider population growth. THE PRODUCTION FUNCTION • In aggregate terms: Y = F (K, L) • Define: y = Y/L = output per worker k = K/L = capital per worker • Assume constant returns to scale:
 zY = F (zK, zL) for any z > 0 • Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y = f(k) where f(k) = F(k, 1) • As F (K, L) = L f(k), we have MPK = f ’(k) THE NATIONAL INCOME IDENTITY • Y = C + I (remember, no G ) • In “per worker” terms: 
 y = c + i 
 where c = C/L and i = I /L THE CONSUMPTION FUNCTION • the saving rate “s”: the fraction of income that is saved (s is an exogenous parameter) Note: s is the only lowercase variable that is not equal to its uppercase version divided by L • Consumption function: c = (1–s)y (per worker) SAVING AND INVESTMENT • saving (per worker) = y – c = y – (1–s)y = sy • National income identity is y = c + i Rearrange to get: i = y – c = sy (investment = saving, like in chap. 3!) • Using the results above, 
 i = sy = sf(k) OUTPUT, CONSUMPTION, AND INVESTMENT DEPRECIATION AN INCREASE IN THE SAVING RATE An increase in the saving rate raises investment… …causing k to grow toward a new steady state: PREDICTION • Higher s ⇒ higher k*. • And since y = f(k) , higher k* ⇒ higher y* . • Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run. THE GOLDEN RULE: INTRODUCTION • Different values of s lead to different steady states. • How do we know which is the “best” steady state? • The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*). • An increase in s - leads to higher k* and y*, which raises c* - reduces consumption’s share of income (1–s), which lowers c*. • So, how do we find the s and k* that maximize c*? THE GOLDEN RULE: THE MATH the Golden Rule level of capital, the steady state value of k that maximizes consumption. To find it, first express c* in terms of k*: c*(k*) = y* − i* = f (k*) − δk* Since c*(k*) is concave, its maximum is determined by c*’(k*) = 0, that is, f’(k*) = δ, or MPK = δ. Students sometimes confuse this graph with the other Solow model diagram, as the curves look similar. Be sure to clarify the differences: 1. On this graph, the horizontal axis measures k*, not k. Thus, once we have found k* using the other graph, we plot that k* on this graph to see where the economy’s steady state is in relation to the golden rule capital stock. 2. On this graph, the curve measures f(k*), not sf(k). 3. On the other diagram, the intersection of the two curves determines k*. On this graph, the only thing determined by the intersection of the two curves is the level of capital where c*=0, and we certainly wouldn’t want to be there. 4. There are no dynamics in this graph, as we are in a steady state. In the other graph, the gap between the two curves determines the change in capital. * goldk = In steady state i* = δk* because Δk = 0 STARTING WITH TOO MUCH CAPITAL STARTING WITH TOO LITTLE CAPITAL • We now write the production function as: • where L × E = the number of effective workers. - increases in labor efficiency have the same effect on output as increases in the labor force. TECHNOLOGICAL PROGRESS IN THE SOLOW MODEL • Notation: y = Y /( LE) = output per effective worker k = K /( LE) = capital per effective worker • Production function per effective worker:
 y = f(k) • Saving and investment per effective worker:
 s y = s f(k) (δ + n + g)k = break-even investment: 
 the amount of investment necessary 
 to keep k constant. Consists of: - δ k to replace depreciating capital - n k to provide capital for new workers - g k to provide capital for the new “effective” workers created by technological progress STEADY-STATE GROWTH RATES IN THE SOLOW MODEL WITH TECH. PROGRESS ( , )Y F K L E= × THE GOLDEN RULE WITH TECHNOLOGICAL PROGRESS To find the Golden Rule capital stock, 
 express c* in terms of k*: c* = y* − i* = f (k* ) − (δ + n + g) k* c* is maximized when 
 MPK = δ + n + g or equivalently, MPK − δ = n + g GROWTH EMPIRICS: BALANCED GROWTH • Solow model’s steady state exhibits balanced growth—many variables grow at the same rate. • Solow model predicts Y/L and K/L grow at the same rate (g), so K/Y should be constant. - In ss sy = (δ + n + g)k. - Hence K/Y = k/y = s/(δ + n + g) This is true in the real world. In the Golden 
 Rule steady state, 
 the marginal product of capital net of depreciation equals the 
 pop. growth rate plus the rate of tech progress. Chapter 8: Economics Growth I: Capital Accumulation and Population Growth WHY GROWTH MATTERS Anything that effects the long-run rate of economic growth, even by a tiny amount, will have huge effects on living standards in the long-run. THE SOLOW MODEL (1956) • Due to Robert Solow, won Nobel Prize for contributions to the study of economic growth • A major paradigm: - widely used in policy making - benchmark against which most recent growth theories are compared • Looks at the determinants of economic growth and the standard of living in the long-run How Solow model is different from Chapter 3’s model 1. K is no longer fixed: investment causes it to grow, depreciation causes it to shrink 2. L is no longer fixed: population growth causes it to grow 3. the consumption function is simpler 4. no G or T (only to simplify presentation; we can still do fiscal policy experiments) 5. cosmetic differences (i.e. lowercase letters) As in Chapter 3, closed economy (NX = 0) Start with fixed L and then consider population growth. THE PRODUCTION FUNCTION • In aggregate terms: Y = F (K, L) • Define: y = Y/L = output per worker k = K/L = capital per worker • Assume constant returns to scale:
 zY = F (zK, zL) for any z > 0 Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y = f(k) where f(k) = F(k, 1) This equation shows that the amount of output per worker Y/L is a function of the amount of capital per worker K/L. f(k) is the “per worker production function,” it shows how much output one worker could produce using k units of capital. • As F (K, L) = L f(k), we have MPK = f’(k) • Decreasing marginal productivity of capital and labor: MPL, MPK By using per-capita variables, it is possible to run cross-country comparisons, even if countries have different sizes. THE NATIONAL INCOME IDENTITY • Y = C + I (remember, no G, and no NX) • In “per worker” terms: 
 y = c + i 
