Firms and Markets in Global Economies (P. Natale), Appunti di Microeconomia

Scarica Firms and Markets in Global Economies (P. Natale) e più Appunti in PDF di Microeconomia solo su Docsity! 1 Firms and Markets in Global Economies Lecture notes, 1st year, AY 2019-20, INTECO, Sara Cucaro Prof. Piergiovanna Natale Introduction We’re going to analyze the following main models: • 3d model • Melzil • Ricardo • Hesker-Ohlin Introduction What is this course about? We see the main ingredients in the title: the firm part is fundamental, we will build a theory of the firms in open economies. Individuals tend to maximize utility (the happiness for their self). Firms maximize profits. But firms do not exist in nature: firms are not primitive. So we are imposing that firms are collection of individuals. Do we need a teory of the firms? Yes. • Global firms are ever more important in shaping economies and they are different. • To have a better understanding of the world we live in, we need a theory of global firms. Informations are passed by individuals by a system of prices. Individuals take decision according to the prices. When are the firms that take decisions, is not the prices system that move firms to take decisions. Are the people in the firms that take decisions, based on gerarchical system.Employment system decide what and when(and who) do same types of tasks. So we need a theorem of firms that analyse the behaviour of the firms, taking account that firms are not primitive. Firms that operate in different mkts are different from firms that operate in other mkts. Theory of the firm. Contracts are incomplete. This is the reason why firms exist. Contracts can not take in account all the possibilities. When contracts not take in account all the contingencies, firms start to exist. When contracts are incomplete, you have to turn to auto… International contest: the problems of the incompleteness of the contracts is more stressed. Theory of the firms is more effective also. We can provide a theory that explain the behaviour of the firms in global mkts. What globalization means to us and how our approach to globalization will impact to the theory. A bird’s eye view of globalization: • Globalization: a large share of the population can access goods made available by long distance trade. Relevant characteristics in many transactions, till the Roman empire. Globalization: access to good from long distance, also the Roman empire used tableware ,for example. The Roman peasants living in the Po river plane ate off tableware from Naples…… Flow of people continues across Asia America and other countries The Fall of the Roman Empire: the end of trade? We derive our study, regarding this period, from Findlay and O’Rourke (2007, Table 2.1) document that around 1000 C.E.: 2 • Western Europe exports 1. swords to Eastern Europe; 2. slaves and swords to the Islamic World • Eastern Europe exports 1. slaves, furs and silver to Western Europe and the Islamic World; 2. furs and swords to Central Asia • The Islamic World exports 1. pepper, spices, textiles, silk and silver to Western Europe; 2. textiles and silver to Eastern Europe; 3. textiles to Central Asia; 4. textiles, swords and horses to Sub-Saharan Africa • East Asia exports 1. silk to the Islamic World, Central Asia, South Asia and Southeast Asia; 2. porcelain to the Islamic World and South Asia; 3. tea to Central Asia; 4. copper to Southeast Asia. A complex web spanned across Europe, Africa and Asia. Trade flow between Euro and Asia. The age of discoveries1: But a hundred years earlier: • Between 1403-1430, China’s trade routes link the Far East to Malindi and the Red Sea • 20/9/1414……The first giraffe in town…… • A typical Zheng Hue’s expeditions: 370 ships and 30.000 men. 1 Source: Helpman Elhanan. 2010. Understanding Global Trade (p. 6). 5 How we explain the surge in trade in the ’90? Mind: the forces at work then are at work also nowadays. 1) The widespread adoption of ICT: • Internet users as % of world population: 0.45 in 1994; 45.91% in 2016 [World Bank data]; • The fall in download time • Consequences: vast improvements in market efficiency [read about Kerala fishing fleets on the course website]; Information and communication technology made possible the transmission of blueprints, which is drawing and specification of a product, production specifications. ICT was therefore the main driver of the increasing trade. Starting from the early 90s, we have increasing treaties for liberalizing trade. 2) Liberalization of trade and fall in transport costs: • NAFTA (1994), a trade agreement between Canada, US and Mexico. • Mercosur (1991-1994), trade agreement among all Latin American countries. • China and the WTO (2001), which opened a large number of markets to the Chinese products. • European Enlargement The US-China confrontation today is not a war in the strict sense. In the WTO system, retaliation measures are perfectly legitimate: if a country does impose rules against WTO, since there is no supranational authority ruling the WTO decision mechanism, the affected countries are authorized to impose tariffs as retaliation measures. This is the case of Trump’s and Obama’s tariffs against China and other countries. Therefore, we should not mislead what is happening today in this sense. The trump administration denounced two fundamental trade agreements: • Trans-Pacific Partnership (TPP): denounced by Trump in the early days of his Presidency, it is back on its Asian feet! Why? Because today we have the CPTPP. • Comprehensive and Progressive Agreement for the Trans-Pacific Partnership (CPTPP): launched on the 11/11/17 by the remaining 11 countries (previously part of the old agreement). 3) The fall of the Soviet Union and the opening up of East and Far East markets; pro-competitive government coalitions in the West (shift to the right). That explains and is one of the causes of the change we observe. As said before, the main consequences of what we witness is an increase in trade flows, which means an increase in flows of final goods, and most importantly of intermediate goods (which is not raw materials). This showed up dramatically in statistics: In 2000: • 50% of US imports were intra-firm trade. Therefore, you have two firms, one in the US and an affiliate in country X, interchanging intermediate goods between each other. • 33% of US exports were toward affiliates. Again, trade in intermediate goods. The main consequence that we’re living is today the disintegration of production processes across borders. The labor statistics tell the same story (e.g. diagnostic imagining: sending medical images to doctors in other countries). This matters, because there is always someone working, 24/7. 6 Who are the Zue Hang of our time? Remember that we mentioned how important was in the 15th century the trade from China to Africa. The head of that expedition was Zue Hang. Therefore, who is driving this incredible increase in trade flows? We know that, behind these flows, there are not only countries, but mostly firms. Firms operating in international markets have some characteristics. If we consider Europe, we see that there are differences between purely domestic and internationalized firms: Exporting firms are the minority. According to Mayer, T. and Ottaviano, G. (2008)4: • 10% of exporting firms account for’80% of exports • Firms exporting more than 10 products in more than 10 countries accounts for 75% of exports • Exporting firms are larger, more productive, pay higher wages and makes more profits than non- exporting firms in the same industry This is true for exporting forms, and for multinational companies (firms exporting abroad). Let’s take LEGO as an example. All sorts of things can be made with LEGO. Decades ago, there were only two colors (red and white) and one shape (rectangular). If we look back the last 30 years, the world trade went through the same transformation LEGO went through: from two colors and one building block we moved to so many combinations and customized products, that basically we have been moving toward a world where trading relationships are ever more customized/taylor made. Is like a 3D printed world, accomplished on the requests of the customer. With 3D printing, production shifted from subtracting material (e.g. as sculpture, taking away marble to obtain a specific shape) to addition (adding layer on layer) which allows customization. Production is contract-intensive. Contructs prescribe how people must behave in the environment in which they’re living, actions to be performed. Basically, are a kind of roadmap: describe actions that people will undertake in the future. The more tailored and risky is the action for the need of the customer, the more need there’s for a contract. Most of contracts regulating important transactions are written contracts, but in some cases can be also oral contracts and have legal status as well. Everytime I buy a product, for example a book, I don’t enter a contract with the seller, not even an oral one. However, if a want a dress to be made for me by a tailor, I will define characteristics with the seller entering an oral contract. In companies, the more tailor-made are the relations, the more specific are the need to be satisfied, the more important is the contract as an ingredient for this relationship. The contract is there to make sure that you get exactly what you need. But contracts are notoriously difficult to write and to enforce: a) State contingency: not of this world! Contracts are unable to provide guidelines for parties to act in all possible relevant contingencies (conditions). Take for example natural limitations: there are contingencies we cannot foresee and anticipate. We moreover have endogenous incomplete contracts: incomplete because parties themselves don’t cover all possible contingencies, since they know they will not find an agreement on those, parties find it optimal to leave them incomplete. The ways of facing these cases of contract incompleteness change as you cross your border. At the end of every contract, there is a clause to decide what to do in case of a contingency not covered by the contract. In most of cases, the parties choose to rely on a third part, being a court. When the parties are in the same country from the same country (Italian companies in Italy) can choose a domestic country. However, if an agreement is signed between companies from two different countries, the contract at the end will specify in the clause to which court (belonging to one of their countries) they will apply. b) Choice of law (the court may reject…) 4 Mayer, T. and Ottaviano, G. (2008) The Happy Few: The internationalisation of European firms. Intereconomics: 135- 148 7 c) Are local courts fair to foreigners? A court may favor the local company, being biased towards locals. For example, consider a dispute in which there is the risk of closing down a local branch, as the discussion about ILVA and Arcelor Mittal. d) The enforcement of remedies across borders may be quite complex, even if there is no bias in court. It’s complex, takes time and it’s costly. This is one of the cases, after having gone through a number of local courts, in which firms rely on supranational courts (European, UN, etc). e) Heterogeneity: how long does it take to clear a bounced check? 39 days in Netherlands; 645 days in Italy (early 2000’s data) Tentative solutions5: • United Nations Convention on Contracts for the International Sale of Goods: not all countries have signed it. • International Arbitration: competent but not cheap! These bodies are not an emanation of any sovereign power but are completely private. Countries buy, as a service, competence in dispute resolution. Therefore, parties voluntarily submit their disputes to a body which is known for the quality of its rulings (e.g. acting in the interests of both parties). We have evidence that only very large transactions apply for international arbitration. • Reputation? Parties will take into consideration two elements, when deciding how to act when a contingency not included in the contract arises: o will the two parties keep having relations in the future? o It may be the case it’s the last transaction with a customer. But, at the same time, reputation could be affected. Even if there’s not future with a particular customer, our relations may have an effect on my reputation on future possible customers. The risk is collective punishment: cheating against one consumer may result in ending the trade with all other customers, since they may decide not to perform any trade with me anymore. Reputation works as long as there is collective punishment. How do firms deal with contract incompleteness? Contracts incompleteness shapes organizational and location choices: • Outsourcing vs. Vertical Integration (organizational choices) • Off-shoring vs. Domestic Production (localization choices) We will study how firms behave on international markets under the assumption of contract incompleteness: • we will consider exporting and investing firms • we will discuss the implications of imperfections on capital markets • we will study policy implications. GATT, and other treaties, were signed having in mind a world of perfect competition. However, this changes when relationships become specific and tailored. Before that we will revise: Ricardo Heckscher-Ohlin Krugman The giants whose shoulders most recent contributions stand on. 5 See: Greif, A. (1993). Contract enforceability and economic institutions in early trade: The Maghribi traders' coalition. American Economic Review, 83: 525-548. Is an interesting story, starting in the Middle East: trade through Europe was mapped thanks to a series of letters and contracts, found in a hidden chamber in a synagogue, where these had been kept for centuries. All those countries and letters were not thrown away because they mentioned God, and according to the Jewish tradition no paper containing the name of God can be thrown away. 10 How does a country allocate labour to the production of F and C? Consider country i deciding how to allocate one extra unit of labour to the textile industry. How many units does that county obtain by allocating that extra unit? It depends on the production coefficient 𝟏 𝒂𝒄 𝒊 . For country i, every additional unit generates an additional product equal to the production coefficient. By allocating one unit of labour to the production of C, country i obtains 1 𝑎𝐶 𝑖 units of C. By selling the so produced C on the world market, country i obtains revenue 𝑃𝐶 𝑊 1 𝑎𝐶 𝑖 . How much F can country i buy on the world market? 