Industrial Organisation – Business and Economics, Appunti di Organizzazione Aziendale

Scarica Industrial Organisation – Business and Economics e più Appunti in PDF di Organizzazione Aziendale solo su Docsity! Industrial Organisation Flavio Delbono L. Cabral, Introduction to Industrial Organization, second edition, Mit Press, 2017. Except: 7.4 (meaning section 4 of chapter 7), 8.3, 19.4, 14.4, 14.5, chapter 16. MAKE SURE IT’S THE SECOND EDITION Written exam lasts 1h - short exercises - Multiple choice questions - Randomised sequence of questions - Two partials The course will start with a revision of Microeconomics. Industrial Organisation is about more realistic markets. In Microeconomics the firm is the main actor, while IO takes into consideration other factors, not simply input and output, example how much to spend on innovation, advertisement, etc. The course contains both “positive analysis” (as in like scientific, descriptive) and “normative analysis” (information about how the situation could be, so it requires some evaluation, some judgment). Neither criteria is best, because both are useful and necessary. It is suggested to do the end of chapter exercises, not just the microeconomics ones. Office hours: Tuesday before class, room 125 Class starts 15 minutes past the start. LECTURE 1: Introduction What is industrial organisation? Ch.1 During this course, we will be using the “Marshall approach”, namely “partial equilibrium analysis”, which focuses on just one market, enabling us to go deeper into the market, but neglecting some important consequences. Industry: “manufacturing productive enterprises collectively, especially as distinguished from agriculture” It also means “Any large scale business activity”. Industrial: refers to the word “industry” as explained in the first following definition. In fact, industrial organisation applies equally well from tourism to steel industries; as far as IO is concerned, there is nothing special about manufacturing. IO is concerned with the workings of markets and industries, in particular the way firms compete with each other. Why isn’t IO simply a chapter of microeconomics? The study of how markets operate, however, is the object of microeconomics, meaning that industrial organisation is nothing but a chapter of microeconomics. The main reason for considering industrial organisation as a separate subject is its emphasis on the study of the firms’ strategies that are characteristic of market interaction: price competition, product positioning, advertising, research and development, … Microeconomics typically focuses on the extreme cases of monopoly imperfect competition, in this organisation is primarily concerned with the intermediate case of oligopoly, that is, competition between a few firms. For the above reasons are more appropriate definition of the field would be something like "economics of imperfect competition”. Industrial organisation is concerned with the working of markets and industries, in particular the way firms compete with each other. 
 Goal of IO: address four broad questions: − Do firms have market power?
 − How do firms acquire and maintain market power?
 − What are the implications of market power?
 − What role is there for public policy with regard to market power? WHAT IS A MARKET? It is a complicated concept, because people refer to it in very different ways. 
 You can use, for example, the word market to mean demand (e.g. a fall in the market for apples, i.e. a decrease in demand for apples), or in other cases to mean supply. Market: a setting into which two separate groups of people (potential buyer and potential seller) try to trade as far as one well identified good or service. This definition accommodates every kind of market. Market power: ability to set prices above cost, specifically above incremental or marginal cost, that is, the cost of producing one extra unit. Is there market power? If there is no market power, then there is little point in the study of industrial organisation. One estimate can be obtained from data on prices, output and profit rates. As long as there’s free entry, expect insignificant levels of market power. If a firm were to persistently set prices above cost, a new firm would find it profitable to enter the market and undercut the incumbent. Therefore, market power cannot persist. Many industries exhibit little to no market power, but in some cases, the opposite is true. 2.2 DEMAND ELASTICITY Elasticity of demand: we presume that the demand for a product increases if we lower its price. The question is how sensitive demand is to price. We measure things in relative terms, that is, in terms of percent changes. Specifically the sensitivity of demand changes in price by the price elasticities of demand: The price elasticity of demand is the ratio between the percentage change in quantity and the percentage change in price, for a small change in price. The first part represents the slope, while the second part represents the coordinates. Ps. Elasticity of demand means the same as Price Elasticity of demand. • ⎮ε⎮> 1 has any elastic demand, meaning the quantity demanded is very sensitive to price. • 0<⎮ε⎮<1 has an inelastic demand, meaning that the quantity demanded is relatively insensitive to price. They exist to extreme cases: • a vertical demand curve (ε=0), such that for any price the quantity demanded is always the same. • A horizontal curve (ε=-♾ ) the extreme case such that even a very small change in price leads to an infinite increase in quantity demanded. It should be clear that elasticity is not the same thing as slope, although slope is an input to it (dq/dp). We can have curves with constant slope but varying elasticity and curves with constant elasticity but varying slopes. If ⎮ε⎮<1, inelastic demand, then an increase in price leads to an increase in revenue. If ⎮ε⎮> 1, elastic demand, then a decrease in price leads to an increase in revenue. This is a basic point, but one that some have missed: that to increase revenue in markets with elastic demand, you need to lower price, not raise it. Elasticity and revenue: the percent change in revenue following a price change is: (1+ elasticity) X (% change in price). (1+ε)dp p Knowing price change, quantity change may be estimated based on elasticity: dq ≈ ε dp q p Cross-price elasticity: demand for a product depends not only on its own price, but also on the prices of other goods. For example, the demand for a ski boots depends on the demand for skis: if skis gets more expensive, we expect people to buy fewer skis – and fewer boots too. If gasoline becomes more expensive, people drive their cars less and take the train more often. We summarise the sensitivity of demand to the price of another product with the cross price elasticities. Cross elasticity between x and y is: Exy = Percentage change in Quantity of X = ΔQx × ΔPy Percentage change in Price of Y Qx Py • If the cross-price elasticities is positive, we say that the products are substitutes. • If the cross-price elasticity is negative, we say that the products are complements. • If the cross-price elasticity is zero, we say that the products are independent. Income elasticity: changes in income also affect demand. Higher income generally means greater demand for all products, but some products benefit more than others. We defined the income elasticities of a product by: dq q η= dy y That is, the income elasticity of demand is given by the percent change in quantity demanded endorsed by 1% change in income. • Inferior goods have negative income elasticities • Normal goods have positive income elasticities. Within normal goods, those with a elasticities between zero and one or refer to as necessities, and those with elasticity is greater than one are luxuries. Demand for specific products is more sensitive to price changes than demand for a category as a whole. Long-run demand is more sensitive to price changes than short-run demand. 1. Be careful about the demand function being written in the proper way when calculating elasticity 2. Remember that elasticity of a curve IS NOT its derivative. Derivative gives a local information because its calculated in a point. The elasticity can be written as (notes). Remember that elasticity can’t be calculated in general, but it must be calculated in a point, so it only makes sense to calculate it exactly in the equilibrium point, which requires we know the slope of the function and the coordinates of the equilibrium point. 2.3 ESTIMATING THE DEMAND CURVE In an ideal world, firms would know the demands for the product. In practice, it's not so easy. One reason is that it's hard to get reliable market data. Another reason is that it's inherently difficult to tease out the effect of price from the effect of other variables, especially when the latter might be changing at the same time as price. - If only demand shifts, data plots supply (e.g., ABC or DEF) 
 - If only supply shifts, data plots demand (e.g., AD, BE or CF) 
 -If both curves shift and if shocks are positively correlated (common occurrence) then data corresponds to DB or DC; connecting such points yields neither demand nor supply curve. i.e. suppose that, overtime, the supply curve shifts between S1 and S2 and the demand curve between D3 and D4. Suppose there is an observable variable X that is positively correlated with shift in the supply curve: when X=X1, S=S1; when X=X2>X1, S=S2. The important question is whether the demand curve is also related to X.
 Key to identifying demand: find shocks that primarily shift supply curve, not demand curve. Such shocks are called instrumental variables: they are correlated with the supply curve but are not related with the demand curve. As a result, measuring the equilibrium points are resulting from variation in instrumental variables such as production disruptions is akin to measuring various points along with the demand curve, which intern allows us to estimate its shape and the value of elasticity. Statistical estimation: -From historical market data on quantity and price (q, p), estimate demand as 
 ln q = α + β ln p + γ ln x + ξ where x denotes demand shifters, ξ unobservables; 
 parameters to estimate: α, γ and β (demand elasticity) -β < 0 for agricultural products, β > 0 for industrial products! - Suppose that price-setters observe demand shocks that statistician does not; then p is positively correlated with ξ: 
 ξ = λ ln p + ε
 where ε is unobserved by price-setters and statistician - Then elasticity estimate is biased
 ln q = α + (β + λ) ln p + γ ln x + ε -If λ ≫ 0, then will obtain positive estimate of demand elasticity even though (as theory predicts) β < 0 Example: gasoline demand
 - Over time, increase in quantity and price - Connecting dots implies positive “demand” elasticity! - Possible solution: find controls x that shift demand: income, population, price of cars - Expanded equation yields negative coefficient on ln p, but... - Is this an unbiased estimate? Are there variables observable by market participants but not by me? Most likely. Solution (as mentioned earlier): find shocks that primarily shift supply curve, not demand curve 
 - Hurricane Katrina (2005) affected US gasoline supply considerably - Arguably, effect on demand was small (drivers in southern LA) - Supply shock implied higher price - Estimate demand elasticity as ∆ log q/∆ log p for this period - General procedure more complicated but same basic principle -Var. “supply disruption” is called an instrumental variable 
 Takeaways: empirically estimating consumer demand can be tricky. 2.4 ARE CONSUMERS REALLY RATIONAL? The economic edifice is built on a central premise: that agents are rational, optimising agents. Suppose consumers have transitive preferences with respect to all choices {A,B,C,...} 
 - Transitivity:A≻B and B≻C⇒A≻C - Suppose consumers choose what’s best for them. Example, if A ≻ B then consumer chooses A. 
 Theorem: consumer choices can be represented as maximisation of a “unique” utility function, subject to a budget constraint. Experimental evidence suggests that consumers are more sensitive to losses than to gains.
 Framework may be enriched with dynamic considerations, limited awareness, computation costs, altruism, etc. However, if too many “bells and whistles” are added, model loses sharpness.
 Prospect theory: Preferences depend on reference point. Example: buying an apple. 
 - Case A: consumer expects to eat an apple. Will buy apple if: u1 −p>u0 +μL (u1 −u0) - Case B: consumer expects not to eat an apple. Buy apple if: u0<u1+μG (u1−u0)−p 
 If μL is negative and greater than μG in absolute value, then there exist values such that: (1+μG)(u1 −u0)<p<(1−μL)(u1 −u0) Implying that the consumer buys apple if it was expecting to have one and does not buy one if it was not expecting to have one. 
 Some examples of “irrational” behaviour are: COST FUNCTION The firm's cost function, typically denoted by C(q), shows the least total cost of imports the firm needs to pay in order to produce output q; that is, the cost of producing q assuming the firm does so efficiently. For given input prices r,w, and for a given output level q, we find optimal input mix K,L. This, determines cost rK+wL. Cost function c(q): minimum cost required to achieve output level q. The cost of function leads to a series of related cost concepts: • Fixed cost (FC): the cost that does not depend on the output level, C(0) • Variable cost (VC): that cost which would be zero if the output level were zero, C (q) − C (0) • Average cost (AC) (a.k.a. “unit cost”): total cost divided by output level, C(q)/q • Marginal cost (MC): the unit cost of a small increase in output. Definition: derivative of cost with respect to output, dC/dq. Approximated by C(q) − C(q − 1). Examples: - Bagels: modest fixed cost (space), relatively constant marginal cost (labor and materials) - Electricity generation: large fixed cost (plant), initially declining marginal cost (large plants are more efficient, and many plants have startup costs) - Music CDs: large fixed cost (recording), small marginal cost (production and distribution) T-shirt factory example: To produce T-shirts: - Lease one machine at $20/week - Machine requires one worker, produces one T-shirt per hour - Worker is paid $1/hour on weekdays (up to 40 hours), $2/hour on Saturdays (up to 8 hours), $3 on Sundays (up to 8 hours) Factory costs: Suppose output level is 40 T-shirts per week. Then, - Fixed cost: FC = $20. Variable cost: VC = 40 × $1 = $40 - Average cost: AC = ($20+$40)/40 = $1.5 - Marginal cost: MC = $2 
 (Note that producing an extra T-shirt would imply working on Saturday, which costs more.) 
