Mid-Term Exam
Durable goods monopoly.
a) (8 marks). Explain how the market power of the monopolist can be reduced if they sell a durable good. How can this problem of reduced market power be overcome if the monopolists leases rather than sells the product.
Consider the following version of the textbook example done in class. A seller has 2 units of a durable good. The good provides the buyer with 2 periods of use if it is bought in period 1 and only 1 period of use if bought in period 2 (i.e. good is obsolete after period
2). There are 2 buyers. Buyer 1 values the good at $100 per period in periods 1 and 2. Buyer 2 values the good at $75 per period in periods 1 and 2. Both buyers get zero value from the good after period 2. Production costs are zero and there is no discounting.
b) (6 marks) Determine whether the monopolist (i) sells to both buyers in period 1 or (ii) sells to Buyer 1 in Period 1 and to Buyer 2 in Period 2 or (iii) leases to both buyers in both periods or (iv) leases to Buyer 1 in both periods.
c) (6 marks). Indicate which option in part b) yields the highest welfare.
Price Discrimination
a) (10 marks). What is price discrimination? Under what circumstances is it feasible? Why is it profitable? If a monopolist can practice third degree price discrimination then what is the profit maximizing pricing rule involving elasticities? Give some examples as to how this rule is applied in practice. Under what circumstances does price discrimination increase welfare? Use diagrams to explain your answer.
Suppose that demand is given by qa = 32 – pa in Market A and by qb = 40 – pb in Market B where pi, and qi are price and output in market i = a, b, respectively. Marginal cost is constant and equal to 4. Fixed costs are zero.
b) (5 marks). Find the profit maximizing prices, quantities and profit if the monopolist can price discriminate.
c) (5 marks). Find the profit-maximizing price, quantity and profit if the monopolist cannot price discriminate. Determine whether it is more profitable to serve both markets or to serve only Market B.
Versioning
a) (4 marks). What is versioning? Give examples. Under what circumstances is versioning profitable? What are damaged goods?
the price of that version, the number of buyers served, profits and welfare.
(ii) If the seller offers both versions then determine the prices of both versions, the number of buyers served, profits and welfare.
c) (8 marks). Let x = 80. Repeat part b).
- Capacity constrained Bertrand. Use diagrams and verbal argument to explain the following results from the capacity constrained Bertrand oligopoly model.
a) (5 marks). It is not an equilibrium for firms to charge different prices.
b) (5 marks). It is not an equilibrium for all firms to charge a price which yields excess capacity.
c) (5 marks). It is not an equilibrium for firms to charge a price which yields excess demand.
d) (5 marks). It is not an equilibrium for firms to charge a price which clears the market if they choose capacities which are greater than Cournot capacities. - Differentiated Bertrand. Consider a Differentiated Bertrand model in which demand is given by q1 = 100 – p1 + p2 and q2 = 100 – p2 + p1 for firm 1 and firm 2 respectively and where both firms faced zero fixed costs and constant marginal cost = c.
a) (8 marks). Suppose that firms choose prices simultaneously. Solve for the Nash equilibrium (i) price (ii) output and (iii) profits of each firm as functions of c.
b) (8 marks). Now suppose that firm 1 chooses price first and then firm 2 chooses price taking firm 1’s price as given. Solve for the Sub-game Perfect Nash equilibrium (i) price (ii) output and (iii) profits of each firm as functions of c.
c) (4 marks). Use reaction functions to explain why making firm 1 a first mover results in both firm 1 and firm 2 raising price. - Stackelberg and Limit Pricing. Consider the Limit pricing and Stackelberg models done in class in which the incumbent chooses capacity first and entrant then chooses whether to enter or not. If they decide to enter then the entrant chooses the level of output in Cournot fashion taking the incumbent’s capacity choice as given. It is assumed that 75% of
the incumbent’s marginal cost is sunk once they make the capacity choice. Inverted demand is given by P = a – Q, where ‘a’ is the market size parameter. Marginal cost is 10 and fixed costs are 100 for both entrant and incumbent.
a) (10 marks) Find the minimum level of output needed to deter entry (qID). Find the levels of ‘a’ for which entry can be deterred with the monopoly level of output (qIM). For every level of ‘a’ determine which output the incumbent will choose to deter entry and whether or not it will be credible.?
b) (10 marks) Calculate the Stackelberg level of output and profits for the incumbent as a function of ‘a’. For what values of ‘a’ is it credible for the incumbent to produce at the Stackelberg level of output? Pick a value of ‘a’ for which Stackelberg and limit pricing are both credible and determine which strategy is more profitable. - 8. Contracts as a barrier to entry. A buyer and seller exchange a single unit. The buyer is willing to pay v = 10 for the unit. The incumbent seller’s cost is c for the unit, where c > 2 and c < 4. If entry occurs then the entrant and incumbent engage in Bertrand competition except that that the buyer buys from the entrant if the entrant’s price is less than or equal to the incumbent’s price. As a result, if there is no contract then the buyer is charged p = v = 10 by the incumbent if the entrant stays out and p = c by the entrant if the entrant enters. The entrant will enter if their costs are less than or equal to c. If there is a contract then the buyer agrees to pay a price P < v to the incumbent if no entry occurs and a switching cost s to the incumbent and P s to the entrant if entry does occur. The entrant enters if their costs as less than or equal to P s. The buyer will choose the contract provided the expected price of the contract is less than or equal to the expected price without the contract. The entrants unit cost are equal to ce = 2 with probability = 0.4 and ce = 4 with probability = 0.6. a) No contract (6 marks). Without a contract determine and explain the (i) probability of entry (denoted z). (ii) expected price that the buyer faces as a function of c (iii) expected profit earned by the incumbent as a function of c. b) Contract (14 marks). If a contract is offered then determine and explain (i) how the probability of entry (z) depends on P – s (ii) the constraint on P that must be satisfied for the buyer to accept the contract (constraint will depend on c). (iii) the incumbent’s profit function as a function of z, P, s and c. (iv) the profit maximizing levels of P and s as functions of c. (v) whether offering the contract raises the incumbents profits (vi) whether offering the contract raises welfare N.B Use the constraint that c < 4 and c > 2 to answer (iv) & (v). 9. Predation a) (12 marks). What is predation? What is the Chicago school criticism of predation and what is the counterargument to this criticism? Give four non-predatory reasons as to why firms respond aggressively to entry. Is there any evidence that can allow one to distinguish between a predatory and a non-predatory response to entry? Does predation reduce social welfare? b) (4 marks). In the airline industry Northwest (i) responded to entry by dropping prices and adding capacity and (ii) responded to exit by raising prices and reducing capacity. Explain whether these actions consistent with non-predatory Cournot behavior, predation or both. c) (4 marks). In the gas station industry the growth of market share of low cost supermarket chains resulted in the exit of 5000 gas stations and in a fall in the average gross margin. Explain whether this evidence is consistent with non-predatory Cournot behavior, predation or both?