𝑃𝐶 𝑊 1 𝑎𝐶 𝑖 𝑃𝐹 𝑊 By allocating one unit of labour to the production of F, country i obtains 1 𝑎𝐹 𝑖 units of F. As long as 1 𝑎𝐹 𝑖 < 𝑃𝐶 𝑊 1 𝑎𝐶 𝑖 𝑃𝐹 𝑊 country i allocates the extra unit of labor to the production of C. But as long as the amount of food I can produce by myself is smaller than the amount of food I can allocate in the world market. Country I can consume more food by allocating that extra unit of labor to the production of textiles. In fact, country i can consume more of F by allocating the extra unit of labour to C rather than to F! We can rewrite our condition as follows: 𝑎𝐶 𝑖 𝑎𝐹 𝑖 < 𝑃𝐶 𝑊 𝑃𝐹 𝑊 Because of the fixed-coefficient production function, what holds true for one extra unit of labour holds true for all of them: country i specializes. But it does as long as country j specializes too! As one country shifts all units from food to clothing, the opposite happens to another country. If country i fully specializes in the textile industry, it can survive only if country j does the same fully specializing into the production of food. This requires: 𝑎𝐶 𝑖 𝑎𝐹 𝑖 < 𝑃𝐶 𝑊 𝑃𝐹 𝑊 < 𝑎𝐶 𝑗 𝑎𝐹 𝑗 Let i to be England and j to be Portugal: Given 𝑃𝐹 𝑊 and 𝑃𝐶 𝑊, England specializes in the production of C and Portugal in the production of F: 11 𝑎𝐶 𝐸 𝑎𝐹 𝐸 < 𝑃𝐶 𝑊 𝑃𝐹 𝑊 < 𝑎𝐶 𝑃 𝑎𝐹 𝑃 (T.1) What condition T.1 tells us? 𝑎𝐶 𝐸 𝑎𝐹 𝐸 < 𝑃𝐶 𝑊 𝑃𝐹 𝑊 < 𝑎𝐶 𝑃 𝑎𝐹 𝑃 (T.1) • T.1 holds only if 𝑎𝐶 𝐸 𝑎𝐹 𝐸 < 𝑎𝐶 𝑃 𝑎𝐹 𝑃 Remember: 1 𝑎𝐹 𝐸: it tells us how much F can be produced by applying one unit of labour to production of F in England 1 𝑎𝐶 𝐸: it tells us how much C can be produced by applying one unit of labour to production of C in England Thus: 𝑎𝐶 𝐸 𝑎𝐹 𝐸 = 1 𝑎𝐹 𝐸 1 𝑎𝐶 𝐸 how many F units England must give up to produce one unit of C T.1 tells us that: • England specializes in C as long as it gives up less F than Portugal to produce C • Portugal specializes in F as long as it gives up less C than England to produce F We say that England has a comparative advantage in C and Portugal in F. The notion of opportunity cost is at work! Countries specialize in the production of goods in which they enjoy a comparative advantage, not an absolute advantage. Example England Portugal 1 unit of C 100 labour units 90 labour units 1 unit of F 120 labour units 80 labour units Portugal has an absolute advantage in F and C (less units of labour are required in both fields in Portugal), but a comparative advantage in F only, therefore will only produce F. If Portugal removes 80 units of labour from F to C, they will produce less than 1 unit of textiles (since you need 90 labour units to produce one unit of textile). Summarizing, although Portugal has absolute advantage in both, it will not produce both: will find in its own interest to specialize in the production of food. Same for England, if Portugal specializes in food it has interest in specializing in textiles. • How are 𝑃𝐹 𝑊 and 𝑃𝐶 𝑊 formed? Assume perfect competition on input markets and output markets. It follows that prices equates marginal cost of production. 12 To illustrate, consider England: 𝑀𝐶𝐶 𝐸 = 𝑤𝐶 𝐸 1 𝑎𝐶 𝐸 = 𝑤𝐶 𝐸 𝑎𝐶 𝐸 𝑀𝐶𝐹 𝐸 = 𝑤𝐹 𝐸 1 𝑎𝐹 𝐸 = 𝑤𝐹 𝐸𝑎𝐹 𝐸 The marginal cost is equal to the price of the input divided by the marginal product of the input of production labour. Therefore, the wage in England divided by the marginal product of labour in the textile industry, which is 1 ∕ 𝑎𝑐 𝐸. Assume perfect competition: this means that I will have same wages, since if the wage in one sector is higher workers will move to the other, therefore to the highest wage paid. Labour mobility within the country implies therefore that we have the same wages: 𝒘𝑪 𝑬 = 𝒘𝑭 𝑬 ≡ 𝒘𝑬. When England specializes in the production of C, we have: 𝑃𝐶 𝑊 = 𝑤𝐸𝑎𝐶 𝐸 When Portugal specializes in the production of F, we have: 𝑃𝐹 𝑊 = 𝑤𝑃𝑎𝐹 𝑃 We can re-write T.1 as follows: 𝑎𝐶 𝐸 𝑎𝐹 𝐸 < 𝑤𝐸𝑎𝐶 𝐸 𝑤𝑃𝑎𝐹 𝑃 < 𝑎𝐶 𝑃 𝑎𝐹 𝑃 𝑎𝐹 𝑃 𝑎𝐹 𝐸 < 𝑤𝐸 𝑤𝑃 < 𝑎𝐶 𝑃 𝑎𝐶 𝐸 (T.2) How to interpret T.2? A country specializes in the sectors where its relative productivity exceeds its relative wage. • What if 𝑤𝐸 𝑤𝑃 falls outside the interval in T.2? Would that be an equilibrium? Increases so much that it’s not convenient for England to specialize in textiles production: relative wage becomes so high that this inequality fails, so England stops producing textile goods. There will be unemployment, because you stop producing since it’so expensive that it’s better to buy from Portugal. If the ratio jumps on the other side, the wage in Portugal will start going up, and the ratio will go back. The answer is no: demand of labour would change, so affecting market wages. • Note that England is the least-cost producer of cloth: from T.2 𝑤𝐸𝑎𝐶 𝐸 < 𝑎𝐶 𝑃𝑤𝑃 and Portugal is the least-cost producer of food. • English workers are relatively more efficient than Portuguese ones in producing C. Why? Ricardo’s point on this particular question is: English and Portuguese workers have the same skills, but England and Portugal have access to different technology in textile production, and vice versa in food production. This is the route of asymmetry in productivity across countries and industries. H-O had a completely different view on this point (availability of technology). 15 According to H-O: countries have access to the same technology (How that?) Implication: absent returns to scale, unit cost of production depends on input prices, not on location of production. Input prices in turn depends on input availability. Remember that inputs do not move across countries. However, what matters is not whether they move or they don’t, the matter is relative speed. A country endowed with the largest amount of input i is the least cost producer of the commodities whose production is most intensive in input i. In H’s words: “A difference in the relative scarcity of the factors of production between one country and the other is thus a necessary condition for differences in comparative costs and consequently for international trade.” Note: necessary, not sufficient! You won’t have trade unless you have differences in endowement. However, differences in endowement are not enough to generate trade: goods must differentiate in factor intensity. If all goods have the same factor intensity, countries will have the same relative cost in all industries. So you need different goods to be produced with different factor intensities. Trade occurs only if a second condition is satisfied: Goods must differ in factor intensity. Otherwise: countries would have the same relative costs in all industries. Let’s now discuss the implications of the H-O model. • Two countries: England and Portugal • Four industries/sectors: Textiles, Wood, Leather, Food • Two inputs: labour and capital. Assume commodities can be ordered in terms of capital-intensity: (𝐾/𝐿)𝑇 > (𝐾/𝐿)𝑊 > (𝐾/𝐿)𝐿 > (𝐾/𝐿)𝐹 Assume 𝑟𝐸 < 𝑟𝑃; 𝑤𝐸 > 𝑤𝑃 Given the production function in each industry and the prices in the inputs of production, I can compute the unitary (minimum) cost of production for each commodity in each country. I am now considering an autarchy system: the two countries are not connected yet, do not trade. Compute the ratio of such costs for each commodity (the minimum cost): (𝐶𝐸/𝐶𝑃)𝑇; (𝐶 𝐸/𝐶𝑃)𝑊; (𝐶 𝐸/𝐶𝑃)𝐿; (𝐶 𝐸/𝐶𝑃)𝐹 England has a cost advantage in industry i as long as (𝐶𝐸/𝐶𝑃)𝑖 < 1. Because of the above assumption we expect: • (𝐶𝐸/𝐶𝑃)𝑇 to be the smallest ratio • the other ratios to the ordered accordingly Moreover: at least some ratios exceed 1. Otherwise: factor prices would fall in the country with a cost disadvantages in all sectors. 16 It follows that the country with the largest endowment of capital and hence the lowest rental cost of capital specializes in capital intensive commodities. The same holds in relation to labour. In O.’s words: “In short, commodities that embody large quantities of particularly scarce factors are imported, and commodities intensive in relatively abundant factors are exported.”. Which prices? • Trade equalizes commodities’ prices across countries. • H.O. point out that trade should equalize factor prices too. • Consider a country abundant in labour, let it be Portugal. • Trade increase labour demand in Portugal and Portuguese wages rise while English ones fall. People unemployed in England will move in the other industry, and wages will be equalized in England. And because of global labor demand, wages will be equalized globally. True unless we have factor intensity reversals (price changing so much that you have to switch from capital to labour or vice versa). Trade has the same effects of factor mobility: Samuelson, Paul A. 1948. “International Trade and the Equalization of Factor Prices.” Economic Journal 58: 163-184. Enlargement process: guaranteed to that country free movement of goods and people. When the enlargement started, some European countries like Germany allowed for removement of goods but not the movement of people (stop for 7 years of immigration from eastern Europe). Britain didn't, there was a continuous flow to the UK because wages and employment prospects were more favorable. Example of plumbers (stereotype of immigrants in UK): we know observe movement of resources (labor) to provide local services. The outcome is a fall in wages. British people complain continuously that they are losing jobs because of flows of (continental) European people. Mobility of factors and trade have the same effect as long as the set of trade goods is large enough. Otherwise, when discrepancies persist we will have a different situation. The data test: not that simple, after all! First of all, to make a prediction we need to test a 3-way relationship btw factor endowments, factor intensity and trade patterns (choice of specialization). Means simply that all these three assumptions have to be satisfied: if I consider factor endowments and factor intensity, I can derive trade patterns. However, I may get the prediction wrong anyways, because one of the assumptions is failed. Not easy to assess which one is failed. The factor content approach: Indirectly abundant factors of production are exported and scarce factors imported (O.) Leontief, Wassily. 1953. “Domestic Production and Foreign Trade: The American Capital Position Re- Examined.” Proceedings of the American Philosophical Society 97: 332-349. This book explains a paradox, analyzing imports and exports in the US in 1947 (just two years after the end of the IIWW). In these years, if there’s a country rich in capital, that country must be the US. You would therefore expect US export to be rich in capital, and import to be rich in labor. What’s the outcome found? • 1947 imports: 18000$ capital per man-year 17 • 1947 export: 14000$ capital per man-year …just the opposite of how it should be (should be the other way-round, with exports being rich in capital, not imports). A blow to the theory? Not as strong as it could seem: a number of important works have provided ways to reconcile Leontief data and the theory. We can affirm that these results are consistent with H-O model under specific circumstances. Try again! Encouraging results when the appropriate factor content measures are adopted. For example, the input- output measures were used (huge tables establishing for each industry the contribution in the economy to the production). E.g, US input-output table overestimated the capital content of US import (not the right choice for measuring import, although good use for measuring exports); see Hakura, Dalia S. 2001. “Why does HOV Fail? The Role of Technological Differences within the EC.” Journal of International Economics 54: 361-382. 2001. With input-output tables you are assuming that the same factor intensity of the US is valid for other countries. In fact, input-output table overestimated the capital content of US import because if was assuming the production had always the same capital intensity. 20 3) model the opening of the economy as a k-fold replica of the closed economy and then study the market equilibrium and welfare for the new open economy and its components (the formerly closed ones). Remember that our aim is to explain trade among similar countries → therefore, model the opening as if you’re replicating your own economy and let these identical twins trade (e.g. k-fold replica). THE CLOSED ECONOMY Consider an economy populated with L consumers. Preferences: - Consumers value variety: other things equal, the larger the number of goods/brands they consume the better they are (→ note that for measuring varieties we can use indifference curves, and make also use of Cobb-Douglas utility functions which are of the form 𝑈 = 𝑥𝛼𝑦𝛽 → you are indeed implying that the consumer has tastes. The Cobb-Douglas utility function captures the love for variety). - Consumers care about quantity: other things equal, the more they consume for each good/brand, the better they are. The consumer’s utility function Krugman uses should be able to capture the preferences: 𝑼 = ∑ 𝒗(𝒄𝒊) 𝑵 𝒊=𝟏 , where 𝒗 ′(𝒄𝒊) > 𝟎; 𝒗 ″(𝒄𝒊) < 𝟎 The consumer’s budget constraint: ∑ 𝒑𝒊𝒄𝒊 = 𝒘 𝑵 𝒊=𝟏 , where is w is labor income. → total expenditure (summation of price of good i multiplied by the amount I consume of such good) of the consumer cannot exceed his ability to spend. We pose this total expenditure to be no larger than w. We should write ≤ 𝑤. However, there is just one period ahead, and I assume this problem solves (lifelong-utility is maximized). We write down the constraint as an equality because of the principle of no-satiation: the more you have, the better you are (nothing is left on the table), therefore we assume the consumer spends all he/she has (money left = not maximizing). The consumer solves (selecting the amount of each good to consume to maximize utility under the budget constraint, making sure to spend all): 𝑚𝑎𝑥 𝑐1,....𝑐𝑁 ∑ 𝑣(𝑐𝑖) 𝑁 𝑖=1 such that ∑ 𝑝𝑖𝑐𝑖 = 𝑤 𝑁 𝑖=1 What is 𝑝𝑖 telling me about the demand side of the market? That there is perfect competition on the demand side (lot of consumers, very large). We can tell this because the price I take on the good is independent of the quantity I consume → for each consumer, 𝒑𝒊 is a constant → the consumer has no market power. If the consumer had market power, 𝑝𝑖 would be a function of 𝑐𝑖. To solve this problem, I combine my two functions, and my Lagrangian function is the following: 𝑚𝑎𝑥 𝑐1,....𝑐𝑁 ∑ 𝑣(𝑐𝑖) − 𝜆 (∑ 𝑝𝑖𝑐𝑖 − 𝑤 𝑁 𝑖=1 ) 𝑁 𝑖=1 21 To solve this problem, I compute the first order condition 7 : 𝑣′(𝑐𝑖) − 𝜆𝑝𝑖 = 0, 𝑖 = 1. . . . . 𝑁 (C.1) ∑ 𝑝𝑖𝑐𝑖 − 𝑤 = 0 𝑁 𝑖=1 We will have n first order conditions to sum → I take the derivative of that summation with respect to 𝑐𝑖. I take then the first order condition with respect 𝜆 and equate it to 0. From C.1 (out of the first order condition) we obtain the demand function for good i. Compute the elasticity of demand with respect to (w.r.t.) price. Taking the total differential: 𝑣″(𝑐𝑖)𝑑𝑐𝑖 − 𝜆𝑑𝑝𝑖 = 0 (C.2) In the end I will solve a system of equations in which I have n equations like C.1, but just one equation like C.2 to solve. Exogenous variables: price and output. Demand elasticity (sensitivity of consumption to price) with respect to price. For computing it, I have to go back to the demand function, which in turn comes from C.1. I want to see what happens to the leften side of the expression C.1 𝑣′(𝑐𝑖) − 𝜆𝑝𝑖 = 0 for a change in price or quantity. To do that, I take total differentiation of C.1, therefore the second-order derivative → 𝑣″(𝑐𝑖)𝑑𝑐𝑖 − 𝜆𝑑𝑝𝑖 = 0. If I’m in equilibrium this change must be such that it’s still equal to w (→ such that C.1 still holds). The change in 𝑐𝑖 and 𝑝𝑖 will be such that the relation still holds. Coming back to elasticity: 𝜀𝑖𝑖 = 𝑑𝑐𝑖 𝑑𝑝𝑖 𝑝𝑖 𝑐𝑖 We derive from C.1 and C.2: 𝜀𝑖𝑖 = 𝑑𝑐𝑖 𝑑𝑝𝑖 𝑝𝑖 𝑐𝑖 = 𝜆 𝑣″(𝑐𝑖) 𝑝𝑖 𝑐𝑖 = = 𝜆 𝑣″(𝑐𝑖) 𝑣′(𝑐𝑖) 𝜆 𝑐𝑖 = = 𝜆 𝑣″(𝑐𝑖) 𝑣′(𝑐𝑖) 𝜆𝑐𝑖 = 𝑣′(𝑐𝑖) 𝑣″(𝑐𝑖) 1 𝑐𝑖 < 0 𝜀𝑖𝑖 = 𝑣′(𝑐𝑖) 𝑣″(𝑐𝑖) 1 𝑐𝑖 < 0 For expositional convenience, take the absolute value: 𝜂𝑖𝑖 = − 𝑣′(𝑐𝑖) 𝑣″(𝑐𝑖) 1 𝑐𝑖 > 0. 