 Similar calculations can be made for other output levels, leading to the cost function… Scenario A: BenettonTM, sole buyer of T-shirts, offers price p = $1.8 per T-shirt (for any number of T-shirts) Should factory increase output beyond 40 T-shirts/week, thus operating on Saturdays? 
 • p=1.8,AC=1.5,MC=2. • Although factory is making money at q=40 (because p > AC), profits would be lower if it produced more (because p < MC); it would lose money at the margin. (Verify this: compute profit at q=40, 41.) Scenario B: BenettonTM, sole buyer of T-shirts, offers price p = $1.3 per T-shirt (for any number of T-shirts) No matter how much factory produces, price is below per-unit cost; i.e., no matter how much factory produces, it will lose money: 
 p < AC implies q × p < q × AC implies Revenue < Cost Optimal decision is not to produce at all 
 Suppose fixed cost has already been paid for the week; then it’s a sunk cost Define Average Variable Cost (AVC) as average cost excluding fixed cost Short-run supply switches to zero at min AVC 
 
 
 Here is the general case: Marginal cost is the appropriate cost concept to decide how much to produce, whereas average cost is the appropriate cost concept to decide whether to produce at all. In the picture, P0 denotes the minimum of the average cost function. For prices below this minimum, a price – taking firm would prefer not to produce at all. For values of P greater than p0, the optimal output level for a price-taking firm is given by the marginal cost function. For example, if P = P’, then the optimal output is Q’. More generally, a price-taking firm's supply function is given by the marginal cost function for values of price greater than the minimum of the average cost. 3.2 PRICING In the previous section we assume that firms are price takers. However, most firms have some control over the price they set. Although they may have competitors, they can charge a higher or lower price, and generate less or more demand as a result. A high price generates more revenue per unit, but fewer units are sold. A low price generates less revenue per unit, but more units are sold. Bottom line, optimal price is a trade-off between margin and quantity sold, as given by the elasticity rule: 
 p = MC 1 + 1 ε 
 Example: Ice-cream truck: driver/operator rents truck, buys ice-cream from factory, keeps all of the profits. - Fixed cost (truck rental): $15/hour - Marginal cost (wholesale cost of ice- cream): $3 - Inverse demand (per hour): p = 10 − 0.5 q
 What price generates the most profit? 
 OPTIMAL PRICING: CALCULUS APPROACH - Since there is a one-to-one correspondence between price and demand (the demand curve), we can either determine optimal price or optimal output (we would do this by using the inverse demand function). - Profit is normally an inverted-U-shaped function of output - If slope is positive, then higher output leads to higher profit - If slope is negative, then lower output leads to higher profit. - At the optimal output level, derivative of profit with respect to output is zero. This is a necessary (though not sufficient) condition.
 General assumption: the firm chooses a price to maximise profits. • If the inverse demand curve is p= P(q), then revenue, expressed as a function of output is: R(q) = pq = P(q)q • Formally, marginal revenue (increase in revenue we obtain by an infinitesimal increase in output) is given by the derivative of revenue with respect to output level (the inverse demand function): MR(q) = dR(q) = d(P(q)*q) dq dq • Marginal cost MC(q)=dC(q) dq • The optimal output level can be found by maximising profit: π(q)=R(q)-C(q) Which means finding the maximum of π, in other words, setting the derivative equal to zero. dπ(q)=MR(q)-MC(q)=0 dq Or simply MR=MC The profit maximising output level is such that marginal revenue equals marginal cost. So, the whole process consists of: 1. Find revenue expressed by means of the inverse demand function 2. Find MR of R(q) 3. Equate MR to MC 4. Find q* 5. Find p* Note on the marginal revenue: - What do you get from selling an extra unit?
 You get the price for which you sell it, but the additional (marginal) revenue is less than that. - Price must be lowered in order for an extra unit to be sold; this lowers the marginal on all units sold. - Formally, MR ≡ dR = d (p × q) = p + dp q < p dq dq dq Very useful formula!! Product market discipline: Product market competition may also contribute to aligning shareholders' and manager' objectives. The idea is that, when product market competition is very intense, firms cannot survive unless they maximise profits, which would cause the manager to lose his job. Under intense competition only the best survive. “Only when the tide goes out do you discover who’s been swimming naked” —Warren Buffett. One can think of competition as yardstick, i.e. benchmark, a standard used for comparison. The competitors themselves provide information to discipline managers actions, and signals about the firm’s productivity. In other words, they reduced the shareholders' informational disadvantage with respect to the manager. Capital market discipline: One of the most compelling arguments in favour of the assumption of profit maximisation is the role played by capital markets, i.e. non profit maximising firms have lower than potential value, hence, they are price target for mergers and acquisitions. In that case, a raider could acquire the firm, change of management in order to maximise profits, and thus make a capital gain. Often, even the threat of takeovers is sufficient to discipline managers. • Problem 1: If raider can increase firm value, why haven’t shareholders done so? In many cases it’s because they don’t have all information. • Problem 2: If raider is going to increase firm value, why do I sell my shares to the raider?
 What determines the firm’s boundaries? Why should firms be of the size they are; why not smaller or bigger? What does economic analysis have to say about firm size? It is useful to divide this into two questions: (a) what determines the horizontal extension of the firm (b) what determines the degree of vertical integration 
 Horizontal boundaries: Horizontal extension means how much of a given product does a firm produce and how many different products it offers. • Largely determined by the cost function. If average cost is U shaped and there is free entry into the industry, then firms will tend to produce at a level where average cost is minimised. • Examples: there is an optimal size for a cement plant that minimises costs. Plants of much smaller size or much larger size would probably incur a higher average cost and be unable to survive for very long. However, empirical evidence suggests average cost functions are u shaped with a flat bottom. This implies that there is a range of output levels which attain the minimum average cost, i.e. costs may not entirely allow us to pin down the size of the firm. Vertical boundaries: how many stages of the production process takes place within the firm. Why do we observe a great degree of vertical integration in some industries and very little in others? Make (vertical integration) or buy (vertical separation) question. - Relationship specific assets: those that are only worth something if paired with something else. - Hold-up problem: when the owner of two specific assets is not the same for both. Once the buyer pays for the relationship-specific asset, the seller can charge a higher price. One possible solution for this problem is vertical integration. E.g. in the US, mine-mouth power plants and their respective coal mine are typically owned by the same entity. - However vertical integration does not solve all the incentive problems: if I buy from an external supplier, that supplier has strong incentives to perform. If I buy the external supplier and make it part of my organisation, that supplier now has weaker incentives. - Both the extreme cases (vertical integration and vertical separation) imply incentive problems call and sometimes the optimal solution is in between. One possibility is that of tapered integration: a given input is bought from an affiliated supplier and from an independent one. - A second intermediate system is that of franchising, a system that has been used in a variety of industries. Franchising combines the benefits of vertical integration (specific investments) with the benefits of vertical separation (franchises retain most of the profit they generate, and thus have strong incentives to be efficient). - Mergers is a very extreme form of vertical integration. In other words, the definition of the boundaries of the firm is far from being a well-defined problem with a well-defined answer. It seems safe to summarise that: The horizontal boundaries of the firm are largely determined by cost considerations (including managerial costs). The vertical boundaries result from the balance between investment incentives (specific assets) and performance incentives. Why are firms different? • Only 20% of the variance in firm profit rates can be explained by variables that relate to some size, the type of industry in which the firm operates, and so forth. • Where does the remaining 80% come from? Why do some firms hold a sustained competitive advantage? Why don’t lower performance firms imitate? Three elements: 1- In the world of business, there may be impediments to imitation that allows some firms to perform persistently better than others: and obviously limit to imitation is given by legal restrictions like patents. Other unique resources are: patents, tacit knowledge (capabilities that are developed by experience and rarely written down), trade secrets, stars (who are people capable of influencing others to consume more) 2- Causal ambiguity: culture and tacit knowledge, e.g. even if one of Toyota's rivals were to recruit some key employees and managers from Toyota, the latter would have difficulty in expressing their knowledge in the new organisation, let alone interpreting it.
 3- Firm strategy: some firms play their cards better than others. In a business context, there are many dimensions in which strategy can have a lasting effect on firm performance: entry timing, capacity expansion, mergers and acquisition, technological improvement, special contract with customers and suppliers, pricing, advertising. Firm strategy is the focus of industrial organisation. - Quality of management is also an extremely important resource - History: very important in determining firm performance. A steep learning curve is an important aspect of competition, allowing firms to lower costs of producing by experience. - Network externalities is another advantage. Firm performance varies a great deal. Firms are different because of impediments to imitation, causal ambiguity, firm strategy, management quality, or historical events. Does management matter? Evidence is consistent with management quality affecting firm performance; but it does not imply causal relation. I.e. management quality varies across firms, but the idea that management matters is not immediate. Field experiment to test causality: - randomly split Indian textile firms in two groups - offer one of the groups consulting services from Anderson Consulting. - as a result of the consulting, the treatment group changes management practices, corresponding to an increase in the measurement quality score. - significant improvements in productivity - Persistence of differences in firm performance, i.e. effects last after treatment ends SUMMARY: Although management and ownership are normally separated, there are reasons to believe that deviations from profit maximisation cannot be too large. The precise meaning of “not too large” remains an unresolved empirical question. The horizontal boundaries of the firm are largely determined by cost considerations. LECTURE 3: competition, equilibrium, efficiency (chapter 4) DO FIRMS MAXIMISE PROFITS? Economics frequently treats firm as “blackbox” which transforms inputs into outputs through a process of profit maximisation. How realistic an approximation is this? 
 In reality, firms involve a collection of individuals and stakeholders with different interests.
