1. A firm is considering whether to introduce a new product. No other firms are considering producing the product. The product costs F to introduce and can be produced at zero marginal cost once the firm has spent F. If the firm introduces the product, it must charge the same per-unit price to all customers. The demand for the product is D(p) = 10 – p where p is price.
a. Are there values of F such that the firm would not introduce the product even though it would be socially optimal to have the product produced? If not, explain. If so, what are the values of F such that the firm does not introduce the product when a social planner would?
b. Consider the following extension of the problem. Suppose that the buyer is a single customer, e.g., a big downstream producer that earns surplus by selling in a final market (although you do not need to analyze activities in the final market to answer this question). Suppose the seller can charge the buyer a fixed fee K in addition to a per unit price p. In this case, are there values of the fixed cost F such that the seller will fail to introduce the product when it would be socially optimal to do so? Explain your answer with reference to the concepts of “business stealing” and “incomplete appropriation.”
2. Two undifferentiated firms are considering entering a market for a product that has market demand D(p) = 10 – p. Each firm must pay a fixed cost of 5 to enter and has zero marginal cost. Firms simultaneously decide whether to enter, and if they do enter, they price as a monopolist if there is only one firm in the market and as Bertrand duopolists if there are two firms in the market.
a. In a pure strategy equilibrium to the entry game, how many firms enter and what is the equilibrium price?
b. If the government could regulate price and could choose to subsidize either one or two entrants, what would be the socially optimal tax and subsidy policy?
3. Linear City Model with Horizontal and Vertical Product Differentiation and Privacy Effects. Two firms, labelled 1 and 2, are located at opposite ends of a line of length 1. Each firm produces a single product (products 1 and 2, corresponding to the firm labels) at constant marginal and average cost, c. L consumers are uniformly distributed along the line. A consumer located distance d from firm 1 receives utility v1 – p1 – td if it purchases from firm 1 where p1 is firm 1’s price and t is the consumer’s disutility per unit distance from the firm from which it purchases. A consumer located distance d from firm 1 is located distance 1-d from firm 2 receives utility v2 – p2 – t(1-d) if it purchases from firm 2.
a. Assume that v1=v2=t>c>0.
(i) Find the Bertrand equilibrium prices.
(ii)The upward pricing pressure index for product 1 due to a merger that combines products 1 and 2 is the upward pricing pressure discussed in class divided by the pre-merger price of product 1. What is the upward pricing pressure index for product 1 due to a merger between firms 1 and 2?
b. Assume now that v1=v2=v and that v is large enough that every customer purchases the product.
(i) Find the Bertrand equilibrium prices.
(ii) What is the upward pricing pressure index for product 1 due to a merger between firms 1 and 2?
(iii) Explain intuitively the relationship between upward pricing pressure index and the degree of product differentiation as measured by the disutility per unit distance parameter t in the linear city model. What do you conclude about the accuracy of a simple index like the upward pricing pressure index for measuring potential merger effects?
c. If v1 and v2 are allowed to differ, what are the Bertrand equilibrium prices in the case where both firms sell and all customers purchase the product.
4. Circular City Model with Various Mergers. Four firms, labelled 1, 2, 3, and 4 are located equidistant from each other around a circle of unit circumference, and each produces a single product (labelled products 1, 2, 3, and 4 to correspond with the firm label) at constant marginal and average cost c. L consumers are uniformly distributed around the circle, and each is willing to pay v for one unit of the product. A purchase requires a consumer to pay a “transport” cost equal to t per unit distance between the consumer and the firm from which it purchases. Assume that v is large enough that every consumer around the circle purchases the product.
a. (10 pts) What are the pre-merger Bertrand equilibrium prices?
b. (10 pts) Suppose firms 1 and 2 merge and continue to sell from their pre-merger locations. Assume that all firms are able to adjust their prices in the new equilibrium. What are the post-merger equilibrium prices for each of the four products?
c. (10 pts) Suppose firms 1 and 4 merge and locations do not change. Assume that all firms are able to adjust their prices in the new equilibrium. What is the effect of this merger on the prices?
d. (10 pts) Compare and contrast (if there is a contrast) your findings in 4.b and your findings in 4.c.
5. Free Entry, Retail Services, and Vertical Restraints. Best Skis Corp. sells skis from ski shops located near ski hills and through a competitive supply of internet distributors. A service provided by ski shops is to allow skiers to try out the skis before buying. Best sells both on the internet and online because some customers prefer to demo their skis before buying, while some customers are happy relying on reviews and avoiding the time and effort of purchasing from a demo shop. The demand for skis from customers that do not wish to demo their skis before buying is D1 = 10 – p. The demand from customers that prefer to demo their skis is D2 = 10 + s – p where s represents demo service, which we assume can take on one of two values: s = 0, or s = s*. Thus, total demand for Best skis if service is zero is DT(p) = 20 – p, and the total demand for Best skis if service is s* is DT(p) = 20 + s* – p . A skier that demos skis and likes them does not have to purchase from the ski shop. Assume that both types of customers view the demo ski shops and the internet vendors as perfect substitutes once they have tried out the skis (if they do so). Best’s marginal cost in the upstream market is c, an internet provider’s marginal cost in the downstream market is v, and the demo operator’s marginal cost in the downstream market is v+(1/2)s. Assume that the demo shop incurs cost (1/2)s for each customer that demos the skis whether or not the customer purchases skis from the shop.
a. Suppose Best charges a single per-unit wholesale price and does not use vertical restraints. Find the equilibrium wholesale price, retail price, and service level.
b. Suppose Best can use RPM to specify the retail price and can charge different wholesale prices to the ski shops and internet distributors. Find the equilibrium wholesale prices, retail price, and service level.
c. Does Best make the socially optimal choice of whether to use RPM? Explain.
6. AT&T-Time Warner Merger with Hypothetical Variations. Time Warner produces cable programming service at marginal cost 50. AT&T and DirectTV are differentiated distributors of cable television services to final customers. One unit of Time Warner’s cable programming service is required to produce one unit of cable television service. AT&T and DirectTV produce at marginal cost 0 plus the wholesale price they pay to purchase programming. In some local markets, AT&T is a monopolist, and in some local markets, AT&T and DirecTV compete. In markets where both compete, the demands for their products are D1(p1,p2) = 140 – 2p1 + p2 and D2(p1,p2) = 140 – 2p2 + p1 where product 1 is AT&T’s service, product 2 is DirecTV’s service, and p1 and p2 are the corresponding retail prices In the market where AT&T is a monopolist, its demand is D1M(p1) = 210 – (3/2) p1. Suppose that Time Warner can charge different prices for programming in monopoly and duopoly markets.
a. Suppose Time Warner charges a per-unit wholesale price and cannot charge a fixed fee.
(i) In monopoly markets, find the the pre-merger wholesale and retail prices.
(ii) In monopoly markets, find the post-merger retail price Provide a brief intuition for any differences between the pre- and post-merger situations in 10.a(i) and 10.a(ii).
(iii) In duopoly markets, find the pre-merger wholesale and retail prices.
(iv) In duopoly markets, assume that DirecTV’s price is fixed at the pre-merger level. Find the the post-merger retail price for AT&T under this assumption Provide a brief intuition for any differences between your answer in 6.a.(iii) and your answer here.
b. Suppose Time Warner can charge a per-unit wholesale price and a fixed fee.
(i) In monopoly markets, find the pre-merger wholesale price and fixed fee.
(ii) In monopoly markets, find the post-merger wholesale price an