Industrial Economics Commentaries 2020

Examiners’ commentaries 2020 Examiners’ commentaries 2020 EC3099 Industrial economics Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2019–20. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide and the Essential reading references Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2015). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refer to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section. General remarks Learning outcomes At the end of this course and having completed the essential reading and activities you should be able to: describe and explain the determinants of the size and structure of firms and the implications of the separation of ownership and control describe and explain the pricing behaviour by firms with market power and its welfare implications apply analytical models of firm behaviour and strategic interaction to evaluate various business practices, including tacit collusion, entry deterrence, product differentiation, price discrimination and vertical restraints recognise and explain the basic determinants of market structure and the key issues in competition policy and regulation. What are the examiners looking for? Some examination questions will be problem-type questions, while others will be essay-type questions. In general, problem-type questions are quite specific as to what you are supposed to do, and a good answer generally involves some use of mathematics. When you answer problem-type questions in an examination, all the necessary steps must be shown. Moreover, you should take care to explain what the mathematics show – do not simply list equations. 1 EC3099 Industrial economics Essay-type questions can be more or less specific, although a good answer to an essay-type question must include some rigorous economic analysis, usually with reference to some economic model or models. Reading and preparation for the examination It is important to read more widely than just the subject guide. In essay-type questions in particular, you get a higher mark by including relevant material not in the subject guide. Whatever the question, exposure to a wider set of readings is usually necessary to understand in depth the economics involved and to be able to provide correct and comprehensive answers in the examination. While there is no single best way to organise your study, it may be useful, for each topic in the syllabus, to start with the relevant chapter of the subject guide, then read the essential and some of the recommended reading for that particular topic, then come back to the subject guide and attempt the various learning activities and sample examination questions. Planning your time in the examination Use your time efficiently bearing in mind that all questions carry equal weight in the final mark. Your answers must be as detailed and comprehensive as possible given the time constraints (unless you are specifically asked to discuss something briefly), but you should not include material which is not relevant to the question. Steps to improvement Your answers to problem-type questions should not simply list mathematical results but they should also explain what the mathematics mean. Your answers to essay-type questions must be focused, not too descriptive and must contain rigorous economic analysis. Examination revision strategy Many candidates are disappointed to find that their examination performance is poorer than they expected. This may be due to a number of reasons, but one particular failing is ‘question spotting’, that is, confining your examination preparation to a few questions and/or topics which have come up in past papers for the course. This can have serious consequences. We recognise that candidates might not cover all topics in the syllabus in the same depth, but you need to be aware that examiners are free to set questions on any aspect of the syllabus. This means that you need to study enough of the syllabus to enable you to answer the required number of examination questions. The syllabus can be found in the Course information sheet available on the VLE. You should read the syllabus carefully and ensure that you cover sufficient material in preparation for the examination. Examiners will vary the topics and questions from year to year and may well set questions that have not appeared in past papers. Examination papers may legitimately include questions on any topic in the syllabus. So, although past papers can be helpful during your revision, you cannot assume that topics or specific questions that have come up in past examinations will occur again. 2 Examiners’ commentaries 2020 If you rely on a question-spotting strategy, it is likely you will find yourself in difficulties when you sit the examination. We strongly advise you not to adopt this strategy. 