Repeated games and collusion
a) (7 marks). What is the discount factor in the repeated game model? What are the 4 factors which determine that magnitude of the discount factor? Briefly explain why the discount factor has to be sufficiently high in order make collusion feasible.
b) (7 marks). Use the repeated game model to explain why collusion is more likely if there are few firms or there is multi-market contact.
c) (6 marks). In 1918 the U.S. congress passed a law allowing American firms to form export cartels. Empirical evidence suggests that cartels were more likely to be formed in industries where American exporters had a large market share, in capital-intensive industries, in industries selling standardized goods, and in industries that enjoyed strong export growth. Explain.
- Cournot and Stackelberg Mergers. Consider a Cournot model in which prior to merger there is one low cost firm with marginal cost equal to 12 and 2 high cost firms with marginal cost equal to 24. Fixed costs are zero and inverted market demand is given by P = 48 – Q. In the post-merger setting the low cost firm merges with one of the high cost firms. The merged firm has marginal cost equal to 12 (i.e. equal to the marginal cost of the low cost firm). Outsider marginal cost remains at 24.
a) (6 marks). Solve for the pre-merger level of (i) output and profit for each firm (ii) Herfindahl index and (iii) Welfare.
b) (7 marks). Solve for the post-merger level of (i) output and profit for each firm (ii) Herfindahl index and (iii) Welfare assuming that the merged firm acts like a Cournot firm.
Is the merger profitable for the insiders? Does it raise welfare? Does it increase concentration?
c) (7 marks). Repeat b) except assume that the merged firm acts like a Stackelberg leader and the non-merged firms act like Stackelberg followers. - Differentiated Bertrand Mergers and Merger Waves
a) (5 marks). Use reaction function analysis to explain why differentiated Bertrand mergers are always profitable even if there are zero cost efficiency gains.
b) (5 marks). If the own price elasticity is 2 and the cross price elasticity is 0.5 then explain how the differentiated Bertrand model can be used to determine the impact of merger on price cost margins.
c) (5 marks). Explain the impact of mergers of two neighbouring firms on prices if firms are spatially differentiated and engage in spatial price discrimination. Be sure to indicate whether the merged firm raises prices for all buyers and the price response of outsiders.
d) (5 marks). Explain why merger waves occur.
Vertical Merger. Consider a model in which there is 3 vertically integrated firms, 2 nonintegrated dealers and 2 non-integrated manufacturers. The marginal cost of the integrated firm and non-integrated manufacturer are both zero. The marginal cost of the non-integrated dealer is equal to the wholesale price (w) charged by the non-integrated manufacturers. Retail demand is given by P = 120 – Q.
a) (10 marks). Solve for the equilibrium outputs and profits of each dealer and
manufacturer, the retail price (P) and the wholesale price (w).
b) (10 marks). Now suppose that a non-integrated manufacturer and a non-integrated
dealer decide to merge. Solve for the equilibrium outputs and profits of each dealer and
manufacturer, the retail price (P) and the wholesale price (w). Determine whether the
merger is profitable and whether it raises or lowers the retail and wholesale prices.
- Vertical Price Restraints
a) (6 marks). Consider the case in which the retailer chooses the retail price but does not provide retail services. Show that a non-integrated manufacturer can use either RPM or two-part tariffs to achieve the vertically integrated level of profits both for the case in which there are competitive retailers and in the case where the retailer is a monopolist.
b) (6 marks). Consider the case in which the retailer chooses the retail price and the level of retail services. Show that a non-integrated manufacturer can use two-part tariffs to achieve the vertically integrated monopoly profit when the retailer is a monopolist but not when the retailers are competitive. Show that the non-integrated manufacturer can use RPM to achieve the vertically integrated profit when the dealers are competitive.
c) (8 marks). Consider the case in which the retailers are competitive and have to purchase inventories prior to the state of demand being known. Explain the two cases which can arise if the non-integrated manufacturer is not permitted to use RPM. Explain the profit and welfare consequences of allowing the non-integrated manufacturer to use
RPM in both cases. - Non-Price Vertical Restraints.
a) (10 marks). What are exclusive territories (ET)? Explain 4 reasons why a manufacturer would be willing to grant an ET to a dealer? Under what circumstances are ET in the public interest? Discuss the possible impacts of car manufacturers granting ET to their car dealerships.
b) (10 marks). What is exclusive dealing (ED)? Explain 4 reasons why manufacturers would want to impose ED on their dealers. Under what circumstances is ED in the public interest? Discuss the possible impacts of beer producers imposing ED on dealers (i.e. pubs) in the UK