 where c = C/L and i = I /L Summary: As long as k < k*, investment will exceed depreciation, and k will continue to grow toward k*. A NUMERICAL EXAMPLE Production function (aggregate): To derive the per-worker production function, divide through by L: Then substitute y = Y/L and k = K/L to get Assume: • s = 0.3 • δ = 0.1 • initial value of k = 4.0 I.e., “The economy saves three-tenths of income,” “every year, 10% of the capital stock wears out,” and “suppose the economy starts out with four units of capital for every worker.” AN INCREASE IN THE SAVING RATE An increase in the saving rate raises investment… causing k to grow toward a new steady state: The Solow model shows that the saving rate is a key determinant of the steady-state capital stock. If the saving rate is high, the economy will have a large capital stock and a high level of output in the steady state. If the saving rate is low, the economy will have a small capital stock and a low level of output in the steady state. Prediction • Higher s → higher k*. • And since y = f(k), higher k* → higher y*. • Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the LR. THE GOLDEN RULE: INTRODUCTION So far, we have used the Solow model to examine how an economy’s rate of saving and investment determines its steady-state levels of capital and income. This analysis might lead you to think that higher saving is always a good thing because it leads to greater income. Yet suppose a nation had a saving rate of 100 percent. That would lead to the largest possible capital stock and the largest possible income. But if all of this income is saved and none is ever consumed, what good is it? • Different values of s lead to different steady states. • How do we know which is the “best” steady state? • The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*). • An increase in s - leads to higher k* and y*, which raises c* - reduces consumption’s share of income (1–s), which lowers c*. • So, how do we find the s and k* that maximise c*? To keep our analysis simple, let’s assume that a policymaker can set the economy’s saving rate at any level. By setting the saving rate, the policymaker determines the economy’s steady state. What steady state should the policymaker choose? The policymaker’s goal is to maximise the well-being of the individuals who make up the society. Individuals themselves do not care about the amount of capital in the economy or even the amount of output. They care about the amount of goods and services they can consume. Thus, a benevolent policymaker would want to choose the steady state with the highest level of consumption. The steady-state value of k that maximises consumption is called the Golden Rule level of capital and is denoted k*gold. How can we tell whether an economy is at the Golden Rule level? To answer this question, we must first determine steady-state consumption per worker. Then we can see which steady state provides the most consumption. To find steady-state consumption per worker, we begin with the national income accounts identity y=c+i
 and rearrange it as c=y−i. THE GOLDEN RULE: THE MATH k*gold: the Golden Rule level of capital, the steady state value of k that maximises consumption. To find it, first express c* in terms of k*: c*(k*) = y* − i* = f (k*) − δk* Since c*(k*) is concave, its maximum is determined by c*’(k*) = 0, that is, f’(k*) = δ, or MPK = δ. According to this equation, steady-state consumption is what’s left of steady-state output after paying for steady-state depreciation. This equation shows that an increase in steady-state capital has two opposing effects on steady-state consumption. On the one hand, more capital means more output. On the other hand, more capital also means that more output must be used to replace capital that is wearing out. Students sometimes confuse this graph with the other Solow model diagram, as the curves look similar. Be sure to clarify the differences: 1. On this graph, the horizontal axis measures k*, not k. Thus, once we have found k* using the other graph, we plot that k* on this graph to see where the economy’s steady state is in relation to the golden rule capital stock. 2. On this graph, the curve measures f(k*), not sf(k). 3. On the other diagram, the intersection of the two curves determines k*. On this graph, the only thing determined by the intersection of the two curves is the level of capital where c*=0, and we certainly wouldn’t want to be there. 4. There are no dynamics in this graph, as we are in a steady state. In the other graph, the gap between the two curves determines the change in capital. THE GOLDEN RULE CAPITAL STOCK The problem is to find the value of k* that maximises c* = f(k*) − δk*. Just take the first derivative of that expression and set equal to zero: f′(k*) − δ = 0 where f′(k*) = MPK = slope of production function 
 and δ’(k*)= δ = slope of steady-state investment line. Because these two slopes are equal at kgold*, the Golden Rule is described by the equation MPK=δ. At the Golden Rule level of capital, the marginal product of capital equals the depreciation rate. - If k is below the Golden Rule level, an increase in the capital stock raises output more than depreciation, so consumption rises. In this case, the production function is steeper than the δk* line, so the gap between these two curves, which equals consumption, grows as k* rises. - By contrast, if the capital stock is above the Golden Rule level, an increase in the capital stock reduces consumption because the increase in output is smaller than the increase in depreciation. In this case, the production function is flatter than the δk* line, so the gap between the curves, consumption, shrinks as k* rises. - At the Golden Rule level of capital, the production function and the δk* line have the same slope, and consumption is at its greatest level. - If MPK−δ>0, increases in capital increase consumption, so k* must be below kgold*. - If MPK−δ<0, increases in capital decrease consumption, so k* must be above kgold*. - Therefore, the following condition describes the Golden Rule: MPK−δ=0. At the Golden Rule level of capital, the marginal product of capital net of depreciation (MPK−δ) equals zero. As we will see, a policymaker can use this condition to find the Golden Rule capital stock for an economy. In steady state i* = δk* because Δk = 0