 Is there enough discipline to lead firm to profit (value) maximisation? CHARACTERISTICS OF THE MODEL: The "perfectly competitive" industry, is an industry with no barriers to competition. The followings are sufficient conditions to yield a perfectly competitive industry: 1. Agents are small: this must be true for both the demand and for the supply. I.e. the quantity demanded/supplied by the individual, divided the total quantity demanded/supplied by the market approximates to zero. 2. It can be assumed that the product is homogeneous: sources of differentiation for a product are physical, temporal (e.g. availability through time), space/location where it’s sold/made/delivered, time, contingencies (e.g. umbrella if it rains or if it doesn’t). When we say that a product is homogeneous, we are ruling out all those differences. In other words, firms sell almost identical product. 3. Complete information: all agents know everything, and all agents know that every other agent knows everything, e.g. where to find the product, physical features. So there is no advantage, no asymmetric information. 4. No entry or exit barrier (i.e. free entry and free exit). We are talking about economic barriers, not administrative barriers. Other than the normal entry costs, there are no barriers to the establishment of a new firm. Exit barriers sometimes become entry barriers, because if I know that once I’m in then I’m going to lose a lot of money if I want to exit, then I’m not going to enter at all. E.g. entry is free but consumption is compulsory. Also, another example of exit barriers are sunk costs, subset of fixed, irrecoverable costs. The notion of equilibrium in a perfectly competitive market: Equilibrium price: price such that total demand equals total supply Remember: it has to be greater than zero, otherwise it’s meaningless. Here’s why: you need to rule out the situation in which p*=0, because it does not end with a trade, so it’s not worth studying. The supply and the demand coincide but they do not cross. Properties of the equilibrium in the perfectly competitive market: These 3 characteristics are displayed: 1. Agents are small → agents in equilibrium are price takers. Being small means being irrelevant as to the ability to make the prices. I.e. each firm faces a flat demand curve. 2. 3. Homogeneity and complete information → “law of one price” all transitions, between homogeneous products, happen at one price. Combination of homogeneity and awareness of agents. 3. NO entry or exit barrier → in the long run extra profit tends to 0, because extra profit can only be temporary It’s more important to be agile, and be able to respond quickly, than it is to predict. Being agile [allows you to] capitalise on change. That’s what it’s all about. —Jack Welch, remarks at NYUSern, May 2, 2002 In other words, if profit opportunities are short-lived, it’s important to be able to respond quickly when they arise, and to abandon mistakes when they happen We are not sure that a competitive firm operating in a perfectly competitive market is happy as maximising profit by choosing the q*. The firm can survive by producing q*? It depends on fixed costs. All costs have to be considered, fixed costs do not vary in the future. If there are fixed costs we need an additional constraint. We have to maximise this function, subject to profits ≥ 0 (non-negative). It is non-negative if the firm is producing a positive outcome, then from π=p*q-c(q)≥0 we can divide by q since it is positive, and we get p≥c(q) q which is the average cost. We conclude that the firm needs to produce an output such that the average cost is not greater than price: p≥AC. • Technological efficiency: is reached when each firm produces the min AC which coincides with the intersection with MC. • Locative efficiency: is reached when extra profit is zero, when the difference between MC and p is minimised. When q* is produced, we reach both technological and locative efficiency. 1. q* technological efficiency → each firm produces its best 2. p* locative efficiency → impose zero extra profit condition 3. n* firms will enter until an extra entry would make no profit Firstly, we decide whether it’s worth producing by checking that AC<p. Then, we decide how much to produce. What is the supply function of a company? It coincides with the Marginal Cost curve. However, it is only the part of the MC curve which is above the Average Cost curve. By producing exactly q*, we happen to be minimising AC and maximising efficiency. To summarise, under perfect competition a profit maximising firm, chooses the output it produces in such a way that p = M.C. if there are no fixed costs. If there are fixed costs, profit maximisation entails average supply. (maximising average cost(?)) If the firm produces on the blue line before the intersection it means that the AC is greater than the price, so you make losses. The individual demand curve coincides with the MC curve after it crossed the AC. 4.2 COMPETITIVE SELECTION We discovered how much each firm is going to produce, but how many firms would survive in such a market? Considering the single firm in the long run, we know it can survive only if it supplies the amount of output which maximises its average cost. Firms are small compared to the whole market, so the AC of the individual firm is small and will produce q*, if we plot on the vertical axes the corresponding value we will find p*, that is the condition minAC(q*) = p*. The question is: how many firms would succeed to operate in such a market? - If active firms are making extra profits, then new firms are attracted to the industry. - If active firms are making losses, then some of those firms exit. In the long run there is no extra profit, and firms pricing at the average cost are making zero extra profit. Now we plot p* on the demand function, and we get Q* , but since firms are identical, then Q* = n x q*. If we know the technology and we know the demand function we can easily obtain the number of firms that can operate in such a market by computing the ratio: n= Q* q* Steps to find the number of firms that can operate at zero extra profit: - Start from the individual cost function - Minimise the average cost - Set that equal to price, that corresponds to total output - The ratio between total output and single firm output gives us the number of firms. - n* is not bound to be an integral number (could be 7.3), so it would be the maximum integer lower than actual ratio. Empirical evidence suggests that profit rates are persistent in the long run. PRODUCTIVITY The data suggests that some firms and plants have superior skills in using inputs, allowing them to produce much higher output levels with the same quantity of inputs, and giving them a greater chance of survival. EXTRA INFORMATION FROM THE BOOK: DIFFERENCES FROM THE MODEL SUGGESTED BY EMPIRICAL EVIDENCE • Empirical evidence suggests that, in any given time period and industry, entry and exit take place simultaneously. • Empirical evidence suggests that entrants and exiters’ average size is much smaller than the industry average size. A model of competitive selection: • Considering that firms must pay sunk costs in order to access a perfectly competitive market, and that not all firms have access to the same technology, they have different productivity levels, and each firm is uncertain about its own productivity level. Given these elements we conclude that: - firms that get a series of bad signals (high production costs) gradually become “pessimistic” about their efficiency level, gradually decrease their output, and, eventually, may decide to exit the industry. - By contrast, firms that receive a series of good signals (low production costs) remain active and gradually increase their output. Taxes incidence Who ends up really paying the tax: the seller or the buyer? - Elastic demand: seller - Inelastic demand: buyer 4.3 MONOPOLISTIC COMPETITION One of the criticisms frequently addressed to the model of perfect competition is that it is based on the assumption of product homogeneity, that is, the assumption that all firms produce the same product. If we think about industries such as shampoo or small restaurants we conclude that the assumption of product homogeneity is clearly wrong. Nevertheless, these industries share several features with the perfect competition model. We say there is a monopolistic competition when the following assumptions hold: a. Large number of firms, i.e. many competitors, so the impact of each firm upon its rivals is negligible. b. Due to product differentiation, the demand curve faced by each firm is not horizontal, that is, each firm is a price maker, not a price taker c. There is free entry and free access to all available technology. In summary, it shares all the assumptions of perfect competition, except that of product homogeneity. The baseline is: Equilibrium profits under monopolistic competition are zero, but firms do not produce at the minimum of their average cost. The monopolistic competition model suggests that perfect competition is best thought of as an approximation. However, if the product is approximately homogeneous, then outcomes are approximately like those of perfect competition. In fact, as the degree of product differentiation decreases, the residual demand faced by each firm becomes flatter and flatter, and the point at which price equals average cost (LR equilibrium) becomes closer and closer to the point where price equals marginal cost, as in the perfect competition model. 4.4 EFFICIENCY Perhaps it’s not immediately obvious, but trade creates surplus. If trade is voluntary, this has to be true, or people wouldn’t do it. - For buyers, the (inverse) demand curve represents their willingness to pay. The difference between the demand curve and the market price (area A) is thus surplus to buyers, we will call it consumer surplus. - Similarly, the (inverse) supply curve measures the price at which sellers are willing to sell. The difference between price and the supply curve (area B) is thus surplus to sellers, we call it producer surplus. Total surplus generated by trade, the sum of areas A and B, measures the increase in economy- wide value that results from production and trade: how much better the economy is with the existence of that product. We may distinguish different types of efficiency: • Technological efficiency (or productive efficiency): is reached when each firm produces the min AC which coincides with the intersection with MC. Refers top how close the actual production cost is to the lowest cost achievable. Low productivity results from using the wrong input mix or from making a suboptimal use of existing inputs. In graphical terms, low productivity implies a higher marginal cost curve. This is illustrated in the right panel of Figure 4.8, where two marginal cost curves are depicted. The area between the high marginal cost curve (SH) and the low marginal cost curve (SL), which we assume is the lowest cost possible, measures the extent of inefficiency in production associated to SH. • Allocative efficiency: is reached when extra profit is zero, when the difference between MC and p is minimised. Requires resources to be allocated to their most efficient use. The degree of allocative inefficiency when output is q’ is given by the area C. Chapter 5: Market failure and public policy: Lecture 4 5.1 EXTERNALITIES AND MARKET FAILURE • Free riding problem: an agent's decisions do not take into account the costs imposed on other agents. As a result, the total quantity consumed is likely to be higher than the socially efficient. E.g. when ordering one more beer at a big table, providing the final bill will be split, you will probably order more than the socially efficient because you will think "one more beer, five more dollars on the total tab, that's five cents for me”. More generally we say there is an externality when an agent's actions have any effect on other agents that goes beyond the market transaction per se. This effect can be negative (when I smoke people around me suffer) or positive (when a plant flowers in my yard, everyone who passes by benefits). Here are some of the most common types of externalities: • The tragedy of the commons: is the situation when a common resource is overused with respect to the socially optimal level. For example fisheries and clean air: when a fishing boat decides how much cod to catch, the owner compares his own benefits and his own costs, ignoring the fact that this will have on the overall stock of cod. In this case, the market equilibrium involves an output level that is too high from a social point of view, possibly even leading to species extinction or at least over-fishing. • Congestion: example, when an airline decides to schedule a flight during rush-hour, it does not take into account the extra delay it will impose on all flights departing right after. • Public goods: it is a positive externality. If I build a park, I create a benefit for myself, but others can enjoy it at no extra cost. National defence, health, and education are also examples of investments and expenses that have some elements of public good. Economists' favourite solution to externalities is externality-correcting taxes. SOCIAL COST AND PIGOU TAXES In markets with externalities, the Fundamental Theorem fails to hold: market price is no longer the right guide for consumers and producers; something else besides the “invisible hand” is required to establish social efficiency. Many economists will tell you the solution is to apply a Pigou tax. To motivate this idea, consider the problem of climate change, caused by industrial production. Figure 5.1 depicts the supply and demand curves in a given industry. Recall that, in a competitive industry, the supply curve reflects the sellers’ marginal cost curves, whereas the demand curve - specifically, the inverse demand curve - reflects the buyers’ willingness to pay for the product in question. - The free market equilibrium implies price p0 and output q0. 
 By the Fundamental Theorem, this is the output level such that a marginal buyer’s willingness to pay is just equal to the seller’s marginal cost: there is no trade that would increase total gains from trade; total surplus is maximised. - Suppose however that each unit of output implies a social marginal cost of c(q), that is, a value that changes as q changes. Then the total marginal cost of producing the qth unit is given by the sum of production marginal cost and social marginal cost, the curve S+c. This corresponds to output level q*. Not surprisingly, q* is lower than q0: whenever there is a negative externality, the equilibrium output level is greater than the socially optimal output level. - Is there any hope for the market? Yes, so long as we impose an output tax or an output subsidy (if the externality is positive). Suppose that a tax t is levied on suppliers for each output unit. This implies an upward shift in the supply curve, from S to S+t. The market equilibrium is now given by q*, the socially optimal output level. ALTERNATIVE SOLUTIONS TO THE EXTERNALITY PROBLEM Pigou taxes are by no means the only way to deal with externalities. One important alternative is direct regulation of the externality-creating activity. For example, smoking creates an externality, thus it can be solved by banning it. THE COASE THEOREM One of the most creative ways of solving the inefficiency created by externalities may be to let interested parties negotiate. The Coase Theorem states that, if property rights are properly assigned and negotiations are costless, then all externalities will be “internalised”, so that the market solution leads to an efficient solution. Consider, for example, the case of a steel plant dumpling waste in the river. Society may decide: a. Downstream parties have a property right to clean water, or b. The plant has the right to dispose of its waste as it sees fit Once those rights have been clearly established, then individuals can bargain over how to exercise those rights. - If downstream parties have the right to clean water then the steel plant can pay them in order get permission to pollute. - If the plant has the property rights, then downstream parties can compensate the steel plant to restrict its pollution inducing activities. Suppose that the value that the plant gets from the opportunity of dumping waste in the river is greater than the cost it imposes on downstream residents. Then, in equilibrium, negotiations will lead to an agreement whereby waste dumping takes place. Notice that this equilibrium is achieved regardless of the initial property rights allocation. If the factory owns the rights, the residents have to incentive to buy the rights from the factory. If the residents own the rights, then the factory will make them a proposal they cannot refuse. The reasoning underlying the Coase Theorem serves as an additional illustration of the difference between efficiency and fairness. The Fundamental Theorem and the Coase Theorem are about efficiency; they have little to say about fairness. From an efficiency point of view, it makes no difference who owns the rights to clean river. Market externalities imply market failure. Pigou taxes and other mechanisms may reestablish equilibrium efficiency. 5.2 IMPERFECT INFORMATION Suppose you want to buy a 2010 Honda Accord. By consulting the Internet or some other source, you find out that the value of a very well kept car is about $20000. In practice, you know that some owners were not that careful. Let’s assume that, from the perspective of an uninformed buyer (you), the value could be anywhere between $0 and $20000. This means that, on average, you should be willing to pay $10000. Suppose that sellers, unlike you, are informed about the real value of the car they consider selling. If you are unwilling to pay more than $10000 for a car, then the sellers whose cars are in best condition will be unwilling to sell. This unrevealing process of adverse selection (market situation where buyers and sellers have different information. The result is that participants with key information might participate selectively in trades at the expense of other parties who do not have the same information) may go on and on, possibly to the extreme that the market collapses completely. That’s a rather unfortunate outcome. As we saw, under perfect competition all beneficial trades take place, In the present context, there may be many socially profitable trades (where the value of a specific car is greater for buyer than for seller) that do not take place. The key departure from the Fundamental Theorem is that perfect competition assumes perfect information, whereas in the present case you (the buyer) are uninformed about the seller’s product quality. Absent this situation of asymmetric information, each car’s price would reflect its quality and a trade take place if and only if the buyer’s valuation is greater than the seller’s. A particularly important case of asymmetric information and adverse selection is provided by health insurance markets. Suppose that consumers can be ordered in terms of health risk. Healthier people are willing to pay less for a given health insurance policy. So, for a given price, only the consumers whose health risk is greater than a certain threshold choose to purchase health insurance. 