7 we will assume that the second-order conditions are satisfied → we use functions that we are sure will satisfy the 2nd. Most of the economically relevant informations can be obtained with the first order condition. 22 Krugman assumes that the absolute value of the elasticity of demand is decreasing in consumption: 𝒅𝜼𝒊𝒊 𝒅𝒄𝒊 < 𝟎 the more/the less you consume of good i, the less/the more sensitive you are to price changes. Why? Habits/necessities/price level. The more I consume a good, the less my consumption will be deviated by price changes. The third possible justification is the price level: it may be the case that I’m consuming a lot of a good because the price is low. Therefore, it is not affecting my behavior a lot. The larger is the consumption, the smaller is the elasticity of demand with respect to the price. In Krugman’s model we can now turn to the supply side. Assume that firms produce just one good (ruling out multiproduct firms). Production requires only labor, and I can write labour demand by firm I, which is given by 𝛼 + 𝛽𝑗𝑖 . This means that there are fixed components I cannot change. The supply side: Note that firm i produces only good i Labour demand by firm i: 𝐿𝑖 = 𝛼 + 𝛽𝑦𝑖 Total cost of producing good i: 𝑤𝐿𝑖 = 𝑤(𝛼 + 𝛽𝑦𝑖) What can we tell about competition? That the wage is independent from labour demand. The amount of labor services is independent from the amount the firm pays for labor services. Labour demand is not affecting the price of labor services. I can then compute: Average cost: 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑢𝑡𝑝𝑢𝑡 → 𝐴𝐶 = 𝑤(𝛼 + 𝛽𝑦𝑖)/𝑦𝑖 = (𝑤𝛼/𝑦𝑖) + 𝑤𝛽 As long as there are fixed costs of production, there will be economies of scale. Marginal cost: 𝑀𝐶 = 𝑤𝛽 I take the derivative, which will be w times B. This marginal cost is the product of two constants, therefore will be a constant. The marginal cost is therefore not sensitive to y. Any additional unit of production will entail the same increasing total cost. We can provide a graph representing marginal and average costs: 25 Consider C.4: 𝑝 𝑤 = 𝛼 𝐿𝑐 + 𝛽 = 𝛼 𝐿 𝑐−1 + 𝛽. Again: 𝑑 𝑑𝑐 𝑝 𝑤 = − 𝛼 𝐿 𝑐−2 = − 𝛼 𝐿𝑐2 < 0 The curve z-z gives to be all the pairs such that profits are zero, while the p-p gives the pairs where MC=MR. I’m looking for the point where marginal revenues are equal to marginal cost and profits are zero. The equilibrium pair ( 𝑝 𝑤 ) ∗; 𝑐 ∗ belongs to both PP and ZZ. 26 How many goods/variaties are offered in the economy? The question means: since every company produces a variety, how many companies are there in the market? Given full employment: 𝐿 = ∑ 𝐿𝑖 𝑁 𝑖=1 𝐿 = ∑(𝛼 + 𝛽𝑦𝑖) 𝑁 𝑖=1 Because of symmetry: 𝐿 = 𝑁(𝛼 + 𝛽𝑦). Given supply equal demand on the product markets: 𝐿 = 𝑁(𝛼 + 𝛽𝐿𝑐 ∗) Solve for N: 𝑁 = 𝐿 (𝛼 + 𝛽𝐿𝑐 ∗) = 1 ( 𝛼 𝐿 + 𝛽𝑐 ∗) Consider now an increase in labour supply. PP is unaffected, but ZZ shifts to the left (since it depends and changes on L). Go back to C4. Given c, any increase in L means a decrease in value over time. An increase in labour supply implies: 1) a fall in c* 2) a fall in (p/w)* 3) an increase in N* (because L goes up and c* goes down) 27 Consumers/workers have less of each good (c goes down) but consumer a large variety of goods (N increases), therefore they are better off because they have more choices (N goes up) and more purchasing power. They are better off in relative terms. Note: total revenue with respect to elasticity as explained in slides. 𝑇𝑅 = 𝑑 𝑑𝑞 (𝑝(𝑞)𝑞) = 𝑃(𝑞) + 𝑞 ( ⅆ𝑝(𝑞) ⅆ𝑞 ) Factoring out p = 𝑝(𝑞) [𝑦 + 𝑞 𝑝(𝑞) ⅆ𝑝(𝑞) ⅆ𝑞 ] = 𝑝 [1 + 1 𝜀 ] Since this 𝜀 is negative, I can change into absolute values using 𝜇 (𝑤ℎ𝑒𝑟𝑒 𝜇 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 − 𝜀) Therefore, the previous formula can be written as 𝑝 [1 − 1 𝜇 ] where 𝜇 = −𝜀 Open the economy to trade: Assume that our country opens its borders to its identical twin. The twins have identical tastes and technology: • No Ricardian reason for trade. This economy doesn’t have differences in factor endowment. • Production requires just one input: there is no difference of factor intensity on one good. o difference in factor endowment cannot support trade. We don’t have any reason for exchange…nevertheless, we observe trade! However, the total number of varieties available to the consumer in the open economy is larger than the total number of varieties available to the consumer in the closed one. The opening of the economy is akin to an increase in labour supply and production of goods/brands/varieties is distributed across countries as each variety is produced by a single firm. We don’t observe two firms producing the same good because there are economies of scale (lower average cost in increasing the production, each firm ends up to gain each market). We end up in production concentrated in just one country for each variety. We can affirm that: 1) Direction of trade is indeterminate (which country produces what). In Ricardo’s model we know exactly that good x is exported from A to B, and good y from B to A. In this case, we don’t know which company will survive, we will observe trade from one country to the other but we don’t know which ones. Note: I’m assuming zero transport cost. If there were transport costs, it wouldn’t be the same to buy from the company closer to our home country or a foreign one. As long as there are economies of scale, it makes sense to concentrate production in one location as long as the benefits from economies of scale cover transport costs. 2) Volume of trade is determinate (demand conditions) 30 Economies of scale of a different kind: Marshallian economies of scale This notion of economies of scale, the one we just examined, is very recent. One older belongs to Marshall, who says that economies of scale do not belong to companies, but rather to industries. Output in industries determines the average cost od production into firms. This idea came from the observation that production takes advantage of some kind of externality: the easiest one to think of is the agglomeration externality. Agglomeration is a common source of Marshallian economies of scale. We observe geographical concentration of companies: Silicon Valley, medicate district near Mantova, Bicocca is a former industrial district (Pirelli). As the industry output expands, the firm’s (marginal) cost falls: the industry supply function is downward sloping. IRS as a driver of trade: - Graham, Frank D. 1923. “Some Aspects of Protection Further Considered.“ Quarterly Journal of Economics 37: 199-227. - Ohlin, Bertil. 1933. Interregional and International Trade (Cambridge, MA: Harvard University Press). Therefore, those economies of scale are driven by the success of the industry. In 1923, Graham linked Marshallian economies of scale to trade with the following argument: suppose you have a country closed to trade. Inside, there is a sector operating under Marshallian economies of scale. When you open, competition from abroad targets the sector operating under Marshallian economies of scale, so that your sector will lose customers in favour of the foreign production. Marshallian economies dissipate, countries are worse off. This was presented as an argument against free trade. An argument in support of free trade? Knight, Frank H. 1924. “Some Fallacies in the Interpretation of Social Costs.” Quarterly Journal of Economics 38: 582-606: firms are not price takers or IRS are at the industry level as in. Graham’s was based on the idea that firms enjoying Marshallian economies of scale are not aware of that (price takers). However, under Marshallian economies of scale we should have a more advanced model of companies interaction considering that they know the benefits coming from Marshallian economies of scale. Ethier, Wilfred J. 1982a. “Decreasing Costs in International Trade and Frank Graham’s Argument for Protection.“ Econometrica 50: 1243-12682. Summary of Krugman’s concepts: • Firms are identical within sectors. Therefore, we have predictions of intra-industry trade, some countries will become exporters of specific brands and others importers of those brands. • Krugman observes more the industry than the country: at the end of the day, he’s focusing on sectors and predicting importing/exporting of specific brands. • The model has no way to differentiate between firms in an industry: this is inconsistent with the data. According to data proofs, only a subset of firms operating in an exporting sector actually serve foreign markets, and there is no degree of asymmetry in Krugman’s model that is able to generate this result. What you produce at home is going to determine what you export on the market, end on the story. In Krugman’s model, once you are active in the domestic market you are active also in the foreign market. This is not observable in reality: it’s not granted that, if you’re active on the domestic market, you’re active on the foreign one too. 31 Lecture 4 Exporting firms: who are they? Challeging the NTT: In the ‘90, a number of empirical studies based on newly-available longitudinal data at plant and firm level showed heterogeneity in firm characteristics and trade behavior within sectors. The main findings: • They are few Share of manufacturing firms that export, in percent. Country Year Exporting firms, in percent U.S.A. 2002 18.0 Norway 2003 39.2 France 1986 17.4 Japan 2000 20.0 Chile 1999 20.9 Source: WTO (2008) • They are few even within exporting sectors: See Mayer, Thierry. and Gianmarco Ottaviano. 2008. “The Happy Few: The internationalisation of European firms” Intereconomics, 43: 135-148 32 They are different: Exporting firms: • are larger (n. of employees, market shares) • are more productive (labour and capital productivity) • pay higher wages than non-exporting firms in the same industry. Falls in trade barriers are associated with increases in sectorial labour and capital productivity: empirical evidence shows this to be the effect of re-allocation of resources from less productive to more productive firms within industries. After NAFTA, this is exactly what we observed towards Canada. The NNT is unable to explain the above described phenomena, why only a subset of firms are exporters in exporting sectors. A new paradigm was needed, and eventually developed providing a theory encompassing all these new facts. All firms in an exporting sector export. As before, a new paradigm was required! The corner stone of the new paradigm: Melitz, Marc J. 2003 “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity” Econometrica 71: 1695-1725. It became a standard. It’s fair to say that Melitz was not the first one coming up with this idea. However, he was the one able to present a fully coherent model. We will present a simplified (that is, a static) version of the Melitz model. In the exposition we follow: Helpman, Elhanan. 2006. “Trade, FDI; and the Organization of Firms.” Journal of the Economic Literature: 589-630. A “no-frills” Melitz model “No frills”: we ignore the dynamics in the model; that is, we do not study the entry and exit of firms and the evolution of the industries. 35 2) The supply side The cost function has two components: i) no matter the scale, production requires a fixed amount of resources 𝑓𝐷 at unit cost c: so, the fixed cost component is 𝒄𝒇𝑫; ii) variable component of the cost function, an extra unit of output costs 𝒄 𝝑𝒋 . 𝝑𝒋 is a firm specific productivity parameter: the larger, the lower the marginal cost. It captures how good is my firm j at doing its job. Productivity 𝜗 is a random variable. Heterogeneity across firms is driven by this parameter: we assume there is a distribution of possible 𝜗 and firms pick up one on the basis of their different skills. Entrepreneurial talent, for example, is randomly distributed among individuals and therefore across firms. Another example could be the one of previous investments, which can turn to be successful or not in the future. The firm observes the distribution of 𝜗. A firms observes the realization 𝝑𝒋 only after incurring in 𝒄𝒇𝑫. In other words, after they have started. A large number of new entrance in a market disappear within a year. If they knew they weren’t good at their job, they wouldn’t have started, and this happens always and not only in a recession. Data on firms mortality (decreasing sharply as they age) are supportive and justify our assumption that firms don’t know their own ability before starting their operation. Firms draw their 𝜗 from the same distribution (taken as exogenous in the model; we will discuss it later on). 36 3) Market equilibrium (still in closed economy) The firm, to maximize profits, solves: 𝑚𝑎𝑥 𝑝𝑗 𝑝𝑗𝑥𝑗 − 𝑐 𝜗𝑗 𝑥𝑗 − 𝑐𝑓𝐷 = 𝑝𝑗𝐴𝑝𝑗 −𝜂 − 𝑐 𝜗𝑗 𝐴𝑝𝑗 −𝜂 − 𝑐𝑓𝐷 = 𝐴𝑝𝑗 1−𝜂 − 𝑐 𝜗𝑗 𝐴𝑝𝑗 −𝜂 − 𝑐𝑓𝐷 Profits maximization entails to choose the price to maximize profits, which are given by TR-TC. The cost of producing j has a fixed and a variable component. First order condition (first order derivative = 0): 𝐴(1 − 𝜂)𝑝𝑗 1−𝜂−1 − 𝑐 𝜗𝑗 𝐴(−𝜂)𝑝𝑗 −𝜂−1 = 0 S.O.C: always satisfied Price set by the firm in equilibrium will be: 𝑝𝑗 = 𝑐 𝜗𝑗 1 𝛼 ≡ ?̂?𝑗 Let’s talk about 𝑝𝑗. It is the product of two elements: 𝑐 𝜗𝑗 is the marginal cost, the cost of one extra unit of output. So, the equilibrium price is the marginal cost times 1 𝛼 that captures the degree of substitutability across goods. The smaller is 𝛼 the greater the distance between price and marginal cost, therefore the greater its price than marginal cost. It means that the producer of good j has market power. When 𝛼 = 1, the degree of substitutability is infinite. If it’s less than one, the degree is less than infinity, prices more than marginal cost and therefore the producer has market power. The less substitutability there is between goods, the higher the price, the more the consumer it’s going to pay. Maximum profit: value of the profit function when the price is set to ?̂?𝑗 . We proceed by substitution. ?̂?𝑗 = 𝐴?̂?𝑗 1−𝜂 − 𝑐 𝜗𝑗 𝐴?̂?𝑗 −𝜂 − 𝑐𝑓𝐷 = 𝐴 [( 𝑐 𝜗𝑗 1 𝛼 ) 1−𝜂 − 𝑐 𝜗𝑗 ( 𝑐 𝜗𝑗 1 𝛼 ) −𝜂 ] − 𝑐𝑓𝐷 = ?̂?𝑗 = ( 1 𝜗𝑗 1−𝜂) 𝐴 ( 𝑐 𝛼 ) 1−𝜂 (1 − 𝛼) − 𝑐𝑓𝐷 To simplify, we can pose: 𝐵 = 𝐴 ( 𝑐 𝛼 ) 1−𝜂 (1 − 𝛼) It follows that I can write: ?̂?𝑗 = 𝜗𝑗 𝜂−1 𝐵 − 𝑐𝑓𝐷 The firm operates/is active on the domestic market (recall: different from entry) if and only if: 37 𝜗𝑗 𝜂−1 ≥ 𝑐𝑓𝐷/𝐵 As long as my productivity (elevated at elasticity of demand) is more or equal than 0. We can focus on 𝜂: what is the value that give me positive values in this relation? If our 𝜂 < 𝑐𝑓𝐷 ∕ 𝐵, then the result will be negative. Posit: 𝜗𝑗 𝜂−1 ≡ ?̃? Call ?̃?𝐷 the value of ?̃? such that (that make sure that) my maximum profit is zero → ?̂?𝑗 = 0: ?̃?𝐷 = 𝑐𝑓𝐷/𝐵 We can represent ?̂?𝑗 as a function of ?̃?. ?̂?𝒋 is a linear a function of ?̃?, with intercept −𝒄𝒇𝑫 and slope B. Each firm can only have one 𝜗. ?̃?𝐷 = 𝑐𝑓𝐷/𝐵, therefore if I change one of the two it will move. Toward the origin when B goes up, in the other direction when c goes up. This will be true at the same time for every firm and for the share of firms in the market. The share of active firms in the number of entrants is declining in 𝑐𝑓𝐷 and increasing in B. 1) As 𝒄𝒇𝑫 increases, a larger productivity parameter is required to make zero profits. The line shifts down and the crossing point will be at the right of the original one. Remember that 𝜗 is just the realization of a random variable → therefore, I need to increase it to make profits. 