3 EC3099 Industrial economics Examiners’ commentaries 2020 EC3099 Industrial economics Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2019–20. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide and the Essential reading references Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2015). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refer to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section. Comments on specific questions Candidates should answer FOUR of the following EIGHT questions: TWO from Section A and TWO from Section B. If more than four questions are answered, only the first questions attempted will be counted. Section A Candidates should answer any TWO questions from this section. Question 1 Indicate whether each statement below is true or false, and justify your answer. (a) The Cournot oligopoly model is not useful for analysing competition among firms because (i) firms normally choose prices, not quantities, and (ii) firms normally do not make their decisions simultaneously. (8 marks) (b) Entry deterrence and entry accommodation call for the same strategy when the firms’ actions (for example, setting price or setting quantity) are strategic substitutes and for opposing strategies when the firms’ actions are strategic complements. (9 marks) (c) Price competition is less intense in more concentrated industries. (8 marks) 4 Examiners’ commentaries 2020 Reading for this question Part (a): Chapter 3 of the subject guide, Tirole (1988, Chapter 5), Church and Ware (2000, Chapter 8). Part (b): Chapter 5 of the subject guide, Tirole (1988, Chapter 8), Church and Ware (2000, Chapters 13–16). Part (c): Chapters 3 and 9 of the subject guide; Sutton, Sunk Costs and Market Structure. Approaching the question (a) False. When firms are capacity-constrained, the Cournot model adequately describes a two-stage game with capacity choice in the first stage followed by price competition in the second stage. A good answer can outline such a model and provide intuition for the results. Also, simultaneous decisions can refer to the information available rather than the actual timing: if a firm ‘moves’ after another firm but without knowing the other firm’s action, then the relevant game is a simultaneous-move game. (b) True. If investment to deter entry reduces the profit of the potential entrant, then the optimal strategy for deterring entry is to overinvest irrespective of whether the firms’ actions are strategic substitutes or strategic complements, since the incumbent’s objective is to make entry unprofitable for the potential entrant. However, the optimal strategy for entry accommodation varies depending on whether the firms’ actions are strategic substitutes or strategic complements. The reason is that the objective then is not to make entry unprofitable for the potential entrant but to increase the profit of the accommodating incumbent. When the firms’ actions are strategic substitutes (as in the Cournot model), then the optimal strategy is to overinvest: this strategy secures a higher market share in the competition stage. When the firms’ actions are strategic complements (as in the Bertrand model with differentiated products), then the optimal strategy is to underinvest: this strategy avoids very low prices in the competition stage. Diagrams with reaction curves and/or some simple mathematical analysis can be used to clarify these points. (c) False. Higher concentration is associated with less intense price competition when there is a fixed number of firms in the market. With free entry, however, the opposite may be the case as the causality also now goes from intensity of competition to concentration, and tougher price competition leads to higher concentration in an industry. A good answer could include a comparison of Cournot and Bertrand oligopoly with free entry and a very good answer would describe the competition-concentration link in the context of the economic theory and empirical evidence on the determinants of market structure. Either way, the point that needs to be made is that tougher price competition reduces the profit margin, so it increases the output a firm must produce to cover fixed and entry costs, thereby reducing the number of firms that can survive in long-run equilibrium. Question 2 ‘Vertical restraints can be used to increase efficiency in a market, but they may also restrict competition.’ Discuss, with reference to economic theory as well as any relevant empirical evidence. (25 marks) Reading for this question Chapter 8 of the subject guide, Tirole (1988, Chapter 4), Church and Ware (2000, Chapter 22). 