 One important characteristic about heath insurance is that the seller’s cost depends on the buyer’s type. Specifically, the cost of serving a specific consumer is greater the greater that consumer’s health risk. As a result, the consumers who choose to buy insurance are precisely the consumers whose cost of providing insurance is highest. This implies that the marginal cost of serving the qth consumer is decreasing. It also implies that the average cost of serving the first q consumers (that is the riskiest q consumers) is declining and greater than the marginal cost. The competitive equilibrium correspond to the point where, by means of entry and exit, price is driven to the point where price equals average cost (and firms make zero economic profits. This is given by (qe,pe). By contrast, the social optimum level of q corresponds to the point where price equals marginal cost. This is given by (q0,p0). As can be seen, qe<q0, so the competitive equilibrium implies under-provision of health insurance. Specifically, the social inefficiency of the competitive equilibrium may be measured by the area of the shaded triangle A. This corresponds to all of the trades such that willingness to pay is greater than (marginal) cost, trades that could be efficient but do not take place. One should also mention that another implication of market asymmetric information: moral hazard. Consider the market for an expensive smartphone. Some consumers are risk averse and purchase theft insurance. The problem with this is that, once you are insured, your incentive to be careful about not having you phone stolen are lower. Insurance companies know this, of course, and adjust their premiums accordingly. (Introduction that can’t be found in slides or book) We are familiar with state intervention in the economy. There’s many examples of it: e.g. us being in university is a sign of the government being very active in education. The role of the State is seen with different interests by microeconomics and macroeconomics. Macroeconomics: In Europe, the average presence of the State part in GDP is 30% (state expenditures). Microeconomics: how does the State intervene to affect markets? The State, among its other functions, is also an economic organisation. But there are many subjects in society that have an economic role. With respect to other organisations, what are the distinctive features of the State? - Universality (It takes into consideration social welfare): while the other players think about themselves (in terms of profits), the State also cares about the community. - More costs and a lot of procedures - Coercity of power: the state, and only the state, can make use of a monopolistic power in the use of the law, which is something that no other economic agent can do. These features – universality and coercive power – are mutually dependent and have to be in balance to avoid, on one side, complete anarchy, and on the other, dictatorship.
 There exist two models of state intervention in the market: the EU and the USA 5.4 REGULATION Regulation: a government intervention in economic activity using commands, controls, and incentives. One possible classification of government regulations runs is as follows: a) Market regulation affects directly the workings of the price mechanism. A Pigou tax is an example of a market regulation. Another example is given by the European Union's policy of purchasing butter so as to stabilise the price of butter. b) Entry regulation refers to rules determining firm entry into a market (e.g. the requirement to obtain a license). For example, in order to work as a real estate agent you need to be certified by the government. c) Firm regulation in the case when a firm – typically a public utility – is subject to direct oversight by the government. For example, ConEdison need permission from New York State in order to change its electricity rates. d) Social regulation corresponds to rules that apply to firms, consumers, employers, etc. Examples include automobile safety standards, equal opportunity employment standards, and product labelling standards. Why is there government regulation, in particular economic regulation? • Market regulation may be understood as in attempt by a well-intentioned government to re- establish optimality in the presence of market failure (e.g. externalities, market power, etc). Under this view, known as the normative theory of regulation, consumers, faced with the negative effects of market failure, "demand "regulations from their political leaders. • A more sceptical — and possibly more realistic — perspective is that regulation is demanded not by consumers but rather by firms. Considered example of the US peanut program. Since 1949 the US government limits the number of farmers who can sell peanuts in the country; imports are also severely restricted. In addition, there is a support mechanism that guarantees a minimum price received by each farmer. Altogether, these regulations result in a domestic price 50% higher than the rest of the world. Clearly, this is not regulation at the service of the consumers. More likely, this is an instance of this so-called capture theory of regulation, according to which market regulation is a tool employed by firms to better serve their own interest. Regulatory capture is part of a more general phenomenon: politics are biased towards measures such that benefits are concentrated whereas costs are diffused. Baseline: a small number of people (sellers) extracting significant benefits, a large number of people (consumers) paying the cost. Uneven. The gain for a few people is huge, the damage for lots of people is small (because it is shared among lots of people), and the struggle against these giants make it impossible to change the situation. This is why regulations are needed. How do firms get away with something like that? In part, the reason is that the benefits from regulation such as the peanut program are highly concentrated in a few agents (the farmers), whereas the costs are spread throughout a large number of agents (the consumers). Which is the right perspective: the normative or the capture theory of regulation? Clearly, many regulations such as the peanuts program seem to protect firms more than the consumers. But many other regulations are strongly opposed by firms and supported by the public in general. All in all, it seems safe to say the regulation is like politics: a balancing act of interest and influences. 5.5 COMPETITION POLICY AND ANTI-TRUST The assumption that most obviously fails in many real-world markets is arguably the assumption that there is a very large number of firms, so that each of them is too small to influence market price. We introduced the public policy instruments that address market failure due to monopoly power. Competition policy and antitrust are essentially the same thing: - Competition policy is the term most commonly used in Europe - Antitrust is the term most commonly used in the US. • The oldest and most commonly accepted form of competition policy relates to so-called horizontal agreements, inverted particular price-fixing. In industries that are not monopolies, the tantalising possibility is that firms behave like a monopoly, namely by jointly determining the price as if they were a monopolist. • Many monopolies are created by means of mergers and acquisitions. One important role of merger policy is precisely to prevent excessive concentration of market shares. • In many cases a Monopoly or dominant firm may be unavoidable. While monopoly is not to per se illegal, abuse of such a monopoly or dominant position is. Antitrust makes sure the giants play fair, that he is, refrain from abusive practices, and the competition playing field is as level as possible. The main areas of competition policy are price-fixing, merger policy, and abuse of dominant position. 5.6 FIRM REGULATION If fixed costs are a very large – or, more generally, if scale economies are very significant – Then competition may simply not be a viable alternative. An extreme situation is given by a natural monopoly. In this case, direct firm regulation of the monopolist (or dominant firm) may be the optimal solution. Let us start by considering the simplest case of monopoly regulation. There is a firm with a cost function given by C=F+cq Where F is the fixed (capital) cost and c marginal cost (which we assume is constant). Absent regulation, the monopolist sets price at the monopoly level, pM. Since the social optimum would be to set price at marginal cost level, monopoly pricing implies that output is lower than socially optimal. A first natural solution for a regulator is to force the monopolies to set price equal to marginal cost: pR=c, where R stands for “regulated”. In this case, output is given by qR and maximum allocative efficiency is achieved (i.e., the area E is equal to zero). One problem with marginal cost pricing is that it may imply negative profits for the firm. This is certainly the case when marginal cost is constant: variable profit π, is zero, and total profit is therefore -F. Clearly, a firm that makes losses of F cannot survive. To solve this problem, the regulator might give the firm a subsidy of F. However this would likely create additional problems. - first, in order to obtain the value F the regulator may need to raise taxes elsewhere in the economy. - second, the possibility of transfer from the regulator to the regulated firm gives the former more discretion, and opens the door to the possibility of regulatory capture. Regulatory capture: the situation whereby firms invest resources into influencing the regulator's decisions, to the point that regulation reflects the objective of profit maximisation rather than that of welfare maximisation. In fact, even if the regulator is not actually influenced, the use of resources attempting to do so is socially wasteful. • Given the problems of marginal cost pricing, an interesting alternative is that of average cost pricing. Under this regime , The firm is forced to set the lowest price consistent with making non-negative profits, that is, price is equal to average cost. As can be seen, the solution is intermediate between those of marginal cost pricing and unregulated monopoly. • In the United States, the mechanism that in the past has been used most often is the rate-of- return-regulation. This is a mechanism whereby prices are set so as to allow the firm a fair rate of return on the capital it invests. Roughly speaking, this corresponds to average cost pricing. One major problem with it is that it gives the firm very little incentive for a cost reduction. In fact, lowering the cost implies that the allowed price will be accordingly lower, leaving the firm with the same rate of return. In practice there is a gap between the time when the firm reduces its costs and the time when the new regulated prices take effect, what might be called a regulatory lag, and this may provide the firm some transitory gains. In the terminology of regulation theory, we say that a rate of return regulation is a low-power incentive mechanism: price varies in the same measure as cost, a fact which minimises the incentives for cost reduction. At the other extreme, we have high-power incentive mechanism: price is set beforehand and does not change at all even if cost changes. • This is the essence of a price cap regulation mechanism. This mechanism provides maximal incentives for cost reduction: a $1 saving in costs implies a $1 increase in profits. Following this line of argument, a somewhat extreme appraisal of price-regulation is to view it as a rate of return regulation with a long regulatory lag (usually 5 years). 10 would seem like a reasonable period, sufficient to make price cap regulation substantially different from rate-of- return regulation. But the experience of several countries suggests that revisions of the price cap normally occur at smaller intervals. These in turn cast some doubt over the effectiveness of price- regulation as an incentive scheme. Another problem is that it creates little incentive for the provision of product or service quality. Unable to increase price, the regulated firm may have an incentive to reduce quality, thereby effectively increasing price "per unit of quality”. Finally, implementing price cap regulation raises the problem of determining the price cap. In this sense, rate-of-return regulation is a better mechanism: the risk for the regulated firm is minimal. A high-power mechanism provides strong incentives for cost reduction but little incentives for quality provision. In addition, it implies a high degree of risk for the regulated firm and requires strong commitment on the part of the regulator. ESSENTIAL FACILITIES AND ACCESS PRICING When and to what extent are we in a monopoly situation? Suppose that competition is allowed in the parts of those industries where natural monopoly is not an issue (electricity generation, long-distance communication, and so on). The problem that typically arises is that these parts cannot exist independently from the part that is natural monopoly: an electricity generator needs the distribution network to sell its power. Specifically, what we have is a monopolist (the local telecommunications operator) selling services to firms in the competitive segment (long-distance telecommunications) who in turn sell to the final consumer. In these cases, we say that the monopolist is an upstream bottleneck and that the monopolist’s assets or output are in an essential facility. Another example from this perspective: an airport is an essential input for transportation services. While there may be many competing airlines (downstream firms), there is frequently only one airport in each city, the owner of which is the upstream firm. The regulation of essential facilities shares the same problems as those of monopoly regulation. Moreover, it is frequently the case that the owner of the upstream facility also competes downstream. This type of situation raises a number of additional issues. - One possible concern is that the upstream firm may use its monopoly power to extend its downstream, thus creating monopoly power at the downstream level as well. The upstream firm may be unable to extract from the downstream competitors all of the monopoly rents in the value chain. By foreclosing its downstream competitors from the market, the upstream firm is then able to recapture its maximal monopoly profits. This decreases consumer (and total) welfare. - One way to avoid this is to force the upstream firm to divest its interests in the downstream market: forcing competition downstream, and preserving monopoly in the upstream. - A regulatory alternative to divestiture consists of allowing the upstream firm to compete downstream but to prevent it from discriminating against downstream competitors. One central aspect of this alternative is the regulation of the access price, the price is paid by downstream firms to access the essential facility: Efficient Component Pricing Rule (ECPR), the price offered by an independent downstream firm cannot be higher than the difference between p, the final price set by the integrated firm, and the marginal cost of the integrated firm at the downstream stage. The idea of the ECPR is that it allows the independent downstream firms to survive if and only if they are competitive with respect to the vertically integrated firm, so as to maximise efficiency. Always decreasing and it converges monotonically and asymptotically to the marginal cost k. If the average cost is everywhere decreasing, then it’s a natural monopoly. The lim pushes the average cost function to ∞ . q→0
 The lim pushes the average cost function asymptotically to 0. q→∞ • Natural monopoly: an industry in which technology displays a sub-additive total cost function, and in which the average cost is everywhere decreasing. By looking at the total cost function you can immediately understand whether we are in the presence of a natural monopoly. 