40 From F.O.C: 𝑝𝑗 ℓ = 𝜏𝑐 𝜗𝑗 1 𝛼 ≡ ?̂?𝑗 ℓ Profit function: 𝜋𝑋 ̂ 𝑗 ℓ = 𝜏1−𝜂𝜗𝑗 𝜂−1 𝐵ℓ − 𝑐𝑓𝑋 where 𝐴ℓ ( 𝑐 𝛼 ) 1−𝜂 (1 − 𝛼) ≡ 𝐵ℓ Note: I stress “via export” because there are many ways of serving the foreign market: I could, for example, construct a plant and producing there. The firm operates/is active on the foreign market if and only if the profits they’ll make in the foreign market are non-negative: 𝜗𝑗 𝜂−1 ≥ 𝑐𝑓𝑋/𝐵 ℓ𝜏1−𝜂 Which value of 𝜗 will make sure that my profits are equal or more than zero (non-negative)? 𝜗𝑗 𝜂−1 ≡ ?̃? This value is the following. Call ?̃?𝑿 the value of ?̃? such that 𝑿?̂?𝒋 𝓵 = 𝟎: ?̃?𝑿 𝓵 = 𝒄𝒇𝑿/𝑩 𝓵𝝉𝟏−𝜼 I can graphically represent this: I have two diagrams: one dividing firms in two groups, being firms able and unable to serve the domestic market. My second diagram eventually divides the group into firms able and unable to serve the foreign market. Now, we can unify and compare both. 41 We know, first of all, that the firms able to operate in the foreign market must be able to make at least 0 profits in that market. I ask myself: which value of 𝜗 allows my firm to be active in the foreign market? That value of 𝜗 such that the maximum profit on the foreign market is at least equal to 0. It’s easy to see that such value of 𝜗 must be larger than 𝑐𝑓𝑋/𝐵 ℓ𝜏1−𝜂. I call 𝜗𝑗 𝜂−1 ≡ ?̃?, this last value being the value of 𝜗 for which profits in the foreign market are equal to 0. A firm with this value of 𝜗 is what we call a marginal firm: all firms with a larger 𝜗 will obtain a larger profit on the foreign market, and vice versa for smaller 𝜗 . The marginal firm is indifferent between staying in the market and leave the market. Therefore, being profits a linear function of 𝝑 → different profit levels for different 𝜗 . The slope is given by the derivative of the maximum profit with respect to 𝝑 . 42 Who are the exporters? To answer this question, we compare the marginal productivities ?̃?𝐷 and ?̃?𝑋. These two aren’t the same (as Krugman asserted). These will be all those firms for which ?̃? > ?̃?𝑥 . For doing so, I represent the maximum profits on both markets ?̂?𝑋 ℓ and ?̂?𝐷 in the same space. Assume: 𝐵ℓ = 𝐵, which means that market conditions in the domestic and foreign market are the same. Note from 𝐴ℓ ( 𝑐 𝛼 ) 1−𝜂 (1 − 𝛼) ≡ 𝐵ℓ that the difference between 𝐵ℓand 𝐵 is 𝐴ℓ, which captures the number of firms active on the domestic market and the price set by firms operating on the market. We take a shortcut saying also that 𝐴ℓ = 𝐴, to reinforce that market conditions are the same at home and abroad. We have: • domestic market: 𝜕?̂?𝑗 𝐷 𝜕?̃? = 𝐵; • foreign market: 𝜕?̂?𝑗 ℓ 𝜕?̃? = 𝜏1−𝜂𝐵. Note that, in the foreign market, if we take the derivative of the profits with respect to ?̃?, we get 𝜏1−𝜂𝐵. The difference in the slopes is the 𝜏: how fast my profit is growing in the ?̃?? On the domestic market, any increase in ?̃? drives about an increase in total profit which is equal to B. The same increase in ?̃? in the foreign market drives an increase in profit which is equal to 𝜏1−𝜂𝐵. Note that 𝜂 is larger than one, and 𝜏 is a number larger than one. So, 𝜏1−𝜂 will means a number 1/𝜏 multiplied by B, which will become smaller given that 𝜏 > 1. Because 𝜏 > 1 and 𝜂 > 1, the profit function for the foreign market is flatter than the domestic one. The same increase in ?̃? brings about a smaller increase in profits in the foreign market rather than in the domestic market. Turn to the intercept: increase the productivity. You will have a larger profit my the increase in ?̃?, which will increase profits more in the domestic market than in the foreign market, because of the role played by the transport costs. In an ante-Melitz world (Krugman-type of world): 𝒇𝑿 = 𝟎. Our picture with the two profit functions is as in my fig. 3. Therefore, given this graph, we can deduce that all domestic firms export. This is not in the data! 45 2) modifiable iceberg costs (tariff and non-tariff barriers to trade). There are a number of non-tariff barriers to trade, as safety regulations. Sometimes, these are just instruments to prevent competitions from foreigners. What’s the impact on these on the level of productivity required to enter the foreign market? First of all, let us consider non-modifiable costs. Under 1): Iceberg costs vary across countries; only productive firms enter “difficult” countries (e.g., LDC). The larger is 𝜏, the flatter is your profit function (and therefore, your marginal cost), the lower is your market share, the lower is your proft. To make a positive profit you have to oppose a large 𝜏 with a large 𝜗, which will neutralize it. We can therefore say that only productive firms enter “difficult” countries, e.g. countries which present non- modifiable transport costs. Under 2): Note that 𝝉 is, generally speaking, fixed. For the most, the firm takes it as given. However, 𝝉 is a policy variable for governments. Therefore, suppose a change happens. Consider a unilateral reduction in 𝜏: ➢ a fall in 𝜏 reduces ?̃?𝑋; ➢ the number of active firms increases; ➢ does it? ➢ competition is tougher on the foreign market, firms reduce prices, 𝐴ℓ falls and 𝐵ℓfalls too; ➢ ?̃?𝑋 increases! Suppose until yesterday I was making 0 profits, and today suddenly I’m making positive profits. The implication is that firms that until yesterday were not able to enter my market, now will be. Therefore a fall in 𝜏 reduces ?̃?𝑋, i.e. the value of 𝜗 required to enter. Therefore, active firms increase. However, because of competition, the slope of my profit function will come back to be flatter once again. The net effect is a fall in ?̃?𝑿, but not as large as one would think! The average productivity of domestic firms falls, the average productivity of exporters falls. Domestic firms included a number of firms that have now moved to serve the foreign market (some of them are, therefore, no longer domestic firms) → average productivity decreases. BUT: Trade barriers are not unilaterally reduced. Purely unilateral reductions are very unlikely. Barriers, if reduced, are decreased by many countries at the same time → unlikely that country A is reducing τ if country B is not doing the same. As trade costs fall for exporters from the domestic country, so they do for the exporters from country ℓ: ➢ competition on the domestic market is tougher, firms reduce prices, 𝑨 falls and 𝑩 falls too. This happens because domestic firms have to compete with more firms competing from other markets. ➢ ?̃?𝐷 increases! (→ the value of 𝜗 required to survive in the domestic market increases) This is consistent with data: we observe re-allocation of resources within industries. Market conditions for firms on the domestic market deteriorate (E↓), and therefore to survive as purely domestic firm you will need a larger 𝜗. What we observe in the data is an increase in the average productivity: the more productive firms attract more resources. How many markets? 46 So far we have discussed the decision to serve just one market. How does the story change if we allow the company to serve more than just one market? When entry costs 𝒇𝑿 𝓵 are independent across countries, the decision to enter a market is independent of the number of markets the firm is in, therefore nothing will change in our story. This has no effect on the fixed costs of serving markets A, B, C, etc. When entry costs 𝑓𝑋 ℓ fall in the number of markets a firm serves, few firms serve many markets. Note: first- mover advantage. The main empirical prediction: trade volumes are driven by the intensive as well as the extensive margin. How much I’m going to export depends not only how much I’m going to export, but also how many firms are going to export. In Melitz model, the same change entails a change in how much each firm is exporting and how many firms are exporting. The data bear it out: Helpman, Elhanan, Marc J. Melitz and Yona Rubinstein. 2008. “Trading Partners and Trading Volumes.” Quarterly Journal of Economics 123: 441-487. • If the story is Krugman’s one: we shouldn’t oberve, when tau falls, a change in number of exporters. • In Melitz: we observe not only a change in number of exporters, but also in the amount exported by each of them. This is what we observe in the data. 47 Contractual Frictions and Export behavior Exporting rests on contracts: simply because exporting takes time. Contractual frictions are a very serious problem in the international context for a number of reasons: the greater is the distance, for example, the more difficult is to write the contract. In addition to that, you may have governments and policy actions involving (and having an impact on) export/trade role. Consider the Noble Group Limited case (see Antras 2015, p.59), clear example of government intervening in favor of a local producer (friction generated by government intervention). ➢ Brazilian soybeans to Chinese soybean crushers ➢ Fixed price contract signed in January 2004 (quantity and price are fixed in advance for a specific time in the future, in order to protect yourself against price fluctuations → however, if the price is going to fall, you may pay a price too high). ➢ Delivery scheduled for April 2004. ➢ In the meantime: the price of soybeans declined by 20% ➢ In April, Chinese port authorities detected a discoloration of some Brazilian beans, pointing to the presence of toxic substance ➢ The Chinese government banned all soybeans import from Brazil ➢ NGL lost $25 millions. The timing was, at least, suspicious. This tells us that countries may vary in the quality of contract enforcement. A second example, last year in December, was another somehow related. Somehow related: Consider the Chinese court ruling on the Apple-Qualcomm dispute over some infringement of packets (https://www.nytimes.com/2018/12/10/technology/apple-qualcomm-patents-ruling.html). In other words, the Chinese court ruled on a dispute between two American companies. Let us model contract frictions in a very simple but not trivial way. Serving a market via exports usually requires to contract with an importer. The exporter ships quantity 𝑥𝑗 ℓ to the importer. The importer agrees to pay back to the exporter the amount 𝑠𝑗 ℓ either upon delivery (ex-ante payment) or after selling the goods (ex-post payment). For the time being, let us assume that parties opt for ex-post payment, therefore after selling the good. However, ex-post payment has sense as long as the importer has liquidity constraint. If the exporter is willing to wait, the importer waits until the importer has sold the good: there is no need for the importer to finance the operation. The importer has the option to misreport total revenues, therefore to divert some of the cash flows away from the exporter. He can claim that total revenues are just a fraction 𝝁𝒋 𝓵 of their actual value (therefore, this value will be the fraction of total revenues reported value to the importer). Note that such fraction 𝜇𝑗 ℓ is specific to the countries pair (common legal traditions…. → country-specific). The larger is this value, the larger is for the importer the opportunity of misreporting. This value, therefore, captures the quality of contract-enforcing measures in a country. The importer can divert to himself (𝟏 − 𝝁𝒋 𝓵)𝒑𝒋 𝓵𝒙𝒋 𝓵 For example, if the importer gains 100 and reports 90, then this difference is 10. However, the quality of the legal system is given by the fact that the exporter knows of the existance of this margin. However, if the legal 50 Within countries contractual frictions are smaller than between countries. So, if you’re not very productive, you remain domestic (𝜇 is larger than between markets). Exporters must be productive enough to overcome large contractual frictions. Among exporters, only the top productive ones enter countries with very low contractual enforcement. Firms with low productivity enter countries with high contract enforcement, while those with high productivity can enter either countries with low and with high contract enforcements. 51 Since frictions have a detrimental effect, why don’t we observe significant action to reduce contractual frictions? Well, these frictions have important distributional implications: they reduce quantities, but at the same time permit the importer to gain a larger share of total revenues. Importers in market l benefit more. Therefore, we can affirm that is no lobbying large enough to treat contractual frictions. Also, contractual frictions are unlikely to be the subject of a trade agreement. The firm can invest to improve contract enforcement. The exporter can take some action to shield itself from toxic behavior (asking for advice, select international arbitration as a solution for controversies, and so on). Therefore, the firm may address some fixed costs to improve the quality of contract enforcement. Suppose that by investing 𝒄𝒇𝑳(𝒆𝒈𝒂𝒍𝒂𝒅𝒗𝒊𝒄𝒆) the importer is forced to report at least 𝜇𝑗 ℓ > 𝜇𝑗 ℓ. I can model it as follows: under improved contract enforcement, the underreporting is somehow limited. So, I make sure that the importer must report at least ?̅?. With no protection, the importer can claim that total revenues were 50% of the actual value. With legal advice, I can make sure that indeed he can to some misreporting, but not on such large scale: for example, if total revenues were 100, he can misreport and say it was 80, but not cutting off 50%. So, I’m imposing a limit on misreporting (at least a value ?̅?), so that I don’t have to react through legal acts. Misreporting will be less severe, but there will be higher fixed costs. Who will invest in legal advice? Any firm for which: ( 1 𝜇𝑗 ℓ ) 1−𝜂 𝜏1−𝜂𝜗𝑗 𝜂−1 𝐵ℓ − 𝑐𝑓𝑋 − 𝑐𝑓𝐿 ≥ ( 1 𝜇𝑗 ℓ ) 1−𝜂 𝜏1−𝜂𝜗𝑗 𝜂−1 𝐵ℓ − 𝑐𝑓𝑋 𝜗𝑗 𝜂−1 ≥ 𝑐𝑓𝐿/𝜏 1−𝜂𝐵ℓ [(𝜇𝑗 ℓ ) 𝜂.−1 − (𝜇)𝜂.−1] That is, only the most productive firms invest in contract enforcement (will be willing to buy legal advice). Only productive firms will devote fixed costs to legal advices, since are the only firms able to face larger fixed costs, since they have large market shares on which to spread these additional fixed costs. Total profit from acquiring legal advice is more or at least equal to the total profit of not acquiring legal advice. Only the firms with a 𝜗 large enough to allow them a market share to cover the fixed costs associate to legal advice will invest. Consistent with the fact that arbitration cases for business transactions at the International Chamber of Commerce are usually above $ 1 million. Repetita iuvant I have supposed that the exporter and importer meet once and they trade. In reality, people interact repeatedly over time, or the same importer interacts with the exporter. So, reputation makes its role. In the event exporter and importer trade only once and no information is publicly made available, the importer will always default.But what if they expect to trade repeatedly or the importer expects to trade with other exporters? As long as information are available about the behavior, people behave differently. Example of repeated trade Importers come into two types: are either patient (care about future business) or impatient. The exporter knows that a fraction 𝜒 of importers is patient and thus upon meeting an importer the exporter assign probability 𝜒0 to the importer being patient. At the first encounter, assumed to be patient (for a given prob.). • A patient importer never defaults (will never misreport); • an impatient importer will default given the opportunity. 