5 EC3099 Industrial economics Approaching the question A good answer should start by defining the term ‘vertical restraints’ and by giving some examples of vertical restraints. You should then provide theoretical arguments that support the view that vertical restraints may in some cases increase efficiency in a market (taking care to explain what efficiency means in this context) and in other cases restrict competition. A very good answer might also describe and discuss one specific theoretical model where vertical restraints are used to increase efficiency and one model where they are used to restrict competition. The second part of your answer should discuss empirical evidence that supports the view that the welfare implications of vertical restraints are ambiguous. A good way of doing this would be to discuss in some detail one or two (or even more, if you want) case studies. A very good answer might then conclude with a brief reference to competition policy toward vertical restraints. Question 3 Explain the rationale for government policy toward research and development in the form of (i) a patent system, and (ii) R&D subsidies. Then discuss the advantages and disadvantages of these policies, with reference to any relevant empirical evidence. (25 marks) Reading for this question Chapter 10 of the subject guide, Church and Ware (2000, Chapter 18). Approaching the question A good answer could start by discussing the reasons why the market mechanism cannot generally be relied upon to produce the socially optimal amount of R&D, thus making government policy toward R&D necessary. The answer should then elaborate upon these issues within the specific context of patents and R&D subsidies. Patents are meant to alleviate the appropriability problem and thus directly promote innovation. Moreover, they are meant to encourage disclosure of new discoveries and thus indirectly increase the rate of technological progress. On the other hand, since patents reduce competition after an innovation is made, too much patent protection would not be welfare-enhancing. Another problem with patents is that they may not be very effective in protecting innovations. R&D subsidies are also meant to increase the R&D performed by individual firms. A key distinction is between horizontal subsidies and more selective subsidies, and a good answer should discuss the advantages and drawbacks of both, and also tackle the more general issue of the effectiveness of R&D subsidies. A good answer should conclude by describing some relevant empirical evidence. Question 4 (a) Competition law in the country of Wonderland prohibits all mergers that result in a single firm having more than 75% of sales in any market. A new government proposes to make changes to the law and asks for your advice. Assess this law from a welfare perspective and highlight its shortcomings. (10 marks) 6 Examiners’ commentaries 2020 (b) A researcher has estimated a model of industry profitability using cross-industry data and has found a positive coefficient on the concentration variable. (The results were not affected when different measures of concentration were used.) He claims that the results show that higher concentration leads to higher industry profit. What is the theoretical basis for this claim? Do you agree with the researcher’s conclusion? What would your advice be to a policy maker worried about the high level of concentration in many industries? (15 marks) Reading for this question Part (a): Chapters 9 and 10 of the subject guide; Church and Ware (2000, Chapter 23); Sutton, Sunk Costs and Market Structure. Part (b): Chapters 3 and 9 of the subject guide; Tirole (1988, Chapter 5); Church and Ware (2000, Chapter 8); Sutton, Sunk Costs and Market Structure. Approaching the question (a) This law may prevent some mergers that would reduce welfare but it has several shortcomings. First, there is no justification for setting a particular limit (75% or whatever), since conditions differ across industries and the market share of a firm is only one among several factors that determine the likelihood of a firm abusing its market power. Second, the level of concentration and firms’ market shares in an industry are influenced by a range of economic factors – including market size, the costs of setting up a plant of minimum efficient scale, and the intensity of competition. It is possible that there are some industries where only monopolies can operate efficiently. Third, a very high market share is sometimes the result of a firm being very efficient, innovative etc. and this is not welfare reducing in itself. On guidelines for an effective merger policy, see Chapter 10 of the subject guide. (b) The researcher’s claim is essentially that higher concentration causes industry profits to increase, presumably because