 Example : You need some fixed costs (if costs are variable no) and then a decreasing function for it to be a natural monopoly. -  c(q) = q3 , this is not a natural monopoly because AC = q2 (always increasing) 
 -  c(q) = 2 q2 + q , then the AC = 2q + 1, so no (always increasing). 
 Exercises: 1) c(q)= q2+F AC= q+F Is it decreasing? It depends on the parameter F in this case. We calculate q dAC in order to understand if it’s increasing or decreasing. dq AC’= 1- F I’m interested in the portion where the derivative is q2 negative, so [0;⎷F]. Thus, it is a natural monopoly for q<⎷F (we obviously don’t care about negative q). When the AC function is at all points decreasing, then it is a natural monopoly regardless of the demand. However, it may happen, like in this case, that the average cost function is not monotonically decreasing, mainly because there are diseconomies. Thus: - NM: if it cuts the demand in the decreasing portion (before ⎷F) - Not NM: if it cuts the demand in the increasing portion (after ⎷F) In U shaped cost functions it may happen that a market initially is a NM but then since the demand shifts to the right (due to increasing demand), we do not have a NM anymore. A trade off: NM presents a sort of trade off, a conflict between two desirable goals: • Technological efficiency: requires producing at minimum cost, which can be reached only in the case of one producer market. • Allocative efficiency: rivalry between companies, which allows prices to protect consumers' interests too. The bottomline is, we would like some competition, but it wouldn’t be cost efficient. How do we solve it? Historically, there are three solutions to this problem: - Public enterprise: i.e. State firms. This is the oldest solution. It solves both the technological problem and the allocative problem. In fact, it is only one company and it eliminates extra profits. It hasn’t always worked. - Market regulations: Another solution has to do with market regulation (not administrative but economic). When the State stops playing a role as a player through privatisation (reaching the American model), it starts to play in the market through regulations. Regulation is industry- specific, there would be a regulatory body for any industry (energy, telecommunication, airports). One of the troubles with regulation has been elaborated by the Nobel Prize Stigler: he outlined that regulatory bodies could be captured by lobbies – subject that should be regulated, thus becoming useless. - Demsets 1968: Compete FOR the market when you cannot have competition IN the market. Since it is not possible to create competition in the market, create competition for entering the market. The best bid would be that with the lowest price for consumers. Of course this would not work if the competitors, collude, make agreements in order to let one win (one time I let you win, next time you let me win). Also, take into consideration that it could also happen that an industry that is not a natural monopoly, might become a natural monopoly in the future due to technological progress, changes in consumer taste, etc… Important point to understand, electricity is not a natural monopoly, the DISTRIBUTION of electricity is a natural monopoly . Differences between Antitrust and regulation [General/Universal vs. industry-specific] Antitrust legislation applies to all markets except those that are explicitly excluded. On the other hand, regulation is industry-specific, i.e., there is a regulatory body for each industry.
 [ex ante vs. ex post] Normally, the legislative body sets the rule and if they are not accomplished the Antitrust intervenes. Whereas regulation operates by setting rules and does not sanction. 
 [does not set numbers vs. sets numbers] The Antitrust does not set numbers, while the regulatory bodies do, also because they act earlier and have to set standards. Examples of regulation One can broadly and roughly distinguish between price and non-price regulation, even though the latter may still influence price.
 The most regulated sectors are the pharmaceutical one, the financial market, etc.
 However, it is important to remember that State interventions are really dependent on situations and features of each context. Therefore, it is not appropriate to state whether some kind of regulation is better than another one. Here are some examples of market regulations which we have already seen before: - Market regulation - Entry regulation - Firm regulation - Social regulation Normally State intervention, approved and implemented for justified reasons, which normally refers to some market imperfections, in a way, any intervention is very much dependent on the circumstances. Something that is good in a period can be bad in another time. So we should avoid definite and generalised rankings and judgements (e.g. this is good, this is bad), because it may apply to a situation, but not another. Market structure Market structure depends on a variety of factors, but some regularities have been identified too. Evolution of market structure analysis over time: Industrial Organisation started as an empirical area of research in the 30s, without a formal model, but a collection of empirical evidence on the basis of which studies were conducted. This approach was called SCP (structure, conduct, performance). The idea was that if you have a description of the structure and some reasonable assumptions about the behaviour of agents, then you can make predictions about performance. Key indicators of structure - the number of firms - some index of concentration - some degree of product differentiation - some measure of entry barriers These indicators measure how such an industry depart from perfect competition (small agents, homogeneous product, neither entry nor exit barrier). Also, performance predictions are based on some indicators: - price-cost margin - mark-up - the pace of technological progress Of course, evidence provided some regularities: for instance, normally there is a positive correlation between concentration and Lerner index. LERNER INDEX: Profitability or market power is the ability of a company to make profits (and to maximise it). To make a profit you have to price significantly above the marginal cost. • Lerner index: the main measure of market power. Its value goes from [0,1]: it is 0 in perfect competition and 1 in monopolies.
 In perfect competition, firms have no market power, and they price at marginal cost (they are not price makers). (1) General formulas or Markup: price - MC with respect to marginal cost, relative to price. where L ∈ [0,1] . • L = 0 , when p= MC (under perfect competition) • L > 0 , (under a monopoly) • L = 1 , when MC=0. This could happen under utilities and natural monopoly. Huge fixed costs and the marginal cost is almost negligible. It is a case where L approaches 1 (but it’s never actually equal to 1, it just approaches it).
 (2) Under Cournot oligopoly (firms choose output values) Remember that when talking about an oligopoly, the Lerner index can be of a single firm or of the average of the firms. The two coincide only if firms are identical (same marginal cost) a. Identical firms (symmetric) If I have n firms in a Cournot oligopoly and these firms are identical, the Lerner index for each of them will be identical to the Lerner Index for the market. In this case, both formulas can be used. Recall that the market share in equilibrium if all firms are identical is 1/n. With this L = p − MC p Li = si |ε | (1) Product is homogeneous, firms are identical Since firms produce the same output , the market share will be This is the case where, e.g. in oligopoly, the number of firms n, is a good indicator of industry structure: the lower n, the more concentrated the industry is. Specifically, 1/n might be a good measure of concentration, a measure that varies from 0 (minimum concentration), and 1 (maximum concentration, monopoly). However in practice, firms are not identical, i.e. different firms have different market shares: even if they have the same product, the may differ on the technological side. E.g. five firms of the same size is not the same as one with 96% and the remaining four with 1%. So we need a more general measure of concentration. In general we have that (2) Firms are not identical (q1>q2>q3…>qn) In this case, it is not possible to apply the previous formula since output is not evenly distributed. In this situation, we have two measures of concentration. A. Concentration ratio (CR): CRk is the sum of all market shares considering only the biggest k. The percentage of industry sales that comes from the 4 largest firms. Each market share goes from 0 to 1 and they add up to 1: the greater CRk, the greater concentration, i.e. CR takes values form 0 to 1 If you get CR>1, something must have gone wrong! It has to be lower than 1. How to compute CR? - We rank market shares in decreasing order, then I focus only on the top k, usually 4. - The greater CR, the more concentrated is the industry. Social media is a good idea of a very concentrated industry. Be careful about the geographic dimension of the market. We assume we have already solved the issue of time and place, when we talk about industry. Problem with this method: it doesn’t take into account the entire distribution. Suppose you get CR=0.8 It is different if it is split among 4 or split among 10 companies! In some cases, the sum of the top 4 market share in two industries may be the same, but in one case you have few giants and a lot of negligible firms, while in the other industry they are more distributed. Therefore, we need a measure that takes into account the entire distribution. B. Herfindhal-Hirschman Index (HHI): HHI is the sum for all firms’ Si (from 1 to n) squared. The value of HHI varies from 0 to 1. Why do we need to square them? Cause if I don’t, the sum is equal to 1 in all cases, not just in that of a monopoly. q1 = q2 = qn → Q = nq si = q nq = 1 n CRK = 4 ∑ i=1 si HHI = n ∑ i=1 s2 i It is a better measure but it is more difficult to compute because it requires knowledge of the market share of all firms in the industry, whereas CR only of the largest k. How to compute HII? - Square the market share of each firm competing in the market and then sum the resulting numbers. Different rankings may result if concentration for the same industry is computed by using the two measures, because they focus on different aspects. - CR looks only at the top 4 companies. - HII focuses at the entire distribution, which may change the results to the point of giving the opposite results. The link between measures of market power (Lerner) and measure of market concentration We will see the link in the chapter about Cournot oligopoly. CHECK THE CHAPTER FROM THE SYLLABUS Exercises of the same type we did in class and we will do with the assistant, and we find at the end of the chapter. 75 minutes. Exercises, you can choose which ones you want to do, or all of them. They are 8 points Multiple choice: 1 question, 4 answers. You have to motivate one of the answers. They are 3 points with the right comment. -1 if you get the wrong answer. NO EXERCISES ON PRICE DISCRIMINATION, JUST MULTIPLE CHOICE QUESTIONS WHICH MAY REQUIRE SOME ELEMENTARY ALGEBRA Price discrimination Price discrimination: the practice of setting different prices for the same good, whereby the relevant price in each case depends on the quantity purchased, on the buyer's characteristics, or on various sale clauses. In fact, strictly speaking, the goods sold are not exactly the same. There is some confusion about the names in price discrimination, so when you find them in the slides, check for the correspondent names on the internet. Pigou provided a definition for price discrimination in 1920 “it's amount to selling the same item to different prices to different consumers”, but it was essentially wrong. In fact, in order to provide a proper definition, we need to take into consideration cost differences. PA ≠ PB CA CB • In perfect competition: there is no price discrimination, because agents are price takers • In monopoly: there can be price discrimination, but we have yet to see it. WHY PRICE DISCRIMINATION? For a given (linear) demand curve, and constant marginal cost, the figure depicts your optimal price for a monopolist selling one product. The optimal output level qM is given by the intersection of marginal revenue with marginal cost, and the optimal price pM is given by the demand curve and the optimal output level qM. At this price and output level, the seller makes a profit given by (pM - c)qM (ignoring fixed costs). These values strike the right balance – the one that maximises profit. Nevertheless in this situation the seller is “leaving money on the table”: - First, there are consumers who pay pM but would be willing to pay more than that. (A) - Second, there are consumers who would be willing to pay more than the cost c but don't buy at all because their valuation is lower than the price pM. (B) The goal of price discrimination is to get a slice of these untapped revenue source: selling for a higher price to consumers whose willingness to pay is higher, and selling for a lower price to consumers whose willingness to pay is lower. This is easier said than done, but suppose that the seller: a. Knows each customer's valuation b. Is able to charge a different price for each customer. Custom markets: markets where sales terms are tailored to each individual customer. ARBITRAGE AND PRICE DISCRIMINATION The monopoly has to face two issues in order to perform price discrimination: 1. Identification: know the differences between the customers, know more about the consumers. It is an informational requirement. 