52 Assume that the opportunity of defaulting arises with the same probability in each period: 𝟏 − 𝝆𝒋 𝓵. Is not the case that, being an impatient, you always default: the right condition materializes (ex. Port authorities want to cooperate with you). This probability is country-specific. Simply, given the fact that you don’t know who you’re encountering the first time, you assign a certain probability he’s patient and a certain probability he’s impatient. When he signs his first contract with the importer, the exporter expects it to be enforced with probability: 𝝌𝟎 + (𝟏 − 𝝌𝟎)𝝆𝒋 𝓵 ↓ The overall probability is given by = probability to have met a patient importer + the probability to have met an impatient one that was not given the opportunity to default. As time goes by and reporting/misreporting have been observed, the exporter adjusts his beliefs (and, therefore, his probabilities) to the contract, about the patience of the importer he is trading with as follows. In particular, the exporter will adjust its probability to be trading with a patient importer. 𝜒𝑡 = 𝜒0 𝜒0 + (1 − 𝜒0)(𝜌𝑗 ℓ) 𝑡 In each period t, the exporter expects to receive total revenues [receives in expected terms]. The exporter will adjust its beliefs over time. If he hasn’t seen default, the renewed probability 𝜒𝑡 will be simply equal to 𝜒0 discounted by the fact that no default has occurred so far → 𝜒0 + (1 − 𝜒0)(𝜌𝑗 ℓ) 𝑡 . The probability that I’m dealing with a really patient one, is the fraction of patient people in the population of the importer, divided by this expression, that captures the probability that no defaulting has occurred so far. Therefore, the exporter in each period expects to receive total revenues equal to: [𝝌𝒕 + (𝟏 − 𝝌𝒕)𝝆𝒋 𝓵]𝒑𝒋 𝓵𝒙𝒋 𝓵 ↓ Expected total revenues = probability attached to the importer being patient (now not anymore 𝝌𝟎, but 𝝌𝒕) + probability attached to the importer being impatient (𝟏 − 𝝌𝒕), but unable to default because the opportunity didn’t arise 𝝆𝒋 𝓵, times total revenue. In other words, expected total revenues are total revenues times the probability that also in time t the contract goes through without problems. This probability that the contract goes through is the probability that the importer is patient (updated, taking account of what happened so far) plus the probability that he’s indeed impatient but wasn’t given the opportunity to default up to that point. As time goes by and no default occurs, the exporter grows more and more confident that he’s dealing with a patient time. If the patient type never defaults, you grow confident and increase your exports, 𝜇 comes closer to 1 (𝜇 = 1 if totally patient). We can think of an equilibrium in which exports increase over time as no defaults are observed. Empirical evidence (on Belgian firms) supports the prediction of the model. However, we do have a relevant twist: volumes increase faster in countries with low enforcement (high 𝟏 − 𝝆𝒋 𝓵). Exporters learn faster about the type of the importer! In countries with low enforcement, opportunities for default arrive faster, and if you’re dealing with an impatient type default happens. This means that you learn faster: there are so many opportunities of default that these will occur immediately, so if you don’t see default in such countries for some time, you will become 55 • The importer/exporter can default on his obligations toward the bank. This has two possible effects: o increases in the cost of money; o rationing of credit • Under post-shipment payments, the cost of financing the importer’s operation is borne out by the exporter. • Under cash in advance, the cost of financing the importer’s operation is borne out by the importer himself. The exporter demands cash in advance when contractual frictions are sizeable, but when this is the case the cost of borrowing for the importer is likely to be high/credit is rationed and demand for exports fall. Note that under post-shipment payments, the quality of contract enforcement in the exporter’s country matters: the lower the quality, the higher the marginal costs of exporting and the lower the volume of trade. Cash in advance and post-shipment is a choice btw two evils and it is match-specific as the institutional quality of both the exporter’s and the importer’s country matter. Empirical evidence on the credit channel: • Manova, K. (2012), Credit constraints, heterogeneous firms, and international trade. The Review of Economic Studies 80: 711-744 • Antràs, P. and Foley, C. F. (2015). Poultry in Motion: A Study of International Trade Finance Practices. Journal of Political Economy 123: 809-852. From Antras and Foley: Data from US based firm exporting frozen poultry to 140 countries over the 1996-2009 period: $7 billion in sales. The independent variable of interest is importer country contract enforcement. Variation in the expected contract enforcement has strong effects on the payment method. E.G: Common Law Civil Law Post-shipment 0.8 0.2 Cash in advance 0.04 0.64 Others 0.12 0.12 Post-shipment is a adopted 80% of the time in common law countries, and only 20% in civil law countries. On the other hand, cash in advance is much more frequent in civil law countries. The anticipation of contract friction is lower for common law countries, and the lower it is, the more you feel confident to adopt post- shipment payment measures. First-time buyers are disproportionally more likely to be demanded cash in advance. As a consequence, volume of trade will be low. With passing time, you may shift to post-shipment, and volume trade may increase as long as there are no contractual frictions. 56 Domestic institutions and comparative advantage The most influential contribution in a large literature: • Nunn, N. (2007). Relationship-Specificity, Incomplete Contracts, and the Pattern of Trade. Quarterly Journal of Economics 132: 569-600. We insisted on the fact that exporting activities or trading require contracts. It is as if contracts as an input of production. We know that the more tailored on the needs of the customer is a good, the more important is the role of contracts: if we trade very customized goods, contracts are a very important elements, as contract enforcements. We could re-phrase Ricardo in terms of contract enforcement. → Contracts are a factor of production and we can rank merchandise on a contract-intensity scale. → Relationship-specific or taylor made merchandise (often inputs themselves) are contract-intensive and are more likely to be produced in and then exported from countries with good contract enforcement. Nunn published an interesting paper in which, with a large number of countries and industries analyzed, he was estimating what was the impact of the quality of contract enforcement on the volume of trade (back-on- the-envelope calculation). He did a thought experiment: take two countries, Thailand and Taiwan. The data: International trade data for 146 countries and 222 industries in 1997. Assume Thailand could provide the same quality of domestic institutions as Taiwan. Would that have an impact? Trade would more than triple. “The estimated relationship between judicial quality and comparative advantage, in addition to being statistically significant, is also economically meaningful. For example, if ……Thailand improved its contract enforcement to equal Taiwan’s, then its exports of “electronic computer manufacturing” would increase from 2.83 to 6.97 billion U.S. dollars per year. Thailand’s share of world production in these goods would increase [in 1997] from 1.6 to 4.0 percent.” Here, we had an extra element: countries with a a high contract enforcement can specialize in the production of goods that require a specific technology. 57 Labour Market Frictions and Exports Labour market frictions are a well-established phenomenon and they explain unemployment as well as the co- existence of unemployment and vacancies. LM frictions are associated with higher wages (e.g. think of a firm that incurs costs to search for a new worker…). The country with less LM frictions pays lower wages and when goods are differentiated it can produce at lower average costs and thus export. Consider the effect of LM reforms aimed at reducing frictions: ➢ countries: A e B; ➢ firms from A and B serve market C ➢ country A reforms LM and reduces frictions ➢ country A increases its market share in country C; country B loses its market share in country C ➢ AC in country B increases and the country’s exports suffer an additional fall The productivity parameter In our model, the distribution of the parameter 𝜗 is exogenous. As a matter of fact, it is likely to be policy-sensitive. To exemplify, investments in education can modify the distribution in way such that a firm is more likely to draw a high value and enter the international market. 60 To country l I bring my own productivity, therefore 𝜗 is the same since my organization and therefore productivity is the same. Consider profits generated by selling on market ℓ the output of the plant located in ℓ: 𝜋𝐼 𝑗 ℓ = 𝑝𝑗 ℓ𝑥𝑗 ℓ − 𝑐ℓ 𝜗𝑗 𝑥𝑗 ℓ − 𝑐𝑓𝐼 The firm selects the price to maximise 𝜋𝐼 𝑗 ℓ. Therefore, as in the case of exporting, I choose 𝑝𝑗 ℓ. The difference is that the good doesn’t come from home, but is produce in country l. The firm solves: 𝑚𝑎𝑥 𝑝𝑗 ℓ 𝑝𝑗 ℓ𝑥𝑗 ℓ − 𝑐ℓ 𝜗𝑗 𝑥𝑗 ℓ − 𝑐𝑓𝐼 At the equilibrium: 𝑝𝑗 ℓ = 𝑐ℓ 𝜗𝑗 1 𝛼 ≡ 𝑝𝐼 ̂ 𝑗 ℓ Note that the maximum profit will be a function of 𝜗 of my B, that captures market conditions and the conditions of the inputs. If we compare this B with the B considering exporting, the difference will be over the c (I should consider the unit cost of production in my market, in this case I should consider the unit const of production in that country l and these may differ). The maximum profit is: 𝜋𝐼 ̂ 𝑗 ℓ = 𝜗𝑗 𝜂−1 𝐵𝐼 ℓ − 𝑐𝑓𝐼 Where 𝐴ℓ ( 𝑐ℓ 𝛼 ) 1−𝜂 (1 − 𝛼) ≡ 𝐵𝐼 ℓ Who invests abroad? 𝜋𝐼 ̂ 𝑗 ℓ ≥ 0 if and only if 𝜗𝑗 𝜂−1 ≥ 𝑐ℓ𝑓𝐼/𝐵𝐼 ℓ Therefore, firms making at least 0 profits abroad. Again, I ask myself which value of 𝜗 makes sure that my profts are non-negative? I compute 𝜗 such as my profits are higher or equal to zero. This is, again, the marginal 𝜗. Recall: 𝜗𝑗 𝜂−1 ≡ ?̃?. Profits from FDI are non-negative for ?̃?𝐼 ℓ = 𝑐ℓ𝑓𝐼/𝐵𝐼 ℓ. If 𝜗 is equal to ?̃?𝐼 ℓ, then profits will be zero. Thus: if ?̃? ≥ ?̃?𝐼 ℓ, 𝜋𝐼 ̂ 𝑗 ℓ ≥ 0. 61 This is our first option, because our firm has always the option of serving the foreign market by exports. Now, I have to ask myself: assuming that my 𝜗 is large enough that I can set up production abroad, will I do so? Is a productivity parameter equal or larger than ?̃?𝑰 𝓵 enough to turn a firm into a MNE? The answer is no! A firm opts for FDI if and only if it can make bigger profits in this way: 𝜋𝑋 ̂ 𝑗 ℓ < 𝜋𝐼 ̂ 𝑗 ℓ What I have to do is to compare these two. Recall: 𝜋𝑋 ̂ 𝑗 ℓ = 𝜏1−𝜂𝜗𝑗 𝜂−1 𝐵ℓ − 𝑐𝑓𝑋 𝜋𝐼 ̂ 𝑗 ℓ = 𝜗𝑗 𝜂−1 𝐵𝐼 ℓ − 𝑐𝑓𝐼 The firm is facing a trade-off bwt proximity and concentration. If we set up production abroad, we economize on transport costs. Let’s assume that the unit cost of production is the same as at home (not more expensive, not cheaper, same c). If 𝑐𝑙 is a bit larger than c, there could be uncertainty. However, one of the advantage or producing in the local market can be called proximity (therefore, of producing with FDI, directly in the market you want to serve). What are you giving up moving production? You are giving up the benefits of concentration → sacrifice economies of scale moving part of production. To produce abroad you need an extra plant, extra workers, and therefore you need to double fixed costs. That’s why we assume that fixed costs of serving the foreign market via export is lower of serving the foreign market via FDI. → If FDI, the firm is giving up economies of scale (increasing the number of plants, each plant processes fewer units of the good and AC increases). → We capture this idea setting 𝑓𝑋 < 𝑓𝐼. → On the other hand, FDI cuts on transport costs. If 𝝉𝒄 > 𝒄𝓵, FDI economizes on variable costs. Note that you can economize on variable costs only if 𝑐𝑙 > 𝑐. Predictions of the model: 1. The ratio 𝑬𝒙𝒑𝒐𝒓𝒕 𝒔𝒂𝒍𝒆𝒔 𝑭𝑫𝑰 𝒔𝒂𝒍𝒆𝒔 is the largest in industries where • fixed costs are high • iceberg costs are low; We have two ways to serve the foreign market. If I compare sales via export with those via FDI, I’m looking at the relative importance of these two ways to operate within the foreign market. The largest is the ratio, the more important is export relative to FDI. When I expect this ratio to be high? • When production entails large fixed costs. Implies to give up important economies of scale. For steel production in Italy, for example, transport costs are high and therefore you would give up a greater slice of economies of scale. • Importance of transport costs → iceberg costs are low. 62 2. The ratio 𝑬𝒙𝒑𝒐𝒓𝒕 𝒔𝒂𝒍𝒆𝒔 𝑭𝑫𝑰 𝒔𝒂𝒍𝒆𝒔 is the decreasing in the size of the foreign market, because the larger is the foreign market, the larger is the number of units you supply on the foreign market, the more expensive it is (transport costs are variable costs). At the same time, if you build a new facility, you can spread this cost among a larger market. Corollary: MNEs prefer to invest in high income countries (larger consumption and markets). This is to say that, the larger the market portion a firm gained, the larger the portion on which to spread fixed costs. Both of these points are confirmed by data: • Brainard10 (1997) confirms i). • Yeaple11 (2003) confirms ii). How productive is a firm opting for FDI? We know that exporting firms face lower fixed costs than investing firms. We knoe that the driver of heterogeneity comes from the fixed component that we considered: when we compared domestic vs exporting firms, we concluded that the latter had to overcome the barrier of extra fixed costs involved in entering the foreign market, therefore had to become more productive. In the same way, facing higher fixed costs, we can presume that investing firms are more productive than exporting ones. This is indeed the prediction of our model. Let us draw the by now familiar diagram, comparing the maximum profits for a purely domestic, for a firm serving via export market l and a firm serving via investing (FDI) market l: ?̂?𝐷; 𝜋𝑋 ̂ 𝑗 ℓ; 𝜋𝐼 ̂ 𝑗 ℓ. We assume that market conditions are the same across domestic and foreign market, and that the marginal cost of production c is the same in both markets. For the sake of simplicity, also assume that the combination of parameters B is the same in the markets, and when you export or invest in the foreign market → 𝐵 = 𝐵𝐼 ℓ = 𝐵ℓ. This simplifies the computation of the slope of the maximum profits (derivative of the maximum profits in each market/firm combination) with respect to the productivity parameter 𝜗. The slope of the profit function under exporting will depend on market conditions (B) and the transport costs (𝜏). This computation will result in being the same for both markets. It follows that: 𝜕𝐷?̂?𝑗 𝜕?̃? = 𝐵; 𝜕 𝜋𝑋 ̂ 𝑗 ℓ 𝜕?̃? = 𝜏1−𝜀𝐵ℓ = 𝜏1−𝜀𝐵; 𝜕 𝜋𝐼 ̂ 𝑗 ℓ 𝜕?̃? = 𝐵𝐼 ℓ = 𝐵 Let 𝑓𝐼 > 𝜏 𝜂−1𝑓𝑋 > 𝑓𝐷 The slope of the firm exporting is lower, because of transport costs. However, investing abroad entails larger fixed costs than exporting (because we’re giving up concentration benefits). Therefore the profit function from investing abroad has a smaller intercept than the profit function resulting from exporting (but it grows faster). 