it facilitates the exercise of market power by firms. The theoretical basis for this claim comes from a variety of oligopoly models, including the Cournot model and models of collusion. The researcher’s claim may be true in many circumstances, but it is not necessarily true. A positive correlation between concentration and industry profitability can also be due to the fact that both are determined by a third factor, for instance the degree of cost asymmetry: in industries where some firms are much more efficient than others, both concentration and profitability will be high. It is therefore wrong to conclude from a statistical association between concentration and profitability that there is necessarily a causal link between the two variables. The last part of the question is more ‘open-ended’, although the answer should be related to the previous part. A good answer should be based on a comparison of several different approaches to concentration. One view is that high concentration is a result of entry barriers and facilitates the exercise of market power, thus reducing welfare. Another view is that high concentration may be the result of efficiency differences between firms, in which case it may be welfare-enhancing. A third view is that high concentration may be the result of intense competitive pressure, and so again it does not need to be associated with lower welfare. Section B Candidates should answer any TWO questions from this section. Question 5 Firms A and B are Cournot duopolists producing a homogeneous good. Inverse market demand is P = 100 − Q, where P is market price and Q is the market quantity demanded. Each firm has marginal and average cost c = 40. 7 EC3099 Industrial economics (a) The two firms propose to merge. Derive total output, market price, profit and consumer surplus before the merger and after the merger. Explain intuitively any changes you see to these variables when the merger occurs. (9 marks) (b) A regulator for this market has objective function W = λΠ + (1 − λ)CS , where Π is industry profit, CS denotes consumer surplus and λ is a constant, 0 ≤ λ ≤ 1. Will a regulator with λ = 0 permit the merger? Will a regulator with λ = 1 permit the merger? Interpret these two regulatory stances and explain the implications of your answer for competition policy. At what level of λ would the regulator be indifferent to the merger? (8 marks) (c) The firms now claim that there will be efficiency gains to the merger, so that the marginal cost of production will fall to c = 30. How does this affect your answer in part (b)? Explain the implications of your answer for competition policy. (8 marks) Reading for this question Chapter 3 of the subject guide, Tirole (1988, Chapter 5), Church and Ware (2000, Chapters 8 and 23). Approaching the question (a) Before the merger: Π1 = (P − c)q1 = (100 − q1 − q2 − 40)q1 and similarly for firm 2. Maximising each with respect to their own choice of output, we obtain first-order conditions (the Cournot reaction functions). Solving for the Cournot equilibrium, we get q1∗ = q2∗ = 20. The total Cournot equilibrium output is 20 + 20 = 40. Market price at the Cournot equilibrium is 100 − 40 = 60. Profit for each firm is 400 and consumer surplus is 800. If the firms merge, they become a monopoly. Equating marginal revenue to marginal cost, we obtain Q = 30. Hence monopoly output is less than the Cournot industry output, which makes sense intuitively. Market price is 100 − 30 = 70, profit is 70 × 30 − 40 × 30 = 900 and consumer surplus is (100 − 70) × 30/2 = 450. Diagrams can also be used to illustrate these results. We see that monopoly raises market price and industry profit and lowers consumer surplus. Intuitively, the merger allows the firms to internalise a negative externality they had on each other under Cournot: the more each produced, the lower the market price that the other firm earned per unit. (b) The parameter λ is a weighting factor, showing how relatively important profits are compared to consumer surplus in the regulator’s objective function. The regulator who only puts weight on consumer surplus would see that this merger is surplus-reducing and would not permit the merger. Such a regulatory has λ equal to zero. A regulator with full weight placed on industry profits, in other words a regulator with λ equal to one, would permit the merger. The value of λ for which the regulator would be indifferent in this case would be given by: λ(800) + (1 − λ)800 = λ(900) + (1 − λ)450 ⇒ λ ≈ 0.78. A value of λ exceeding this threshold would result in a positive view of the merger, whereas a value of λ below this threshold would result in a negative view of the merger. (c) If the merger results in efficiency gains, so that we now have c = 