2. Prevent arbitrage (resale): prevent customers buying when prices are low and then reselling. We need to avoid extra trade. Example: suppose you are a car dealer and try to sell a car for $18,000 to regular customers and for $13,000 to students. What would happen is that an entrepreneurial student would start a part- time business of buying cars at the student price and reselling them at the regular price. The point is that, when segmenting the market and setting different prices to different segments, one must be aware of the possibility of resale. In order for more than one price to prevail in equilibrium we must have: a. Physical impossibility of resale (e.g. you can’t resell a haircut) b. Transactions costs: reselling can be hassle c. Imperfect information: customers may simply not know about the different prices 3. Alternative strategy is to charge $1200 for the full version and $500 for the strip down version. This will lead high-end users to pay $1200 and low and users to pay $500. Total profit is now: (500-300)x2M+(1200-300)x1M=$1.3B. By choosing the strip down version, a high-end consumer gets a surplus of $300. By choosing the full version, they get a surplus of $1500-p. The incentive constraint is that: 1500-p≥800-500, i.e. p≤1200 Since profit is greater than greater price is, we choose price equal to $1200. How do we get the value $500 for the strip down version? Basically, since dispersion is intended for the low end customers, price cannot be greater than the low end consumer willingness to pay. We call this the participation constraint. Basically the prices are such that the "low type "gets a net surplus of zero (whatever it takes for the type to participate). The "high type ", in turn, makes a strictly positive surplus, the meaning that he is consistent with the incentive constraint. Bundling Distinction is made between pure bundling, whereby buyers must purchase the bundle or nothing, and mixed bundling, whereby buyers are offered the choice between the bundle or one of the separate parts. Intemporal price discrimination The decision to buy a durable good is one where timing is of the essence. I can buy a computer today or wait for a few months. Pricing durable goods involves one additional dimension of price discrimination: time. By setting different prices now and in the future, and monopolist may be able to engage in price skimming: to sell both to high-valuation buyers at a high price and to low-valuation and buyers at low price. The idea is that valuation and impatience are normally correlated. Unfortunately, the hope that high-valuation buyers will make a purchase now may be just that, hope. In fact, a rational buyer should've put itself in the seller's shoes and figure that it will be in the latter's interest to lower prices in the future. The seller's price discrimination strategy will then have backfired in several way: first, sales are much slower (cause even high-valuation consumers choose to wait); second, average price is a much lower than it would've been if the seller had simply set the monopoly price in both periods. In other words, the possibility of setting different prices in each period, at first sight an advantage to the seller, may turn out to be a curse for total profits. In summary, due to "strategic "purchase delays, profits may be lower under price discrimination. There are a number of ways in which the seller can avoid that durable good curse. - one is to commit to not lower price in the future: the incentive not to lower price in the future is them so strong that buyers have a little reason to expect prices will come down in the future. - Alternatively, the seller may decide not to sell the durable good, only to lease it. This policy effectively turns a durable good into a non durable one. Consumers have no incentive to delay. - Another way is to introduce some sort of product differentiation that further separate high- valuation from low-valuation buyers. - Finally the seller may simply acquire a reputation for not lowering prices arbitrarily. Non-linear pricing Frequently, consumers must decide not only whether to buy a given product, but also how much to buy of it. Linear pricing “leaves money on the table" and non-linear pricing is a strategy for capturing some of that back. Moreover, to the extent that different consumers purchase different quantities of the same product, non-linear pricing also creates the possibility of charging different consumers different unit prices. This effectively corresponds to price discrimination by self-selection, just like versioning or bundling, but it is sufficiently important to justify a separate subsection. Price depends on the quantity purchased by not on the identity of the customer. We can see that unit price falls (it is non linear). q exp Exp/q=p 1 1p p Homogeneous consumers Consider the pricing problem of a golf club owner. Suppose all golfers have the same demand curve, D. the simplest case of non-linear pricing, is a two-part tariff: a fixed part f, which consumers must pay regardless of quantity purchased, and a variable part p, proportional to the quantity purchased. Think of f as the annual membership fee and p the greens fee you must pay each time you play 18 holes. - If marginal cost is constant at c (the additional maintenance cost each time a golfer plays the course), and if the club owner were to set a uniform price, that is independent of the quantity, then the optimal value would be pM, the monopoly price. - Now suppose that the club owner sets a two-part tariff. Whatever the value of p, the seller should set f at the maximum value such that golfers are still willing to join the club. This maximum is given by consumer surplus CS, the area under the demand curve and above price. Let π be the golf course’s variable profit as a function of the price it sets, that is π(p)=(p-c)D(p). Total profit is given by variable profit, π(p), plus the fixed fee, f: Π(p)= π(p)+f. It is optimal for the club to set a fixed fee (membership fee) equal to the consumer surplus corresponding to price p, that is, f=CS(p). Therefore, we have: Π(p)= π(p)+CS(p). If the seller can set a two-part tariff and all consumers have identical demands, then the (variable) price that maximises total profits is the same that maximises total surplus, the is, a price equal to marginal cost. The optimal fixed part is when the consumer surplus corresponding to p=c, that is, f=CS(p)=CS(c)=A+B+C. Notice that a two-part tariff: - increases profits from A to A+B+C, the seller makes no money at the margin but receives a large fixed fee. - Increases total surplus from A+B to A+B+C. The marginal price drops from monopoly price to marginal cost. - Decreases net consumer surplus from B to zero, in fact all of the gross consumer surplus is captured by monopolist via a fixed fee. In other words, total efficiency increases but consumer welfare decreases as a result of non-linear pricing. A monopolist’s optimal two-part tariff consists of a positive fixed fee and a variable fee that is lower than monopoly price. Total surplus is therefore greater than under uniform pricing. Multiple consumer types and multiple two-part tariffs Given that there are different types of consumers, it is natural to assume that the seller sets different two-part tariffs . If the seller could directly identify each consumer’s type, then the solution would be quite simple: the seller would set p=c and f=CSi(c). However this is not feasible and most likely illegal. But suppose the seller offers the consumers the choice of different two-part tariffs. Example: calling plans from telephone operators. If the seller wants consumers to be sorted across different calling plans, then it must make sure that type 2 consumers have no incentive to adopt the first calling plan. Moreover, the seller must make sure that each consumer type prefers to pay the fixed fee and consume its optimal quantity than not consuming at all. In the economic jargon, the seller must take into account (a) incentive constraint, (B) the participation constraint. Returning to the problem of setting a menu of calling plans: 2 2p p 3 2p 2/3 p The low-consumption types pay a lower fixed fee but a higher marginal fee. The high- consumption types pay a relatively high fee but a low marginal fee. THIRD DEGREE: GROUP PRICING / SELECTION BY INDICATORS Third degree price discrimination: the seller can exactly determine whether the buyer belongs to a certain market segment and charge accordingly. This practice is also known as market segmentation. Examples: one common form of market segmentation is based on geographical location. It can also be student discounts, membership discounts, reduce train fares for the elderly. It charges uniform prices within each group, but different among different groups. Takes place when different prices are set in different market segments (though unit price does not depend on quantity). The simplest model consists of a monopolist selling to two separate markets. The seller’s profit function is then given by: Π(p1,p2)=p1D1(p1) + p2D2(p2) - C[D1(p1) + D2(p2)] where pi is price in market i, Di demand is market i, and C(…) production cost. Profit maximisation implies that MR1=MR2=MC. This in turn implies the well-known elasticity rule: p1(1+ 1 ) = p2(1+ 1 ) = MC ε1 ε2 It follows that: Under discrimination by market segmentation, a seller should charge a lower price in those market segments with greater price elasticity. MC= p(1+ 1 ) ε (This is the elasticity rule, same) A model like this explains why the export price may be lower than the price set for the domestic market. In general, demand elasticities tends to be lower (in absolute value) in the domestic market, a feature of the demand function known as home bias. Example: At a small-town college campus, Joe's pizza serves both faculty and students. At lunchtime only students come into Joe's, whereas in the evening only faculty come in. Students have a constant demand elasticities of -4, whereas faculty have a constant demand elasticity of -2. Finally, marginal cost is $6 per pizza. What are the optimal prices at lunch and dinner time? pL(1-¼)=6 pD(1-½)=6 pL=$8 pD=$12 This however wouldn’t work if students wanted to eat for dinner, therefore the issue would have to be solved “manually”. Example 2: BioGar is thinking of selling its medicine also in Europe, but wonders whether it should charge the same price in the two markets. They estimate that the demand curves have the form: qi=ai-bip In the US (market 1) the parameters are a1=12 and b1=2. In Europe (market 2) the parameters are a2=4 and b2=1. Also, the effects of price discrimination go beyond the producer and consumer surplus: "There, on average, consumers dislike paying different prices. Legal matters: In the US, the main concern has been to prevent price discrimination from injuring competition. In Europe, there was a case which ended by punishing the abuse of dominant position. Net neutrality: Most would agree that the definition of net neutrality refers to the principle that ISPs and governments should treat all Internet data equally, that he is, not discriminating or charging differently by user, content, site, platform, application, etc… Privacy: Potentially more serious threat to privacy is the use of cookies, small files placed by a website in a user's web browser that record information about the user's visit. Call keys allow for sellers to know each user's preferences better, which in turn may lead to important efficiency gains. Games and strategies, Ch.7 Game: a stylised model that depicts situations of strategic behaviour, where the payoff of one agent depends on its own actions as well as on the actions of other agents. All agents are aware of that. It is about a situation of strategic interdependence (or interactions). For a situation to be referred to as a game, it is not enough to have different players, it is also necessary to be aware of it: otherwise, agents act as if there were no game at all. Agents are thus assumed to be rational and taking on a strategy in order to reach a specified goal. This type of interaction is relevant in oligopoly situations: in a market with a small number of firms the profits of a given firm depends on the price set by that firm as well as on the prices set by the rival firms. Neither perfect competition nor monopoly deal with games, but simply with decision problems. The concept: The optimal choice for a player – it's optimal strategy – depends on what it expects other players will choose. Since other players act in a similar way, when conjecturing what another player will do, I may need to form a belief about what the other player's belief regarding my behaviour is. Moreover, if the strategic interaction evolves over a number of periods, I should also take into account that my actions today will have an impact on the other players' beliefs and actions in the future. Don’t be confused with the classification of games and strategies. Classifying games is classifying situations, before looking at the strategy. History: Game theory: John Van Neumann 1940, main contributor. It is one of the branches that is born within economics and not taken from other subjects so application is very natural. The first field in which game theory was elaborated was industrial organisation. To sum up the main concept before moving on: - Context: you’re in an industry with a small number of competitor. You’re concerned that if you cut your price, your competitors will, too. How do you act? Ditto pretty much any strategic decision: capacity, entry and exit, product positioning. - Concepts: players, strategies, dominant and dominated strategies, best responses, Nash equilibrium. - Economic principle: must anticipate others’ actions and that your actions might affect theirs. Difference between games and decisions: - in perfect competition it is about decision problems, same in monopoly. Uncertainty is only external in these cases. - In oligopoly, it is about games. There are other players and you have to be aware of them. If you don’t take them into consideration, you are in a game but you act as if you were in a decision problem, which is wrong. We are assuming that players are rational: maximise profits (or minimise losses) Who act with a strategy and are aware that other players also have strategies. Elements of game theory: A game consists of a set of players, a set of rules and actions, and a set of payoff functions. Classification of games is about describing situations. Some of these situations may involve a winner and a loser, other will be more similar to a win-win game – everybody benefits from the situation. To describe a game we need the knowledge of three ingredients: - Players: denoted by (i=1,…,n) - Strategy set: a set of rules and actions. For every player there is a set from which they can choose all (pure) strategies, denoted by Si - Payoffs: the outcomes, the utility that each player gets as a result of each possible combination of strategies. Denoted by Pi. Can either be numbers or functions. E.g. Pi(si;sj) payoff of player i is a function of strategy of i and strategy of j. How to represent games: 1. The matrix: this is known as the normal form, or strategic form. A crucial aspect of the game is that each player's payoff is a function of the strategic choice by both players. But it could also be that I have troubles with this form. If you have a continuous set, like choice of prices, or multiple players, we need equations, cause matrices are not enough. 