10 Brainard, Lael S. 1997. “An Empirical Assessment of Proximity-Concentration Tradeoff between Multinational Sales and Trade.” American Economic Review 87: 520-544 11 Yeaple, Stephen S. 2003. “The Role of Skill Endowments in the Structure of U.S. Outward Foreign Direct Investment.” Review of Economics and Statistics 85: 726- 734 65 The solution: in 2008 and 2009 Boeing acquired operations from its suppliers; see Antras (2015), p.175. They bought out the joint venture with Augusta, and other companies. They brought production in house buying their own suppliers (an example of vertical integration). However, to solve the same kind of problem (lack of profitability) Sony sold its majority stake to cover the cost. Why Sony disinvested? In 2010 Sony sells its majority stakes in a number of LDC TV plant to cut fixed costs and turn around loss-making TV operations; see Antras (2015), p.176 Contracts are incomplete but internalization (handing of the contract) is no easy solution! It’s contract incompleteness that shapes organizational and locational choices. Why contract incompleteness shapes organization? Two approaches: The Transaction-Cost Approach (Coase/Williamson) Since market transactions are costly, it makes sense of thinking of vertical integration (which removes the transaction on the market, instead of buying the input on the market you produce it yourself). Which kind of costs are involved in market transactions? Market transactions entails costs because: • Agents are boundedly rational (hence contracts are incomplete). There are limitations in our languages, we are not able to make inferences about the future, or for specific contingencies, etc. • Agents act opportunistically (self-interest seeking with guile; contract incompleteness has efficiency consequences; the hold-up problem). • Assets are relationship-specific (breeding ground for opportunism) Therefore, there will be efficiency costs in transactions. The buyer can keep inside the production of some inputs, but will not produce them at the lowest possible cost on the market (for example FCA keeps inside 10- 30% of the production of parts). Moreover, the more specific to the parties is the transaction (in terms of output/inputs required) the more scope there is for opportunistic behavior. Contract incompleteness opens the way for this kind of behavior: parties want to protect themselves from opportunism subscribing some kind of insurance policy. This, as any kind of insurance, entails an efficiency loss. But: why we still use the market?! Why don’t we just go for vertical integration always? Firms suffers from governance costs. These include: - A shortage of managerial oversight (why not to hire more of the same?), less effective in controlling activities. There is a loss in terms of incentives: if what matters is not the outcome but the full respect of procedure. - Bureaucratic costs of governance: lack of incentives This approach is convinving for vertical integration. On the other side, it’s not for the other part of the story. For example, discuss the cost of vertical integration: it comes from a very different source. For example: why don’t you employ more managers if you lack managerial oversight? Moreover, within companies there are lots of incentives for people to behave in line with the rules. These are the bases for the “property rights approach”. The Property Rights Approach (Coase/Grossman-Hart-Moore): Why should the contractual frictions affecting nonintegrated entities disappear under integration? Intra-firm relationship are not governed by all-encompassing contracts. If we think of a firm with its divisions, we know 66 that these bargain with the central site for the allocation of resources (which are divided between different projects). Or, a bargain among the units. So, contractual frictions are present within the firm too. What are they governed by then? Ownership is key. Ownership confers the right to decide on the deployments of assets in all contingencies not covered by contracts. It allocates what we call the residual property rights. Suppose, for example, there is a disagreement between the headquarters and the head of a unit, and there is no contract ruling over the disagreement. The headquarter has the power of firing the head of the unit. This is not the case of outsourcing: the company cannot separate the supplier from the asset in case of disagreement, because it’s not a part of my company. The consequence is that the value of the transaction depends on the investment the party does to increase the surplus of trade. In case of ownership, the incentive to invest in the asset falls because you can’t be separated from the asset (and consequently from the return). Ownership affects incentive to invest of the parties and thus overall surplus from trade. References to the original contributions to the theory of the firm Coase, R. (1937), The Nature of the Firm, Economica, 386-405. ➢ Coase, R. (1988b), The Nature of the Firm: Origin, Journal of Law, Economics &Organization, 3-7. ➢ Coase, R. (1988a), The Nature of the Firm: Meaning, Journal of Law, Economics &Organization, 19- 32. ➢ Coase, R. (1988a), The Nature of the Firm: Influence, Journal of Law, Economics &Organization, 33- 47. Grossman, S. e O. Hart (1986), The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration, Journal of Political Economy, 691-719. Williamson, O. (1985), The Economic Institutions of Capitalism, Free Press, New York. We adopt the Property Right Theory (PRT) of the firm. The O&L choice Reference work: Antràs, Pol and Elhanan Helpman. 2004. “Global Sourcing.” Journal of Political Economy 112: 552-580. See also in the Reading material: • Antras (2015), Chapter 7 • Helpman (2010), Chapter 6 • Helpman (2006) • Antras (2014) Firm j produces a differentiated good Demand side: The demand function is: 𝑥𝑗 = 𝐴 (𝑝𝑗 −𝜂) 𝑝𝑗 = ( 𝑥𝑗 𝐴 ) − 1 𝜂 = ( 1 𝐴 ) − 1 𝜂 𝑥 𝑗 − 1 𝜂 67 Supply side: Production requires two inputs: ➢ ℎ𝑗: head-quarter services; ➢ 𝑚𝑗: intermediate input B(uyer) only can produce of head-quarter services; one unit of head-quarter service requires one unit of labour → producer of the final good and it is the only one to be able to produce hj S(eller) only can produce the intermediate input; one unit of intermediate input requires one unit of labour Note: S can be: • An employee of B: vertical integration/internal procurement • A supplier of B: outsourcing/external procurement Full relationship-specificity: both inputs are taylor-made: their value for a firm different from j is zero. We assume full relationship-specificity: the inputs have no value outside the relationship. Both inputs are taylor-made: their value for a firm different from j is zero. Basically I’m normalizing their outside option, whatever it is, to zero. Production function: 𝑥𝑗 = 𝜗𝑗 ( ℎ𝑗 𝛾 ) 𝛾 ( 𝑚𝑗 1 − 𝛾 ) 1−𝛾 where: - 𝜗𝑗 is a firm specific productivity parameter; - 0 ≤ 𝛾 ≤ 1 relates to factor intensity: the larger 𝛾, the more h-intensive is production Depends on the two inputs (h, m). Both are essential for production. So, generally speaking, if one of the two is 0 it could be a problem. Second: the weight of h and m in the production function may not be the same. Factor intensity, therefore, may vary: I capture this factor intensity with the parameter 𝛾. Note that, if 𝛾 = 1, then only h matters since m will be powered to 0, and therefore will be equal to 1. If it’s equal to 0, then only m matters. 𝜗 is the productivity parameter: the larger it is, the larger is x. Therefore, the more productive the firm will be in the use of inputs. We can write the revenues of firm j as a function of inputs: 𝑅𝑗 = 𝑝𝑗𝑥𝑗 = ( 1 𝐴 ) −1/𝜂 𝑥𝑗 −1/𝜂 𝑥𝑗 = ( 1 𝐴 ) −1/𝜂 𝑥𝑗 𝜂−1/𝜂 = ( 1 𝐴 ) −(1−𝛼) 𝑥𝑗 𝛼 = 𝐴(1−𝛼) [𝜗 ( ℎ𝑗 𝛾 ) 𝛾 ( 𝑚𝑗 1 − 𝛾 ) 1−𝛾 ] 𝛼 ≡ 𝑅𝑗(ℎ𝑗; 𝑚𝑗) Total revenues can be written as a function of inputs (h, m). However, let’s assume the characteristics of h and m cannot be defined ex-ante, therefore it’s not possible to define conditions and a price for h and m. 70 Why is that? The larger the revenues share, the larger the marginal benefit of supplying the input. Is that enough to choose? The answer is no. Absent financial constraints (i.e. parties can use transfer payments), parties trade property rights over assets (under vertical integration, B buys assets from S) to produce under the regime that maximizes total surplus from trade. If there are benefits to be obtained when choosing, then the market is able to recognize this potential and will provide finance to the parties to make the deal. Think of mergers and acquisitions: control rights are given up for some assets from one firm to another. 90% of the times, they don’t pay in cash, they search for credit on the financial markets. These provide credit when the deal is considered stable and favorable. Parties identify the value of 𝛽 that maximizes trade surplus and select the regime whose allocation of revenues is closer to the optimal one. (Change in trade surplus = change in willingness to provide inputs). To identify the optimal 𝛽 the parties solve: 𝑚𝑎𝑥 𝛽 𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 ℎℎ𝑗(𝛽) − 𝑤 𝑚𝑚𝑗(𝛽) s.t. ℎ𝑗(𝛽) = 𝑎𝑟𝑔 𝑚𝑎𝑥 ℎ𝑗 𝛽𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 ℎℎ𝑗(𝛽) 𝑚𝑗(𝛽) = 𝑎𝑟𝑔 𝑚𝑎𝑥 𝑚𝑗 (1 − 𝛽)𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 𝑚𝑚𝑗(𝛽) I look for the β that maximizes the input, under the constraint that the values of h, m must be so that the seller and buyer maximize the payoff of both. Therefore, for any β, find the values of h, m that maximize payoffs. To identify the optimal β I need to identify how the buyer and the seller react to β: this is what I find when considering FOCs. Consider first the FOC to determine input supply: 1) The buyer: 𝑚𝑎𝑥 ℎ𝑗 𝛽𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 ℎℎ𝑗(𝛽) FOC: 𝛽 𝜕𝑅𝑗 𝜕ℎ𝑗 − 𝑤ℎ = 0 2) The seller: 𝑚𝑎𝑥 𝑚𝑗 (1 − 𝛽)𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 𝑚𝑚𝑗(𝛽) FOC: (1 − 𝛽) 𝜕𝑅𝑗 𝜕𝑚𝑗 − 𝑤𝑚 = 0 Assume S.O.C to be satisfied. 71 Now turn to the objective function and the choice of beta. Now we search for the value of β for maximization: 𝑚𝑎𝑥 𝛽 𝑅𝑗 (ℎ𝑗(𝛽); 𝑚𝑗(𝛽)) − 𝑤 ℎℎ𝑗(𝛽) − 𝑤 𝑚𝑚𝑗(𝛽) Apply the chain rule of derivation. If h is insensitive to beta, if you change beta then R won’t change. Is the combination of the two that brings a change in R when we have a change in beta. When I change beta there will also be an effect on the cost size: will bring about a change in h, which will in turn bring a change in total cost. FOC: [ 𝜕𝑅𝑗 𝜕ℎ𝑗 𝜕ℎ𝑗 𝜕𝛽 − 𝑤ℎ 𝜕ℎ𝑗 𝜕𝛽 ] + [ 𝜕𝑅𝑗 𝜕𝑚𝑗 𝜕𝑚𝑗 𝜕𝛽 − 𝑤𝑚 𝜕𝑚𝑗 𝜕𝛽 ] = 0 [ 𝜕𝑅𝑗 𝜕ℎ𝑗 − 𝑤ℎ] 𝜕ℎ𝑗 𝜕𝛽 + [ 𝜕𝑅𝑗 𝜕𝑚𝑗 − 𝑤𝑚] 𝜕𝑚𝑗 𝜕𝛽 = 0 . But we know that at the equilibrium: 𝛽 𝜕𝑅𝑗 𝜕ℎ𝑗 = 𝑤ℎ; (1 − 𝛽) 𝜕𝑅𝑗 𝜕𝑚𝑗 = 𝑤𝑚 Substituting above we obtain: [(1 − 𝛽) 𝜕𝑅𝑗 𝜕ℎ𝑗 ] 𝜕ℎ𝑗 𝜕𝛽 + [𝛽 𝜕𝑅𝑗 𝜕𝑚𝑗 ] 𝜕𝑚𝑗 𝜕𝛽 = 0 Therefore, the FOC is the sum of the two square brackets equal to zero. From the above equation we obtain the ratio of the optimal shares. we express it in terms of elasticities of revenues to inputs and inputs to share in trade surplus: 𝛽 ∗ 1 − 𝛽 ∗ = 𝜕𝑅𝑗 𝜕ℎ𝑗 𝜕ℎ𝑗 𝜕𝛽 − 𝜕𝑅𝑗 𝜕𝑚𝑗 𝜕𝑚𝑗 𝜕𝛽 = ( 𝜕𝑅𝑗 𝜕ℎ𝑗 ℎ𝑗 𝑅𝑗 ) ( 𝜕ℎ𝑗 𝜕𝛽 𝛽 ℎ𝑗 ) − ( 𝜕𝑅𝑗 𝜕𝑚𝑗 𝑚𝑗 𝑅𝑗 ) ( 𝜕𝑚𝑗 𝜕𝛽 𝛽 𝑚𝑗 ) ≥ 0 The ratio depends on the sensitivity of the inputs to the share and (???). What matters is how total revenue respond to h, and eccetera. The ratio of the optimal shares is given by ratio of the elasticity of (???). Food for thought: 𝛽 ∗ 1 − 𝛽 ∗ = 𝜕𝑅𝑗 𝜕ℎ𝑗 𝜕ℎ𝑗 𝜕𝛽 − 𝜕𝑅𝑗 𝜕𝑚𝑗 𝜕𝑚𝑗 𝜕𝛽 = ( 𝜕𝑅𝑗 𝜕ℎ𝑗 ℎ𝑗 𝑅𝑗 ) ( 𝜕ℎ𝑗 𝜕𝛽 𝛽 ℎ𝑗 ) − ( 𝜕𝑅𝑗 𝜕𝑚𝑗 𝑚𝑗 𝑅𝑗 ) ( 𝜕𝑚𝑗 𝜕𝛽 𝛽 𝑚𝑗 ) ≥ 0 72 Why is the ratio positive? Can 𝛽 ∗ be larger than 1? No, since the buyer is willing to provide a lot of h, but the seller is not willing to provide m. Can 𝛽 ∗ be equal 1? No, since the buyer won’t provide any input (h). The optimal 𝛽 is a function of the elasticity of revenues with respect to input and the elasticity of input with respect to the share in surplus. a) The larger the revenues elasticity wrt to head-quarter service [intermediate input], the larger the relative share of trade surplus to assign to B [S]. b) The more sensitive is the supply of head-quarter service [intermediate input] to the surplus share, the larger is the relative share of trade surplus to assign to B [S]. How do we reconcile this story with the previous GHM model? 1) The GHM model predicts that control rights are assigned to the party whose investment matters the most in generating total surplus. In our model, this translates into result a. 2) The allocation of control is responsive also to the sensitivity of input supply to the parties’ bargaining power, that is: result b. It matters to allocate control when you change your decision in relation to the share you get. How the a result and the b results interact? To make progress, let us turn to our specific functional form for revenues. Under the latter, we can solve for the optimal 𝛽: 𝛽 ∗= 𝛾(𝛼𝛾 + 1 + 𝛼) − √𝛾(1 − 𝛾)(1 − 𝛼𝛾)(𝛼𝛾 + 1 − 𝛼) 2𝛾 − 1 As we 𝛽 ∗ is a function of the demand parameter 𝛼 (parameter capturing the conditions of demand, and therefore the elasticity for the good with respect to its own prices) and factor intensity 𝛾. Gamma captures the relative importance of h and m in generating total revenues: therefore, the relative importance of the buyer and the supplier. If h is very important in generating total revenues, you must pay a lot of attention to the behavior of the buyer, and want to incentive the buyer to provide h. Same on the side of the seller, if m is relatively more important. Therefore gamma → ability to generate value from trade. Given 𝛼, we can draw 𝛽 ∗= 𝑓(𝛾). 𝛽∗ is an increasing function in 𝛾 (not linear). Let me choose two arbitrary values of 𝛾 along the horizontal axis. 𝛾𝐿 stands for gamma low, and the other for gamma high. 𝛾 Figure 1 75 Figure 3 Again, the profit function for vertical integration starts from a lower intercept, but grows faster, it’s faster in generating revenues! Only the most productive firms opt for vertical integration, and this is something we could have guessed since vertical integration has higher fixed costs than outsourcing (high productivity allows you to charge lower prices, so that you cover a large market share, and you can easily spread your costs on a larger number of units, low average cost). Consider now the L(ocation) choice. Suppose V&N (therefore, that the firm supports the choice, because of its value of 𝜗, of vertical integration in the north). Increase the productivity parameter 𝜗: what’s the impact on L? Our firm will be able to cope with even larger fixed costs, therefore considers moving South, since this location choice entails taking advantage of lower variable costs. Shall we observe V&S? Only for large increases in the productivity parameter! For small changes we observe O&S. Figure 4 We have a switch in O following a change in L! The important thing is that organizational choices go hand in hand with locational changes, there are switches → the two choices are jointly determined! 