30, we need to recalculate the figures in (b) in order to be able to compare the policies. Using the same methods as before, we obtain monopoly values of Q = 35, P = 65, Π = 1,225 and CS = 612.5. In this case, the critical value of λ will be lower (approximately 0.3), so it is more likely that a 8 Examiners’ commentaries 2020 regulator would allow the merger. Indeed, this is the basis of the ‘efficiency defense’ in competition policy, and your answer should conclude with a brief discussion of policy implications. Question 6 A property developer is selling new villas in Spain. The cost of building each villa is 100,000 euros. There are two types of potential buyers. Type 1 buyers are willing to pay up to P1 = 250,000 − 10,000M1 , where M1 is the number of months that they would have to wait before taking possession of the villa. Type 2 buyers are willing to pay up to P2 = 200,000 − 1,000M2 , where M2 is the number of months that they would have to wait. Let us assume for simplicity that the developer could supply all villas immediately if she wanted. Assume further that there are 10 impatient (i.e. type 1) buyers and 10 patient (i.e. type 2) buyers. Each buyer buys at most one villa. The developer cannot tell the different types of buyers apart. Moreover, administrative fees are high enough to prevent any reselling between buyers. (a) Suppose that the developer can choose the number of months M a buyer has to wait as well as the price P a buyer has to pay for a villa. The developer offers two options. In the first option, the villa costs 240,000 and is available immediately. In the second option, the villa costs 190,000 and is available in 6 months. Which option will a type 1 buyer choose? Which option will a type 2 buyer choose? How much profit will the developer make? (13 marks) (b) Can the developer do even better than in part (a)? How? In particular, let (P1 , M1 ) denote the price/waiting time package aimed at impatient (type 1) buyers and (P2 , M2 ) the package aimed at patient (type 2) buyers. What is the most profitable combination of offers (prices and waiting times) that the developer can choose? Explain. (12 marks) Reading for this question Chapter 7 of the subject guide, Tirole (1988, Chapter 3), Church and Ware (2000, Chapter 5). Approaching the question (a) Let us first consider the choice of type 1 buyers. From option 1, they get a surplus of: 250,000 − 240,000 = 10,000 > 0. From option 2 they get: 250,000 − 190,000 − 60,000 = 0. Hence type 1 buyers decide to purchase the houses that are available immediately for a price of 240,000. This yields a profit of: (240,000 − 100,000) × 10 = 1,400,000 for the developer. Now consider type 2 buyers. Option 1 is too expensive and leaves them with a negative surplus. From option 2, they get a surplus of: 200,000 − 190,000 − 6,000 = 4,000. Hence type 2 buyers buy houses for 190,000 and wait 6 months. This yields a profit of: (190,000 − 100,000) × 10 = 900,000. With this dual offer the developer makes an overall profit of 2,300,000. 9 EC3099 Industrial economics (b) Define as (P1 , M1 ) the price/waiting time package aimed at impatient (type 1) buyers and (P2 , M2 ) the package aimed at patient (type 2) buyers. A good answer to this part of the question should describe and then solve the maximisation problem of the developer. The answer should clearly state and explain the relevant constraints: the participation constraint and the incentive-compatibility constraint for each type of buyer. An outline of the principles and intuition is as follows. First, it makes no sense to make the impatient buyers wait since this simply reduces their willingness to pay. Hence M1 = 0. Second, it makes no sense to make the patient buyers wait more than what is just required for discouraging impatient buyers from purchasing the package intended for patient buyers. This point is important: the reason for setting M2 > 0 is to separate the two groups. Hence we must have: 250,000 − P1 = 250,000 − P2 − 10,000M2 . The left-hand side of this equation is the surplus of the type 1 buyers if they choose the package (P1 , M1 ). The right-hand side of this equation is the surplus of the type 1 buyers if they choose the package (P2 , M2 ). The equation is saying that the type 1 buyers must be just indifferent between the two packages – in which case we assume they will choose the package aimed at them, i.e. (P1 , M1 ). Finally, the developer will want to extract all possible surplus from patient buyers, i.e. we have: 200,000 − P2 − 1,000M2 = 0 and, if possible, extract all possible surplus from impatient buyers as well, i.e. set P1 = 250,000. Note that this level of P1 ensures that patient buyers will not buy the package intended for impatient buyers. Combining these