2. Equations: in which payoffs are functions, not numbers. Each payoff depends on the strategies of all players. It’s a system of n equations, each a function of a vector representing the strategies of each player. Pi=f(X,…) x∈ℝn One shot games: means that you play once, and not repeatedly. Simultaneous vs sequential games So far, strategy only involved one action. But what about a game which involves multiple actions, like chess? • Simultaneous games: both players choose their strategies simultaneously. In real life, very seldom do agents make decisions at precisely the same time. So how realistic is the assumptions that players choose strategies at the same time? In this context, it is perfectly possible the players make decisions at different times but that, when decisions are made, neither players knows what the other player's choice is. In other words, it is as if players we are simultaneously choosing strategies. It is a game in which moves cannot be observed. • Sequential games: This assumption does not always work, that's why an explicit assumption of sequential decision-making is more appropriate. It is a game in which moves can be observed. 3. Extensive form: now with the knowledge of sequential games, we can introduce the extensive form, or tree form for sequential games. (Still one shot). One-shot vs repeated games: • One-shot games: are those that are played once. • Repeated games: “super game” is played many times. E.g. deciding the price every morning for a product. From which we can derive: - One shot simultaneous: you play once, and make one move (I can try to predict what the other does). If I play second, it becomes a decision problem, not a strategy. - One shot sequential: you play once, with many moves (I observe what the other does). Variable-sum vs constant-sum games • Constant sum games: the sum of each cell is n (e.g.-2,3 or 1,0 where in both cells we end up getting 1). In each outcome, players split the cake. A special type of constant sum games are zero sum games, where the sum of each cell is zero, thus one wins, one loses. Constant-sum games enjoy the property that any allocation between two or more players is Pareto efficient, because any allocation of payoffs, in order to make one player better off makes the other player worse off. • Variable sum games: the sum of each cell is not constant relative to the others. Cooperative vs non-cooperative games • Cooperative games (not strategies): not the behavior, but the rules of the game. Communication before playing the game, so that the best situation for both can be selected, using the criterion of total payoffs. The conditions under which a game is said to be cooperative are: a. Pre-play (there is a pre-play phase in which players communicate and decide what they will choose. b. Credible commitment (players can credibly commit). In fact, even if there’s contracts, people still cheat. A small portion of games are cooperative, and they often come from criminal activity, such as cartels and collusion. • Non-cooperative games: the vast majority of games are non-cooperative. Games of perfect vs imperfect information • Games of complete information: common knowledge, all players know everything, we are interested in these games. • Perfect information: when players remember the entire history of the game until that point. Perfect information is synonymous of perfect memory. This situation is not very common. • Games of incomplete information: The matrix (one-shot simultaneous game) is a game of imperfect information, because nobody has observed anything yet. We will be mainly concerned with variable sum, non cooperative, complete information, imperfect information. Dubious application of dominated strategies To understand the importance of these assumptions regarding rationality, consider this game: Player 1: no dominant strategy, the reaction is different because it depends on the choice of player 2. L→ T R→ B Player 2: we have a dominant strategy R T→ R B→ R And a dominated strategy L Suppose however, that player 1 entertains the possibility, unlikely as it might be that player 2 is not rational. Then B may no longer be its optimal choice, since there is a chance of player to choosing L, resulting in a payoff of -100 for player one. A more general point is that, in analysing games, it is not only important whether players are rational: it is also important whether players believe that other players are rational. Absolute and relative payoff: The game we just saw also raises the issue of what rationality really means. In game theory, we take it to imply that players seek to maximise their payoff. However, many students, faced with the game, expect player 2 to choose L: while it implies a lower payoff for player 2 (0 instead of one) it also gives player one a very negative payoff. In other words, the outcome (B,L) looks favourable to player 2 in the sense that she wins by a very favourable margin. Although this is a frequent interpretation of games, it's defers from the game theory approach. Instead, we assume that each rational player's goal is to maximise his payoff. It is quite possible that one component of the player's payoff is the success (or lack thereof) of arrival players. If that is the case, then we should include that feature explicitly as part of the player's payoff. For example, suppose that the values of the previous matrix correspond to monetary payoffs; and that each player's payoff is equal to the cash payoff plus a relative performance component computed as follows: earning one extra dollar more than the rival is equivalent to earning $.10 in cash. Then the relevant game payoffs, given that player one chooses B, would be (-110,+10) if player 2 chooses L, and (2.1,0,9) if player 2 chooses R. Nash equilibrium: Introduced by Cournot and then theorised by John Nash in 1951 to give a solution to non- cooperative games, with simultaneous moves, complete and imperfect information, in which there is a finite number of players, whereas the number of pure strategies can be infinite. Let's now consider this game. There are no dominant or dominated strategies in this game. Is there anything we can say about what to expect players will choose? In this game, more than in the previous game, it is apparent that each player’s optimal strategy depends on what the other player chooses we must therefore propose a conjecture by player 1 about a player 2’s strategy and vice versa. A natural candidate for a “solution” to the game is the situation whereby: a. Players choose an optimal strategy given their conjectures of what the other players do and … b. … such conjectures are consistent with the other players’ strategy choice. - Suppose that player 1 conjectures that player 2 chooses R. - And that player 2 conjectures that player one chooses B. - Given this conjectures, player 1’s optimal strategy is B, whereas player 2’s optimal strategy is R. Notice that, based on these strategies, the players' conjectures are consistent: player 1 expects player 2 to choose what in fact player 2 finds to be the optimal strategy and vice versa. This situation is referred to as a Nash equilibrium. Although the concept of Nash equilibrium can be defined with respect to conjectures, it is simpler – and more common – to define it with respect to strategies. • Nash equilibrium a list of pure strategies represents a Nash equilibrium if no player can unilaterally change its strategy in a way that improves its payoff, i.e. if each player simultaneously maximises given what the other players are doing, i.e. if other players are playing their star strategies, it does not make sense to change. Everybody is simultaneously doing his or her best given what the others are doing, so that no player would want to change his strategy unilaterally. It can be checked that, in the game in the figure, (B,R) is a Nash equilibrium and no other combination of strategies is a Nash equilibrium. For example, (M, C) is not a Nash equilibrium, because, given that player two chooses C, player 1 would rather choose B. Note: • A pure strategy is a term used to refer to strategies in Game theory. Each player is given a set of strategies, if a player chooses to take one action with probability 1 then that player is playing a pure strategy. This is in contrast to a … • Mixed strategy where individual players choose a probability distribution over several actions. Important theorem: Consider a game with simultaneous moves, non-cooperative, complete information, where the Nash equilibrium can be applied, then there exists at least one Nash equilibrium in mixed strategies (linear combination of pure strategies). - Nash’s theorem does not grant the existence of an equilibrium in pure strategies. E.g. we could have two equilibria in pure, or one in mixed and the other in pure… The fundamental contribution by Nash was that of finding a solution for a game without dominated strategies and giving a theorem stating the conditions under which such an equilibrium exists. An equilibrium in pure strategies never exists when there is no resting point, i.e., each player always has an incentive to react differently. Best responses A useful way to find a game's Nash equilibrium is to derive each player's best response. Player 1’s best response is a mapping that indicates player 1’s best strategy for each possible strategy by player 2. How are the best responses related to Nash equilibria? Let BR1(s2) and BR2(s1) be Player 1’s and Player 2’s best response mappings, respectively. A Nash equilibrium is then a pair of strategies s1* and s2* such that s1* is the best response to s2* and vice-versa. n < ∞,   i = 1,2, …n Si ∈ ℝ,   si ∈ Si imaxsiPi(s1, s2, …, si, …, sn) s* i s a Nash equilibr ium i f :s* ∈ ℝn: ∀i   Pi(s*1 , s*2 , …s*i , …s*n ) ≥ Pi(s*1 , s*2 , …, ŝi, …, s*n ),   ŝi ≠ s*i Going back to the previous game, a helpful way of representing these best response mappings is to go back to the game matrix and mark with an asterisk the payoff values corresponding to a best response. A Nash equilibrium corresponds to a cell where both payoffs are marked with an asterisk. Nash equilibrium is R,B and B,R. Then notion of Nash solutions: non cooperative games, complete information, imperfect information, simultaneous games, variable sum. All these games where there is a finite number of players n<inf. Si belongs to R, Si is a strategy set, the strategy chosen will be e.g. s1. My payoff depends on: Pi(s1,s2,…,si,…,sn) The objective of each player is to maximise Pi by choosing the right s in the Si set. s*∊ Rn : is a vector depicting the strategies chosen by players ∀i Pi (s1*, s2*, … , si*, … , sn*) ≥ Pi (s1*, s2*, … , ŝi, … , sn*) ŝi≠si* Which means: a mix of pure strategies represent a Nash equilibrium if simultaneously each player is maximising based on what the other players are doing. Players act simultaneously but logically. We have no dominant or dominated strategy. Here, the optimal choice is a consequence of that of the other players. Remember, there is no chronological order. Continuous variables: Consider a gas station's pricing strategy. There are many different values of price you can choose from. If we assume only a few possible values – for example, $2, $3, and $4 per gallon – we may artificially limit the player’s choices. If instead we assume each and every possible price to the cent of the dollar, then we end up with enormous matrices. In situations like this, the best solution is to model the player's strategy as picking a number from my continue sat. This may be too unrealistic in that it allows for values that are not of served in reality (for example selling gasoline at $⎷2 per gallon). However it delivers a better balance between realism and