76 So far: 𝑓𝑆 𝑉 > 𝑓𝑆 𝑂 > 𝑓𝑁 𝑉 > 𝑓𝑆 𝑂 . Does it make sense? We can discuss on this, but we take these as empirican evidences, exogenously determined. However… What if 𝑓𝑖 𝑉 < 𝑓𝑖 𝑂 , 𝑖 = 𝑁, 𝑆? The predictive value of our model wouldn’t change. Simply, we would observe that low productivity firms opt for vertical integration; as productivity increases we observe: ➢ External procurement & domestic sourcing; ➢ Internal procurement & foreign sourcing; ➢ External procurement & foreign sourcing. In other words: a reversal of our bins in figure 4. Empirical evidence: • Yeaple, Stephen S. 2006. “Offshoring, Foreign Direct Investment, and the Structure of U.S. Trade.” Journal of the European Economic Association (Papers and Proceedings) 4: 602-611: • Nunn, Nathan and Daniel Trefler. 2008. “The Boundaries of the Multinational Firm: An Empirical Analysis,” in Elhanan Helpman, Dalia Marin and Tierry Verdier (eds.). The Organization of Firms in a Global Economy (Cambridge, MA: Harvard University Press) • Kohler, W. and M. Smolka. 2014. Global Sourcing and Firm Selection, Economics Letters, 124: 411-415. • Defever, Fabrice and Farid Toubal. 2013. “Productivity, Relation-Specific Inputs and the Sourcing Modes of Multinational Firms.” Journal of Economic Behavior & Organization, 2013, Vol 94, p. 245- 35 Data: survey of French firms. In these surveys, managers report 𝑓𝑖 𝑉 < 𝑓𝑖 𝑂 , 𝑖 = 𝑁, 𝑆. Consistently with the model, firms opting for outsourcing&offshoring are 20% more productive than firms opting for vertical integration&offshoring. 77 Lecture 7 Trade policies when contracts are incomplete “The rise of offshoring raises important questions for commercial policy. Do the distinguishing features of offshoring introduce novel reasons for trade policy intervention? Does offshoring create new problems of global policy cooperation motivating international agreements with novel features? Can trade agreements that are designed to address problems that arise when trade is predominantly in final goods still perform in a world where offshoring is prevalent?” Antràs, P. and R. Staiger (2011) Offshoring and the Role of Trade Agreements, American Economic Review WTO was a system of rules designed when trade was trade of final goods. Now we are in a world where trade is trade of inputs: that’s the meaning of offshoring. The WTO world is one in which prices are set in a competitive way, while the model we are going to analyse is one in which prices are set in a non-competitive way, through a bargaining. In a world of perfect competition, whatever the condition in which you are, you can start bargaining with a partner and if you’re not satisfied you can move away to someone else. The model we’re analysing is one in which parties are blocked in a situation → there is competition ex ante (large number of buyers, large number of sellers) but once they are matched one to the other competition is fixed (→ trade goods that are relation-specific, prices are not set according to the rule of perfect competition). The model: Consider a three-country world: ➢ H(ome): it is a small country ➢ F(oreign): it is a small country ➢ R(est of the world): it is a large country Both H and F have no bargaining power in setting the prices (this is why they are small), and we need a third big country to make a whole world (which cannot be made up of two small countries only). Small country → demand and supply conditions that do not affect the market price. In each of the countries, and in the rest of the world, there are only two goods in these economies: 0 and 1. Good 0 is the numeraire; it is traded at no cost across countries; it is available in quantities such that it is always consumed in positive amounts. → idc about good 0 In H good 1 is produced by B(uyer) and traded on the world market at a price equal 1 (remember: H is a small country and its supply and demand cannot affect the price of good 1). Good 1 is produced by means of an input, m. The (concave) production function for good 1 is x(m), where m is a taylor-made and non- contractable input. The production function, being concave, is increasing at a decreasing rate. m is produced in F only by supplier S and exported to H. Vertical integration is ruled out (in this lecture we are not interested in organizational choices). → the only way to obtain m is to outsource it for the buyer. Timing: ➢ in t =1, B e S are matched ➢ in t = 2, S produces m at marginal cost 1 ➢ in t= 3, B and S bargain over the division of the surplus from trading with each other, their outside option being zero and dividing the surplus according to NBS (non-bargaining solution), with B’s bargaining power equal to 𝛽 (share of surplus). ➢ in t = 4, B imports m (if they reach an agreement in period 3). 80 In fact, efficiency requires to subsidize the production of m and this can be achieved by trade policies. Which trade policy will restore efficiency in the supply of m? Obviously, a subsidy for m. You will try to reduce the cost of producing m for the seller. We can achieve this subsidy through trade policies → trade policies can restore efficiency in the production of m. What we call a “subsidy” is indeed a tax, because the word “tax” is a general expression. A tax can be negative or positive. For example, if I pay 2000 in taxes for university, but I cost 6000, the university is indeed subsidizing (education is fully subsidized) → a negative tax is a subsidy. If it’s positive, keep calling it tax. H and F can apply taxes con good m. Choice variables: ➢ tax on m imports in H: 𝜏𝑚 𝐻 → firms in H import m ➢ tax on m exports from F: 𝜏𝑚 𝐹 → firms in F export m The signs of these 𝜏 can be positive or negative (respectively, a tax or a subsidy). If 𝜏𝑚 𝐻 is negative, everytime the good enters the country, the supplier gets money back. 𝜏 can be: 𝜏𝑚 𝐻 > 0: tariff on imports in H 𝜏𝑚 𝐻 < 0: subsidy to imports in H 𝜏𝑚 𝐹 > 0: tax on exports from F 𝜏𝑚 𝐹 < 0 subsidy to exports from F Each country selects their taxes on m: but they have to do so to correct undersupply → supply of m is sensitive to the taxes on m: which taxes on m will deliver the ideal value of m? which set of 𝜏s (→ which trade policy) will equate ?̂? to m*, making sure that we’re producing the ideal amount of m? We want to identify the values of 𝜏𝑚 𝐻 and 𝜏𝑚 𝐹 - if any - such that: ?̂? = 𝒎 ∗ Call 𝝉 the sum of 𝝉𝒎 𝑯 and 𝝉𝒎 𝑭 . Economic intuition tells me that this will be a subsidy. To answer the question to what level of tau equates ?̂? = 𝑚 ∗, I need to understand what is the reaction of S to a generic level of 𝜏 (its rule of behavior). S selects m to solve: 𝑚𝑎𝑥 𝑚 𝜋𝐹 = (1 − 𝛽)[𝑥(𝑚(𝜏)) − 𝜏𝑚(𝜏)] − 𝑚(𝜏) Therefore, to maximize a share (1 − 𝛽) compared to its total cost. However, m is now a function of 𝝉. For any unit of m produced, S will be taxed by an amount 𝜏. From total revenues [𝑥(𝑚(𝜏))] I have to take away the amount he has to pay because of 𝜏 [−𝜏𝑚(𝜏)]. If 𝜏 turns out to be a subsidy, total revenues will be higher than before. All minus the total cost of producing m [−𝑚(𝜏)]. 81 F.O.C. (1 − 𝛽) [ 𝜕𝑥(𝑚) 𝜕𝑚 − 𝜏] − 1 = 0 (1 − 𝛽)[𝑥(𝑚(𝜏)) − 𝜏𝑚(𝜏)] − 𝑚(𝜏) = (1 − 𝛽)[𝑑𝑥 ∕ 𝑑𝑚 − 𝜏] = 0 In other words: m production goes up, but also the tax associated to m. We can rewrite as: (1 − 𝛽) 𝜕𝑥(𝑚) 𝜕𝑚 = 1 + 𝜏(1 − 𝛽) ➢ Left Hand Side: marginal benefit from m → what I get if I produce one extra unit of m +𝜏(1 − 𝛽), since this extra unit will rise to taxation, affecting total surplus in relation to the share. ➢ Right Hand Side: marginal cost of m, increasing in 𝜏. Remember that ?̂? < 𝑚 ∗; undersupply can be corrected by reducing the marginal cost of m, that is acting on 𝜏. From previous computations we know that: • ?̂? solves 𝜕𝑥(𝑚) 𝜕𝑚 = 1 (1−𝛽) + 𝜏 • 𝑚* solves 𝜕𝑥(𝑚) 𝜕𝑚 = 1 ?̂? = 𝑚* if and only if the righten side in the first expression is equal to the righten side in the second: 1 (1−𝛽) + 𝜏 = 1 → I can fully correct undersupply if I find a value for 𝜏 such that this equation holds true Thus I can solve this equation for 𝜏, which will give be the optimal 𝜏, that is the optimal coordination of 𝜏𝑚 𝐻 and 𝜏𝑚 𝐹 (a subsidy, being negative): 𝜏 ∗= −𝛽 (1 − 𝛽) < 0 As long as the combination 𝜏𝑚 𝐻 and 𝜏𝑚 𝐹 is negative (subsidy), trade policy fully correct the undersupply. → any combination of 𝜏𝑚 𝐻 and 𝜏𝑚 𝐹 such that it is negative, is optimal (one of the two taus can be positive, as long as the other one is negative and small enough (greater in absolute value?), to make sure that the final sum is negative). → the larger is 𝛽, the smaller will be 𝜏; → free trade is no longer optimal: if 𝜏 = 0 we would have undersupply of m → 𝝉 needs to be negative! 𝜏∗ = −𝛽 (1 − 𝛽) < 0 𝜏 = 𝜏𝑚 𝐻 + 𝜏𝑚 𝐹 < 0 82 → if beta is large market conditions are such that the buyer gets a lot and we need to make sure that its share diminishes in favor of the seller by setting greater subsidies. In the presence of incomplete contracts (the price of m is set in a non-competitive fashion) free trade is no longer optimal. Governments in action Consider the governments in countries H and F and allow them to set their own 𝜏. Can governments acting non-cooperatively achieve the efficient outcome? → can they independently generate the optimal 𝜏 by setting their owns independently? No, since each country is not taking into account the benefit to the other country, acting only on its own private interest. We know that the answer is negative because each government ignores the benefits and costs its actions impose on the other country. 𝜏𝑚 𝐹 + 𝜏𝑚 𝐻 > 𝜏∗→ governments fail to subsidize, since they choose levels of 𝜏 too small (they don’t subsidize enough/they tax too much) because they’re under the pressure of local producers → consumers would benefit for right subsidy, but producers don’t benefit equally from subsidies, and at the end of the day they have a “louder voice” in affecting governments decisions. For “producers” we don’t simply mean the owners, but also the unions, being behind trade policies (an example are the US). Industries are well aware of the costs and benefits of trade competition, which is a different consciousness than the one possessed by the consumers. Policies adopted by governments (the Nash equilibrium of the game in taxes) are suboptimal. In particular, governments fails to provide a subsidy large enough to obtain the optimal level of m. The reason is simple: countries do not internalize the consequences of their policy actions on aggregate welfare. How can gov’s tie their hands? Sign a trade agreement! RTA and FDI So far, we dealt with normative analysis (regarding the implementability of policies, what we should do), but now we want to turn to a positive analysis. Recent years have been marked by proliferation of preferential trade agreements: many countries have signed regional agreements, for example (NAFTA, MERCOSUR between south American countries, the Trans- Pacific Trade Agreement). These are regional in nature: the literature has long debated the trade creation and trade diversion effects of regional agreements. However, RTA have effects also on FDI and given our interest in the organizational and location choices by firms in global markets, we devote some attention to the impact of trade policies on FDI. Do these agreements increase trade, or just divert trade? In this latter case, they would just be distorting relations among countries and opposing free trade. Regional trade agreements have an impact also on the decision to invest abroad → impact on FDI. Our work of reference is: Antràs, Pol, and Fritz C Foley. 2011. “Regional Trade Integration and Multinational Firm Strategies,” In Robert J. Barro and Jong-Wha Lee (eds) Costs and Benefits of Economic Integration in Asia. Oxford, New York: Oxford University Press. Consider a world made of three countries: W(est), E(ast), S(outh). Firm j is headquartered in the West and it produces a differentiated good. Firm j faces the following demand function in market/country ℓ: 85 c) Affiliates surviving after a RTA is signed are no smaller (in terms of sales) than affiliates operating before the introduction of a RTA: Survival of affiliates in both markets requires high productivity and implies large market shares; affiliates surviving in just one location are the outcome of concentration strategy. Empirical evidence supports the prediction of the model. Appendix 1 Write the F.O.C. at ?̂?: (1 − 𝛽) 𝜕𝑥(?̂?) 𝜕?̂? − 1 = 0 Multiply the L.H.S and R.H.S by ?̂?: ?̂? [(1 − 𝛽) 𝜕𝑥(?̂?) 𝜕?̂? − 1] = 0 Consider now: (1 − 𝛽)𝑥(?̂?) − ?̂? Factor out ?̂?: ?̂? [ (1 − 𝛽)𝑥(?̂?) ?̂? − 1] Since 𝑥(?̂?) is concave, 𝑥(?̂?) ?̂? > 𝜕𝑥(?̂?) 𝜕?̂? . Thus: ?̂? [(1 − 𝛽) 𝑥(?̂?) ?̂? − 1] > ?̂? [(1 − 𝛽) 𝜕𝑥(?̂?) 𝜕?̂? − 1] However, ?̂? [(1 − 𝛽) 𝜕𝑥(?̂?) 𝜕?̂? − 1] = 0 It follows that: ?̂? [ (1−𝛽)𝑥(?̂?) ?̂? − 1]>0 86 Lecture 8 Capital Markets and Cross-Border Operations We have already discussed the interaction btw capital market imperfections and export choice when we addressed the issue of contractual imperfections in the context of the Melitz model of exports (Do you remember Poultry in motion?). We now turn to discuss the interaction btw capital market imperfections and the decision to engage in activities abroad, i.e to become a MNE/to undertake FDI. We go through a model that uses the same kind of reasoning of our previous discussions to the decision to invest abroad. If you like, it is once again contract incompleteness &organizational choice, where by organizational choice we refer to the choice btw FDI and licensing. Definition of MNE: According to the IMF/OECD definitions: FDI is an investment in a foreign company in which the investor owns at least 10 percent of the ordinary shares, undertaken with the objective of establishing a lasting interest in the country, a long-term relationship, and significant influence on the management of the firm. Our reference work on the topic is: Antràs, Pol, Mihir A. Desai and C. Fritz Foley, 2009, “Multinational Firms, FDI Flows, and Imperfect Capital Markets”, Quarterly Journal of Economics, 1171-1219. The model Consider a world with two countries: Home (H) and Foreign (F). Consumers have identical preferences across countries. Firm j from H considers entering market F to supply quantity q of the differentiated good g sold in F in an imperfectly competitive market. Selling goods on market F generates, obviously, rebenues. Revenues from the sale of g in F are: 𝑅(𝑞) such that 𝑅(0) = 0 𝑅′(𝑞) > 0 𝑅″(𝑞) ≤ 0 Total revenue is increasing at a decreasing rate. Elasticity of the revenues function w.r.t to quantity is constant and above unity (larger than one): 𝜓 > 1. Production of g requires to invest in capacity (therefore, to set up a plant). Investment x in capacity translates into production q → investment in capacity increases output, increasing function. Thus we write: 𝑅(𝑞(𝑥)) = 𝑅(𝑥). Good g is non-tradable: production must take place in F, for the assumption of perishable good. If you want to export in F, you have to set up a plant there. The technology to produce good g is patented; the patent holder lives in H and we call him Inventor or GG (Gyro Gearloose). Production of g in F is carried out by a local firm (LF), therefore GG has no interest in moving to F to start producing there, because the patent can be applied to produce the good in many different markets. GG can’t move to H (suppose he wants to serve more than one mkt). GG can • license the technology to LF (the local firm pays a royalty) • or he can invest in LF (GG has a share in the local firm) 87 When the latter? Undertake FDI means to own at least 10% of shares affecting in this way the management of the firm. Which alternative will prevail between licensing and investing? Is not only a choice for GG, I’m asking the question “how is going production in the foreign market be financed’”, because this would involve investors. LF has no personal wealth/retained earnings: 𝑊𝐿𝐹 = 0. Therefore, there is no way in which LF can provide capital to finance this enterprise. LF must turn to the capital market if it wants to set up production. Assume that in F there are n (large) small investors. They are constrained to invest in F. They can choose btw: i) Investing in asset j which returns 𝑏 = 1 for each invested euro; ii) Investing in the production of g. GG has personal wealth/retained earnings: 𝑊𝐺𝐺 > 0. GG can invest in H or F. • If in H, GG obtains 𝛽𝑊𝐺𝐺 > 𝑊𝐺𝐺. So, the technology available for investing in H perform better than the technology for investment in F. All parties are risk-neutral and act under limited liability. We assume there is a moral hazard problem: investing in a country requires the support of a local entrepreneur (manager). This local has his own agenda, and this agenda does not coincide with the one of GG → divergent objectives between the manager and the owner of a company. The effort of the manager has to be incentivized, otherwise there could be a contrast of interest between the owner and the manager. Suppose LF can take two different actions. Success of the venture depends on a non-contractible action a that only LF can undertake. He chooses an effort that can be either ?