equalities, we have: P1∗ = 250,000, M1∗ = 0, 200,000 − P2 − 1,000M2 = 0 and: 250,000 − P1 = 0 = 250,000 − P2 − 10,000M2 . Solving the last two equations for the two unknowns, we get M2∗ = 50/9 and P2∗ = 194,444. Offering the packages (P1∗ , M1∗ ) and (P2∗ , M2∗ ) yields an overall profit of: (94,444 × 10) + (150,000 × 10) = 2,444,440 which is higher than the overall profit in part (a). A good answer could conclude with a brief discussion of the intuition for this result. Question 7 Answer all parts of this question. (a) Consider two identical firms with no fixed costs and constant marginal cost c which compete in quantities in each of an infinite number of periods. The quantities chosen are observed by both firms before the next round of play begins. The inverse demand is given by p = 1 − q1 − q2 , where q1 is the quantity produced by firm 1 and q2 is the quantity produced by firm 2. The firms use ‘trigger strategies’ and they revert to static Cournot behaviour if cooperation breaks down. Derive the lowest value of the discount factor such that the firms can sustain the monopoly output level and discuss the economic reasoning behind your result. (15 marks) 10 Examiners’ commentaries 2020 (b) An incumbent firm operates a store in a local market and faces the potential entry of a single rival. The entrant’s choices are to enter or to stay out of the market. If the entrant stays out, it earns 1 (the return from the best alternative investment); the incumbent earns 5. If the entrant comes in, then the incumbent must decide whether to cooperate with the entrant (in which case both earn a return of 2) or to fight entry (in which case both earn a zero return). What is the subgame perfect equilibrium of this game? Would your answer change if the incumbent operated 20 stores in 20 separate markets, and faced 20 potential entrants, one in each market, who must make their entry decisions sequentially? Provide a brief discussion of your results in the context of empirical evidence on entry deterrence. (10 marks) Reading for this question Part (a): Chapter 4 of the subject guide, Tirole (1988, Chapter 6), Church and Ware (2000, Chapters 10 and 12). Part (b): Chapter 6 of the subject guide, Tirole (1988, Chapter 8), Church and Ware (2000, Chapters 13–16). Approaching the question (a) A good answer could start by explaining the notion of a trigger strategy in the context of a repeated game between firms. Collusion is sustainable if for each firm the present discounted value of the profits from collusion is at least as large as the present discounted value of the profits from deviating (with subsequent reversion to Cournot behaviour): ∞ X t=0 δt ∞ X ΠM ≥ ΠD + δ t ΠC i i 2 t=1 or ΠM δΠC i ≥ ΠD i + 2(1 − δ) 1−δ (1) where ΠM is the monopoly profit, ΠD i is the profit firm i makes in the period it deviates, and ΠC i is the per-period profit when collusion has broken down. Note that we focus here on the case of perfect collusion, where each of two colluding firms produces half the monopoly output and gets half the monopoly profit. In principle, collusion could involve an overall level of output higher than the monopoly level (and overall profit lower than the monopoly profit). A monopolist would choose q to maximise: Π = q(p − c) = q(1 − q − c). From the first-order condition we obtain q M = (1 − c)/2. Substituting this into the monopolist’s profit function, we get the monopoly profit: ΠM = (1 − c)2 . 4 To derive the Cournot equilibrium, we write down the profit function of each firm as: Πi = qi (1 − qi − qj − c) for i = 1, 2, j 6= i. We then derive the first-order conditions and solve the system of the two equations in two unknowns, q1 and q2 . The equilibrium Cournot quantities are given by (1 − c)/3. The Cournot equilibrium profit of each firm is: ΠC i = (1 − c)2 . 9 Finally, to compute ΠD i consider the following maximisation problem of an optimally deviating firm when the rival firm produces the collusive level of output: firm i chooses qi to maximise:   qM Πi = qi 1 − qi − −c 2 11 EC3099 Industrial economics where q M = (1 − c)/2 is the monopoly output. From the first-order condition of this maximisation problem we obtain the defection quantity 3(1 − c)/8. The corresponding profit is: ΠD i = 9(1 − c)2 . 