tractability. Suppose that player i chooses a strategy xi (for example, a price level) from some set S (possibly a continuous set). Player i’s payoff is a function of its choice as well as its rival’s: πi(xi,xj). In this context, a pair of strategies (xi*,xj*) constitute a Nash equilibrium if and only if, for each player i, there exist no strategy xi’ such that πi(xi’,xj*)>πi(xi*,xj*). An equivalent definition may be given in terms of best response mappings. Let BRi(xj) be i’s best response to player j’s choice. Then a Nash equilibrium is a pair of strategies (xi*,xj*) such that, for each player i, xi*∈BRi(xj*). Multiple equilibria and focal points - Under Cournot: when one firm is more efficient than the other, it constitutes a monopoly. If it isn’t more efficient than the other, then both firms are active. - Under Bertrand: only the most efficient firm is either active and charging monopoly price (if the cost advantage is sufficient), or, only the most efficient firm is active, but not charging the same as monopoly price (if the cost advantage is not sufficient). Under Cournot, the equilibrium smoothly changes with n (number of firms). This property does not extend to Bertrand, since two firms are enough both in the symmetric and asymmetric case. Example: Under symmetry, it is true that there is no Bertrand equilibrium if there are fixed costs, but in asymmetric cases, it is necessary to check whether it is possible to cover fixed costs. The welfare properties are the same as under perfect competition. In this case, even with FC it is able to make money. The symmetric model excludes FC, while in the asymmetric model it needs to be changed. The perfectly competitive outcome can be obtained by definition in perfect competition, but also through n approaching infinite under Cournot and n=2 under Bertrand. The discrete Bertrand game: Let us first consider the case where sellers are restricted to a limited set of price levels. Specifically, suppose that the market demand is given by: - q=10-p - MC=2 - and sellers can only set integer value of price (3,4, and 5) MCA = 20,  MCB = 15,  p*B = 19.99,   F < 4.99 The figure describes the game in normal form. For each possible combination, profits are determined according to the rules described in the preceding paragraph. - If both firms set p=5, then total demand is Q=10-5=5, and each firm’s profit is given by: π=½5(5-2)=7.5 - If firm 1 sets p1=4 whereas firm 2 sets p2=5, then firm 1 captures all of the market demand, which is now given by Q=10-4=6. It follows that π1=6(4-2)=12, whereas π2=0. - The remaining cells of the game matrix are obtained in a similar manner. What is the game's equilibrium? We noticed that there is no dominant strategy. I can however derive each firm’s best response in from this derive the game’s Nash equilibrium. In other words the best response of firm 1 is to undercut firm 2, unless firm 2 is already setting the lowest price. As a result, the Nash equilibrium corresponds to both firms setting the lowest price: p1=p2=3. The continuous case: Suppose that firms can set any value of p from 0 to + infinity, including non-integer values. Now we are unable to describe the game as a metrics of strategies (there are infinitely many strategies). However, we can derive, as before, each firm’s best response mapping, from which we can derive the Nash equilibrium. Recall that firm i’s best response pi*(pj) is a mapping that gives, for each price set by firm j, firm i’s optimal price. The only novelty with respect to the discrete case is that the values of pj and pi now vary continuously. - Suppose that Firm 1 expects Firm 2 to price above the monopoly price. Then Firm 1’s optimal strategy is to price at the monopoly level. In fact, by doing so, he gets all the demands and receives monopoly profits (the maximum possible profits). - If Firm 1 expects Firm 2 to price below monopoly price but above MC, then Firm 1’s optimal strategy is to set a price just below Firm 2’s: pricing above would lead to 0 demand and zero profits; and pricing below gives firm i all of the market demand, but lower profits the lower the price is. - Finally, if Firm 1 expects Firm 2 to price below MC, then Firm 1’s optimal choice is to price higher than Firm 2, say, at the MC level. Since firm 2 has the same marginal cost as a firm 1, its best response is identical to firm 1’s, that is, symmetrical with respect to the 45° line. The figure depicts Firm 1’s best response, p1*(p2). As we saw before, a Nash equilibrium is a pair of strategies, such that no firm can increase profits by unilaterally changing price in terms of the picture, this is given by the intersection of the best responses, that is, point N, which corresponds to both firms setting a price equal to marginal cost. 1 2 0 0 0 0 2 1 Another way of deriving the same conclusion is to think about a possible equilibrium price p’ greater than marginal cost. If both firms where to set that price, each would earn half of the profits coming from that demand. However, setting a slightly smaller price, one of the firms would be able to almost doubled its profits. We can conclude that the only possible equilibrium price is p=c. In summary Under price competition with a homogeneous product and constant, symmetric marginal cost (Bertrand competition), firms price at the level of marginal cost. Notice that this result is valid even with only two competitors. This is a fairly drastic result: as the number of competitors changes from 1 to 2, the equilibrium price changes from the monopoly price to the perfect competition price. Two competitors are sufficient to guarantee perfect competition (i.e. to push the price down to MC). From a consumer welfare point of view, Bertrand competition is a tremendous advantage. From the seller's point of view, however, it is a rather unattractive situation: some call it the Bertrand trap. In fact, it drives prices down to MC. Avoiding the Bertrand trap: There are many real-world markets where the number of firms is a small – two or a few more – and firms compete on price, and still firm profits are positive — sometimes very large. How is this possible? We consider four different solutions: 1. Product differentiation: the Bertrand model assumes that both firms sell the same product. If instead firms sell differentiated products, then duopoly price competition does not necessarily drive prices down to marginal cost. Think of Coca-Cola and Pepsi Cola. By lowering its price, Coca-Cola may increase its sales a bit, but it will certainly not capture all of the market demand. 2. Dynamic competition: the Bertrand model assumes that firms compete in one period only, that is, price is chosen once and for all. One of the likely consequences of undercutting a rival's price is that the latter will retaliate by lowering its price to, possibly initiating a price war. The possibility of retaliation is not considered in the model because of its static nature. 3. Asymmetric costs: one important assumption in the simple version of the Bertrand model is that both firms have the same marginal cost. However if one of the firms has a lower marginal cost (a "cost leader”) then it is no longer true that both firms earn zero profits. 4. Capacity constraints: by undercutting the arrival, a Bertrand duopolist receives all of the market demand. But what good is this if the firm does not have sufficient capacity to satisfy all of these demands? Price competition with different costs: Suppose now that one of the firms, say firm 1, has a lower marginal cost than its rival. The best response curves are derived as before: firm I undercuts the rival all the way down to the rival's marginal cost – that is all the way down to the firm ally's marginal cost. In this case, since firm one has a lower marginal cost, it's best response mapping extends to lower values than firm two’s. As a result, the point where the two best responses cross – the Nash equilibrium of the game that is given by p2=MC2 and p1=MC2-e; that he is, firm one just undercut firm two, and gets all the market demand. In other words, one way out of the Bertrand trap is to be a cost leader. Unfortunately, others can play that game too: in fact competitive advantage based on cost leadership is short lived. To conclude this section, I should mention that this model extends easily to the case when there are more than two firms. Basically, pick the two firms with the lowest marginal cost and apply the analysis above. For example, if Firm 1 has MC c1=53, whereas firms 2 and 3 have MC c2=c3=55, then firm 1 sets p1=55 and captures the entire market. If instead they have the same MC, they share the market. In oligopoly models there is a link between the optimal strategy of each player. 
 The key point is that such a link normally is visualised by the demand function. consumers are willing to pay (y-intersection) and check that it is greater than marginal cost. If it isn’t, drop the exercise. Monopoly, duopoly, and perfect competition: Duopoly is an intermediate market structure, between monopoly and imperfect competition. One would expect equilibrium price and output under duopoly to lie between the extremes of monopoly in perfect competition. We can see that the Cournot equilibrium point N, lies between the two lines of interception (qM and qC). This implies that total output under Cournot is greater than under monopoly and lower than under competition. Same thing with duopoly price. A “dynamic” interpretation of the Cournot equilibrium: It is a stable solution: no firm would have an incentive to choose a different output. But is it a realistic prediction of what will happen in reality? Although the Cournot model is a static game, consider the following dynamic interpretation: At time t=1, Firm 1 chooses some output level. Then, at time t=2, Firm 2 chooses the optimal output level given Firm 1’s. Then, at time t=3, Firm 3 chooses the optimal output level given Firm 2’s current output. Cournot and the number of firms Concentrated industries are not necessarily duopolies, so what happens to the Cournot equilibrium when the number of (identical) firms increases? It can be proved that This shows the asymptotic properties of the Cournot equilibrium: as n gets larger and larger, the Cournot equilibrium tends to a perfectly competitive equilibrium. The Cournot equilibrium will thus be closer to a monopoly as n approaches 1 and closer to perfect competition as n approaches infinite. This implies changes in price, profit, welfare. For instance, a horizontal merge would decrease the number of independent players in the market. Therefore, the market is more concentrated and there is an increase in market power; this could be offset by technological gains. Asymmetric case (different marginal costs) 1. Is the more efficient firm able to monopolise the market? ( ) Probably yes, if the price gap is very large. Probably not in the opposite case. Be careful about the meaning of monopolising the market: this means being the only active firm, but not charging the monopoly price. A firm can monopolise the market when the price charged is lower than the rivals’ marginal cost. Such a test is performed by equalising marginal revenue to marginal cost of the given firm: , , , Example , , (mistake, 5/2 is 2.5) Firm A is able to monopolise the market 2. If the most efficient firm is not able to monopolise the market, then the two firms adopt marginal cost pricing. lim n→∞ CE → PC pA M < MCB MR = MCA MR = α − 2q qA M = α − MCA 2 pA M = α − α − MCA 2 = α − MCA 2 < MCB p = 10 − Q MCA = 5,  MCB = 7 pA M = 5 2 = 7.5 > 7 , , , In the case of the asymmetric duopoly, the equilibrium given by the two reaction functions is not on the bisector. Limit theorems For lim we have that the Cournot equilibrium approaches the perfect competition equilibrium. n→∞ I.e. Numerosity on the supply side implies that the Cournot equilibrium turns into that of perfect competition. As the number of firms becomes smaller, we approach the monopoly equilibrium. A horizontal merge would entail a shift to the left. A merge when n=2 entails a monopoly. MCA < MCB → no monopoly q*A > q*B q*A + q*B = Q* π*A = π*B Useful formulas for the exam: Lerner index in different situations We know that the Lerner index is a measure of market power, and that it goes from 0 to 1. GENERAL FORMULAS Most general formula, it refers to: - single company i - takes into account the possibility that MC varies across firms - elasticity calculated in the equilibrium - Si=qi/Q PERFECT COMPETITION - firms are identical - p=MC - no individual firm enjoys any market power MONOPOLY - calculated in the monopolistic equilibrium (it’s always calculated in the eq.!) - remember: in monopoly, L is not necessarily 1. For it to be 1, we would need MC=0 (think of the other formula). OLIGOPOLY: BERTRAND Symmetric case: implies no market power Asymmetric case: only one firm is active. - can either be able to charge monopoly price or not - “low” refers to the company who has the lowest marginal cost - the high cost company is not producing anything OLIGOPOLY: COURNOT Symmetric case: Li is equal to all other L. - remember: the existence of a Cournot equilibrium doesn’t require constant MC, nor no FC. Asymmetric case: when MClow is a monopolist - MClow is low enough for this firm to monopolise the market Asymmetric case: when MClow is not enough to be a monopoly Asymmetric case: when MClow is not enough to … industry level What is the market power of an industry as a whole? Li = p-MCi p Li = Si ⎮ε⎮ L = 0 L = 1 ⎮ε⎮ L = 0 L = p-MClow p Li = Si = 1 ⎮ε⎮ n⎮ε⎮ L = 1 ⎮ε⎮ Llow = Slow ⎮ε⎮ Llow = p-MClow p Lhigh = Shigh ⎮ε⎮ Lhigh = p-MChigh p L = p-∑MCi*Si p