̅? (high level of effort) or 𝑎 (low level of effort): → If 𝒂 = 𝒂: • with probability 𝑝𝐻, the revenues are 𝑅(𝑥) [→ total revenues of the invested quantity x] • with probability (1 − 𝑝𝐻), the revenues are zero; • thus, expected revenues/cash flow is 𝑝𝐻𝑅(𝑥) →If 𝒂 = 𝒂: • with probability 𝑝𝐿 < 𝑝𝐻, the revenues are 𝑅(𝑥) • with probability (1 − 𝑝𝐿) > (1 − 𝑝𝐻), the revenues are zero; • thus, expected revenues/cash flow is 𝒑𝑳𝑹(𝒙) < 𝒑𝑯𝑹(𝒙) [high level of effort generates higher probability of success] However, if 𝒂 = 𝒂, LF enjoys private benefit 𝑩𝑹(𝒙), assumed to be proportional to total revenues. We assume that LF can divert the fraction B of revenues. There are a number of situations in which the choice of 𝑎 may result in the loss of private benefits for LF → as a consequence, 𝑎 is not beneficial for the venture, but may be beneficial given other activities that LF could be conducting in other ventures or on his own. Fraction B is a function of the degree of legal protection granted to investors in F and the governance of the local firm. LF is expropriating the investors of this company (the subjects entitled to R). Therefore the size of B depends on the legal protection enjoyed by investors in the foreign country. In some countries, for example, you don’t have provisions for the separation of the roles of CEO and Chairman of the board of investors, therefore there is no internal oversight (not providing the ideal governance for the company) Let 0 < 𝜸 < 1 be a parameter measuring legal protection for investors: I assume 𝐵 = (1 − 𝛾) and thus 𝐵𝑅(𝑥) is decreasing in legal protection. So: the higher is 𝛾, the lower is the share of R that LF is able to appropriate. Moreover, rules are not enough for LF not to appropriate. 90 So, the first two addenda capture the positive entries, minus the cost of monitoring → if the value of investment is positive. If he doesn’t invest, there is no cost of monitoring. Which are the constraints? We solve this problem such that: 1. feasibility constraint: 𝑥 ≤ 𝐸 + 𝐼. The amount raised to finance this venture must be enough to cover the amount investment (capacity) selected for the venture. If x is the investment in the venture, it must be that E + I (the resources made available for this venture) are at least as large as x. 2. small investors’ participation constraint: 𝑝𝐻𝜑𝐸𝑅(𝑥) ≥ 𝐸. Small investors will provide E as long as the expected revenue is larger than what they could get investing locally (in local assets that at the end of the year will give them back their capital). They, in their country, can always get E. They will invest if the amount given by the venture is at least as large than E, than investing in the primitive technology that they got. They will get 𝑝𝐻𝜑𝐸𝑅(𝑥), E is what they can get in the alternative investment (the safe asset). 3. LF’s participation constraint: 𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ 0. The value of the outside option for LF is normalized to 0 (important that is a constant, not affected by any of the elements in my model). LF can choose between the outside option (getting 0) or going for the venture, that will give him a share 𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥). 4. LF’s incentive constraint: 𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ 𝑝𝐿(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) + (1 − 𝛾)𝛿(𝐶)𝑅(𝑥) (𝑝𝐻 − 𝑝𝐿)(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ (1 − 𝛾)𝛿(𝐶)𝑅(𝑥) If LF works hard, he’s going to miss out on his private benefit: so there are no private benefits associated to ?̅?. However, selecting 𝑎 he’s going to sacrify expected revenues (decreased probability of success → from 𝑝𝐻 to 𝑝𝐿). Therefore we have the first portion of the constraint: 𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ 𝑝𝐿(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥). But, if he puts on little effort he will get private benefits, which are B𝑅(𝑥), and we know that B depends on (1 − 𝛾)𝛿(𝐶), therefore +(1 − 𝛾)𝛿(𝐶)𝑅(𝑥). If I want LF to behave, it must be true that the leften side (selecting ?̅?) is at least as profitable as choosing a low level of effort. All my variables are chosen so that he’s compatible with the incentive given. In the second equation, I rearranged the first one so to relate everything to private benefit. I’m comparing the change that the share of total revenues with behaving and misbehaving, with the private benefit from misbehaving. 5. GG’s incentive constraint: 𝑝𝐻𝜑𝐺𝐺𝑅(𝑥) − 𝐶𝑅(𝑥) ≥ 𝑝𝐿𝜑𝐺𝐺𝑅(𝑥) (𝑝𝐻 − 𝑝𝐿)𝜑𝐺𝐺𝑅(𝑥) ≥ 𝐶𝑅(𝑥) He can do monitoring, that is costly. He will do monitoring as long as the share of large expected revenues minus the cost of monitoring is at least as the share of small expected revenues. 91 At the equilibrium16: Constraint 1: shall I raise more capital than the one I need (equation holds as an inequality) or shall I provide just the one that’s needed (hold as equality)? ?̃? = ?̃? + 𝐼 Suppose that the capital provided is higher than needed. LF will get extra cash. LF has no use for capital (i.e. for the extra cash) other than to invest in the venture. On the other hand, GG and small investors can use the extra capital to invest in their home countries. Thus, LF borrows no more than required to finance equilibrium capacity ?̃?. Constraint 2: can small investors get more than E? 𝑝𝐻?̃?𝐸𝑅(?̃?) = ?̃? Recall that the number of small investors is large, and there is just one venture. Small investors in F compete to finance the venture and thus total return equals the amounted invested. They won’t get more as they would get investing in the safe asset at home.17 Constraint 3 and 4: can they both hold? That is: 𝑝𝐻(1 − ?̃?𝐸 − ?̃?𝐺𝐺)𝑅(?̃?) = 0 and (𝑝𝐻 − 𝑝𝐿)(1 − ?̃?𝐸 − ?̃?𝐺𝐺) 𝑅(?̃?) = (1 − 𝛾)𝛿(?̃?)𝑅(?̃?) On the righten side we have the private benefit from misbehaving. On the leften side, the changing benefit from choosing ?̅? instead of 𝑎. The answer is no. For C.4 to hold as an equality, the LHS in C.3 must be positive: 𝑝𝐻(1 − ?̃?𝐸 − ?̃?𝐺𝐺)𝑅(?̃?) > 0 and (𝑝𝐻 − 𝑝𝐿)(1 − ?̃?𝐸 − ?̃?𝐺𝐺)𝑅(?̃?) = (1 − 𝛾)𝛿(?̃?)𝑅(?̃?) In other words, if we want the first equation to hold as an equality we can’t have the second equality holding. C.4 is LF’s incentive constraint. LF behaves (that is: he selects 𝑎 = 𝑎), but he enjoys a rent (his utility from the venture is above his reservation value). A rent → more than he would get outside. Moreover, he would just be indifferent between the two actions, and we assume that he chooses the one more compliant with the principles, which is 𝑎. At the end of the day, you have to compensate the local manager for giving up his discretion in the choice of 𝑎 or 𝛼: you have to provide the right incentive to the manager. Constraint 5: captures the moral hazard problem between doing monitoring or not: ?̃?𝐺𝐺 = ?̃? (𝑝𝐻 − 𝑝𝐿) The share in total revenues optimally accruing to GG is such that GG is just indifferent (no rent) btw to behave (monitor) and misbehave (not to monitor). Therefore, I’m going to give GG the smallest possible share. 16 Just discuss the equilibrium solution: for the exam, just understand the economic solution. In the appendix there is the formal demonstration using the Lagrangian (which, however, should be not asked). 17 𝑝𝐻 doesn’t have a tilde because it’s no variable, it’s a parameter. 92 Why? The larger GG’s share, the smaller the share available to compensate small investors and thus the smaller E. But funds from small investors are the cheapest. Thus, GG finds it in his own interest to receive a share in R as small as possible. This means that I’m rising capital from GG (capital provided by GG to the venture). This venture can be financed by: capital provided by GG or by the small investors. These sources have different costs. For each euro provided by a small investor, you have to give the small investor back just 1 euro. GG has the option to invest in his own country, and this provides him a beta larger than one for each euro invested → capital more expensive than the one provided by small investors. Therefore, the capital provided by the small investors won’t be that much, but it’s the cheapest. It’s also in the interest of GG to select the smallest possible share. If you get too much from GG → acquiring capital at an excessive price. Note that GG’s share in revenues is decreasing in (𝑝𝐻 − 𝑝𝐿). When 𝑝𝐻 and 𝑝𝐿 are far apart, the LF has a strong incentive to behave and thus it makes no sense to give GG a large share in revenues to secure his monitoring. Cheaper capital can be raised from small investors. GG’s share in revenues is increasing in the resources invested by GG in monitoring. Why do I keep the share of GG to the lower possible level? If the probability of failure is so high that LF will never monitor GG, involving him in the venture wouldn’t have sense. Less severe moral hazard problem → less need for monitoring Where ?̃? comes from? It depends on the benefits and costs of monitoring. The benefit from monitoring is reducing the private benefit for LF in misbehaving. Consider the benefits first. Monitoring is valuable as long as legal protection is lacking. The larger is 𝛾, the smaller 𝜕𝐵(𝐶;𝛾) 𝜕𝐶 = (1 − 𝛾)𝛿 ′(𝐶) < 0 (→ smaller marginal benefit of monitoring). The cost of monitoring is independent of the legal production. Therefore, the lower is gamma, the lower is the equilibrium cost of monitoring. More formally: the marginal cost of monitoring is constant w.r.t 𝛾. Thus, the larger is 𝛾, the less monitoring is required and thus ?̃? falls in 𝛾. To invest in the venture, GG requires at least 𝛽. The larger is 𝛽, the more costly is monitoring. Thus, GG’s share in total revenues is falling in the degree of legal protection and in the return from capital in H (𝛽). Remember the IMF definition of FDI (MNE): at least 10% of shares owned to be considered as FDI. Basically, the IMF definition is just telling us: what qualifies as FDI is a significant, not immaterial share of total revenues. What you get as equities translates into a share of total revenues. Therefore, this is the condition to be an investor. If 𝜑𝐺𝐺 must be above a threshold (e.g. 10%) to have a MNE, then there is a value of legal protection – call it 𝛾 - above which we do not observe MNEs. In other words, we can re-formulate our story as a threshold for 𝛾. In 𝛾 the share of GG into the venture will be small, immaterial. Let us now turn to ?̃?𝑬: Consider constraint 4 (𝑝𝐻 − 𝑝𝐿)(1 − ?̃?𝐸 − ?̃?GG)𝑅(?̃?) = (1 − 𝛾)𝛿(?̃?)𝑅(?̃?) 95 Fonte: Antras et al (2009). Implication: take a country with a very low legal protection, with lot of need for GG. Assume that in the same country there is a cap on the share of investment by GG (by a foreigner). In many countries the amount that foreigners are allowed to invest in a local company is cut. Now take an identical country with a high degree of legal protection and a cap on the amount that GG is allowed to invest. If you remove the cap, there will be a country in which the investment by GG will go up faster: the one in which there’s more need for GG intervention. What they do is: to look at countries in which there is a cap for foreign investment, and look at the size on the venture in those country (vertical axis, sales level). Considering a country which has low private-credit rights: when you liberalize investment (given that year 0 is the year of liberalization), sales increase both in high-protection and low-protection countries, but much faster in the latter. To conclude: “In the prior literature, MNCs arise because of the risk of a partner expropriating a proprietary technology. In the model presented in this paper, the exploitation of technology is central to understanding MNC activity, but the critical constraint is the nature of capital market development and investor protections in host countries……. Previous findings that FDI flows to developing countries are limited reflect two opposing forces. Weak investor protections and shallow capital markets limit the efficient scale of enterprise but also result in greater parent provision of capital and more parent ownership of affiliate equity….” (p. 1208). 96 APPENDIX We present the GG maximization problem and show that all constraints but one bind. GG solves 𝑚𝑎𝑥 𝐼,𝜑𝐺𝐺,𝜑𝐸,𝑥,𝐸,𝐶 𝛱𝐺𝐺 = 𝜑𝐺𝐺𝑝𝐻𝑅(𝑥) + (𝑊 − 𝐼)𝛽 − 𝐶𝑅(𝑥) s.t: 1. 𝑥 ≤ 𝐸 + 𝐼; 2. 𝑝𝐻𝜑𝐸𝑅(𝑥) ≥ 𝐸; 3. 𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ 0 4. (𝑝𝐻 − 𝑝𝐿)(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) ≥ (1 − 𝛾)𝛿(𝐶)𝑅(𝑥) 5. (𝑝𝐻 − 𝑝𝐿)𝜑𝐺𝐺𝑅(𝑥) ≥ 𝐶𝑅(𝑥) The Lagrangian: 𝑚𝑎𝑥 𝐼,𝜑𝐺𝐺,𝜑𝐸,𝑥,𝐸,𝐶 𝐿 = 𝜑𝐺𝐺𝑝𝐻𝑅(𝑥) + (𝑊 − 𝐼)𝛽 − 𝐶𝑅(𝑥) + 𝜆1(𝐸 + 𝐼 − 𝑥) +𝜆2[𝑝𝐻𝜑𝐸𝑅(𝑥) − 𝐸] +𝜆3[𝑝𝐻(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥)] +𝜆4[(𝑝𝐻 − 𝑝𝐿)(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) − (1 − 𝛾)𝛿(𝐶)𝑅(𝑥)] +𝜆5[(𝑝𝐻 − 𝑝𝐿)𝜑𝐺𝐺𝑅(𝑥) − (𝐶)𝑅(𝑥)] We know that 3. cannot bind and thus we write: 𝑚𝑎𝑥 𝐼,𝜑𝐺𝐺,𝜑𝐸,𝑥,𝐸,𝐶 𝐿 = 𝜑𝐺𝐺𝑝𝐻𝑅(𝑥) + (𝑊 − 𝐼)𝛽 − 𝐶𝑅(𝑥) + 𝜆1(𝐸 + 𝐼 − 𝑥) +𝜆2[𝑝𝐻𝜑𝐸𝑅(𝑥) − 𝐸] +𝜆4[(𝑝𝐻 − 𝑝𝐿)(1 − 𝜑𝐸 − 𝜑𝐺𝐺)𝑅(𝑥) − (1 − 𝛾)𝛿(𝐶)𝑅(𝑥)] +𝜆5[(𝑝𝐻 − 𝑝𝐿)𝜑𝐺𝐺𝑅(𝑥) − (𝐶)𝑅(𝑥)] Let us now check the equilibrium values for the remaining mulitipliers. We consider FOCs only, as SOCs are satisfied because of the assumptions on the functional forms. A. 𝜕𝐿 𝜕𝐼 = −𝛽 + 𝜆1 = 0 B. 𝜕𝐿 𝜕𝜑𝐺𝐺 = 𝑝𝐻𝑅(?̃?) − 𝜆4(𝑝𝐻 − 𝑝𝐿) + 𝜆5 = 0 97 C. 𝜕𝐿 𝜕𝜑𝐸 = 𝜆2𝑝𝐻𝑅(?̃?) − 𝜆4(𝑝𝐻 − 𝑝𝐿) = 0 D. 𝜕𝐿 𝜕𝑥 = 𝑝𝐻?̃?𝐺𝐺𝑅 ′(?̃?) − ?̃?𝑅′(?̃?) − 𝜆1 + 𝜆2𝑝𝐻?̃?𝐸𝑅 ′(?̃?) = 0 E. 𝜕𝐿 𝜕𝐸 = 𝜆1 − 𝜆2 = 0 F. 𝜕𝐿 𝜕𝐶 = −𝑅(?̃?) − 𝜆4(1 − 𝛾)(𝑝𝐻 − 𝑝𝐿)𝛿 ′(?̃?) − 𝜆5 = 0 By A: 𝜆1 = 𝛽. Consider E: 𝜆1 = 𝜆2 and thus 𝜆2 = 𝛽. Consider C: 𝜆4 = 𝜆2𝑝𝐻𝑅(𝑥) (𝑝𝐻−𝑝𝐿) = 𝛽𝑝𝐻𝑅(𝑥) (𝑝𝐻−𝑝𝐿) Consider B: 𝜆5 = −𝑝𝐻𝑅(?̃?) + 𝜆4(𝑝𝐻 − 𝑝𝐿) = −𝑝𝐻𝑅(?̃?) + 𝛽𝑝𝐻𝑅(?̃?) (𝑝𝐻 − 𝑝𝐿) (𝑝𝐻 − 𝑝𝐿) = (𝛽 − 1)𝑝𝐻𝑅(?̃?) At the equilibrium all mulitpliers are positive and thus all constraints bind. By algebraic manipulations from FOCs we obtain the equilibrium values for GG’s choice variables.