64 C Substituting these expressions for ΠM , ΠD i and Πi in (1), we obtain that collusion is sustainable for δ ≥ 9/17. The discussion of the result should focus on the fact that collusion is sustainable when firms care sufficiently for future profits. (b) It is straightforward to solve for the subgame perfect equilibrium of the constituent game: the entrant enters and the incumbent cooperates. With 20 stores the constituent game is repeated 20 times. The same equilibrium is repeated 20 times as there is always one last store, and backward induction applies. You should describe the backward induction and explain why the subgame perfect equilibrium outcome is that entry occurs in all markets. The empirical evidence sometimes suggests otherwise, i.e. that entry in these circumstances does occur in at least some markets. A good answer should describe some evidence and discuss theoretical arguments to support this evidence, including models where firms have incomplete information about their rivals. Question 8 Consumers are uniformly distributed on a linear city of length one and at each point on the line lies a single consumer. All consumers are similar and each of them consumes exactly one unit of a homogeneous good. In addition to the money price, consumers incur linear transport costs: cost t per unit of distance travelled. There are two firms, one located at the left-hand end of the line, and the other at the right-hand end. Each firm produces a product with an undesirable ingredient at zero marginal cost. Suppose that unless they are informed, consumers are not aware of this ingredient. The firms compete by simultaneously setting prices. (a) Compute the equilibrium prices and profits in this market if firms cannot inform consumers that their product contains the undesirable ingredient. (10 marks) (b) Now suppose that, at an initial stage, firms simultaneously and independently decide whether to inform consumers that their product contains an undesirable ingredient (and further suppose that such provision of information is costless). Then, at the second stage, the firms simultaneously set their prices. If a consumer knows that product i has the undesirable ingredient, her utility from consuming that product is reduced by d, where 0 < d < 3t. Derive the equilibrium prices and profits in this two-stage game. (15 marks) Reading for this question Chapter 6 of the subject guide, Tirole (1988, Chapter 7), Church and Ware (2000, Chapter 11). 12 Examiners’ commentaries 2020 Approaching the question (a) Let us call the firm on the left L and the firm on the right R. The ‘marginal consumer’, i.e. the consumer who is just indifferent between buying from firm L or firm R, is located at distance x from the left end of the line, where x is defined by: pL + tx = pR + t(1 − x) ⇒ x= 1 pR − pL + . 2 2t Profits are given by: ΠL = pL x and ΠR = pR (1 − x). The first-order conditions are: 1 ∂ΠL = (t + pR − 2pL ) ∂pL 2t and ∂ΠR 1 = (t − 2pR + pL ). ∂pR 2t The Nash equilibrium is the solution to the system of the two first-order conditions. Solving the system we obtain p∗L = p∗R = t. We can also substitute into the expressions for profit to get: t Π∗L = Π∗R = . 2 (b) We start at stage 2 of the game. If both firms have chosen not to inform consumers, then the stage 2 equilibrium is the same as in part (a). If both firms have chosen to inform consumers, then the marginal consumer’s position on the line remains the same as in part (a), so the stage 2 equilibrium prices are the same. Since the provision of information is costless, the profits too remain the same. If firm L has informed and firm R has not informed consumers, then the marginal consumer’s position is defined by: pL + tx + d = pR + t(1 − x) ⇒ x= t − d pR − pL + . 2t 2t Profits are:  ΠL = pL x = pL t − d pR − pL + 2t 2t   and ΠR = pR (1 − x) = pR t + d pL − pR + 2t 2t  . Solving the system of the two first-order conditions, we obtain: p∗L = t − d 3 d and p∗R = t + . 3 Note that x∗ = (t − d/3)/(2t), and we have 0 < x∗ < 1/2 because 0 < d < 3t. In other words, the output of the firm that has informed consumers of the undesirable ingredient in its product is lower than the output of the other firm. Finally, we substitute p∗L and p∗R into ΠL and ΠR to get: Π∗L = 1 2t  t− d 3 2 and Π∗R = 1 2t  2 d t+ . 3 It can be checked that the profit of firm L is now lower than its profit in part (a), while the profit of firm R is now higher. If firm R has informed and firm L has not informed consumers, then the above payoffs are reversed. We now go back to stage 1 of the game, where each firm has two possible actions, Inform and Not Inform. We can construct a matrix of all possible outcomes, with payoffs as previously calculated, and derive the Nash equilibrium of the reduced-form simultaneous-move game which is equivalent to the original two-stage game. We have: 13 EC3099 Industrial economics Firm R Inform Firm L t t , 2 2 Inform Not Inform Not Inform 1 2t  d t+ 3 2 1 , 2t 1 2t  d t− 3 2  2  2 1 d d , t− t+ 3 2t 3 t t , 2 2 The Nash equilibrium of the reduced-form game is (Not Inform, Not Inform). Therefore, the subgame perfect Nash equilibrium outcome in the two-stage game is that none of the firms informs, and the prices and profits are the same as in part (a). 14