There are two firms. Firm 1 (or, a small firm) produces a single product, product A,...

 

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There are two firms. Firm 1 (or, a small firm) produces a single product, product A, at zero cost. Firm 2 (or, a big firm) is a multi-product firm that sells both products A and B. Firm 2 is less efficient in producing A. It incurs a constant marginal cost c> 0 for producing A. However, firm 2 is a monopolist of the market of product B and its cost of producing product B is zero. A unit mass (i.e. a total measure of 1) of consumers all have the same preference which is known to producers, and view the two products as independent. To consumers, the value of product A is A > c while the value of product B is up > 0. If a consumer buys both products, the gross payoff is vA + UB. (Note that, unlike in the lecture slides where consumers are heterogenous and their values are distributed in [0, 1], here the setting is simpler and all consumers are homogenous and have the same VA and Firms compete in prices and set their prices simultaneously and inde- pendently. We assume whenever indifferent, consumers buy from the firm that can slightly reduce its price without making a negative profit. Firstly, suppose firm B separately sets prices for the two products. a. (0.5 pt) What price på does firm 2 set for product B? b. (1 pt) The two firms basically engage in Bertrand competition in the market for product A. What are the equilibrium prices pha and på? c. (0.5 pt) Based on [a.] and [b.], calculate both firms' profits ¹ and T². d. (1 pt) What is the consumer surplus, CS? Second, suppose that firm 2 uses pure bundling and set a bundle price PAB Firm 1 still sets price p for product A (which may differ from what was found in [b.]). e. (0.5 pt) Calculate a consumers' payoff of buying only product A from firm 1 (and therefore don't buy B) when the prices are given by p and PAB f. (0.5 pt) Calculate a consumer's payoff of buying the bundle from firm 2 when the prices are given by på and påB g. (1 pt) When will consumers prefer buying the bundle from firm 2 instead of buying only A from firm 1 (identify a suitable range for PAB). h. (2 pt) What PB will firm 2 set? What på will firm 1 set? i. (0.5 pt) Compared to the first part of Q1, does firm 2 prefer us- ing bundling? What is firm 1's equilibrium profit when firm 2 uses bundles the products? j. (0.5 pt) Calculate the consumer surplus. Are consumers better off compared to under separate selling? Finally, map the model to a situation with one incumbent (firm 2) and one small entrant/start-up (firm 1). Firm 1 has developed this better technology of producing product A and therefore has a lower production cost. However, in order to develop this new technology, firm 1 needs to incur a developing cost. If firm 1 does not develop the technology, it will not enter market A forever, which makes firm 2 a monopolist of both markets in the long run. If firm 1 enters the market, it will stay there forever. Assume there is no future participation from other firms. k. (1 pt) Anticipating firm 2 will use the bundling strategy upon its entry, will firm 1 still want to incur the developing cost? 1. (2 pt) From this long-run perspective which takes into account firm l's innovation incentive, what is the impact of bundling on competition and consumer welfare? There is no calculus involved in this question. Simply give your intuition in words. (Hint: even though firm 2 may not have incentive to use bundling in the short run, but the short-run loss can be more than offset by the benefit of becoming a long-run monopoly) There are two firms. Firm 1 (or, a small firm) produces a single product, product A, at zero cost. Firm 2 (or, a big firm) is a multi-product firm that sells both products A and B. Firm 2 is less efficient in producing A. It incurs a constant marginal cost c> 0 for producing A. However, firm 2 is a monopolist of the market of product B and its cost of producing product B is zero. A unit mass (i.e. a total measure of 1) of consumers all have the same preference which is known to producers, and view the two products as independent. To consumers, the value of product A is A > c while the value of product B is up > 0. If a consumer buys both products, the gross payoff is vA + UB. (Note that, unlike in the lecture slides where consumers are heterogenous and their values are distributed in [0, 1], here the setting is simpler and all consumers are homogenous and have the same VA and Firms compete in prices and set their prices simultaneously and inde- pendently. We assume whenever indifferent, consumers buy from the firm that can slightly reduce its price without making a negative profit. Firstly, suppose firm B separately sets prices for the two products. a. (0.5 pt) What price på does firm 2 set for product B? b. (1 pt) The two firms basically engage in Bertrand competition in the market for product A. What are the equilibrium prices pha and på? c. (0.5 pt) Based on [a.] and [b.], calculate both firms' profits ¹ and T². d. (1 pt) What is the consumer surplus, CS? Second, suppose that firm 2 uses pure bundling and set a bundle price PAB Firm 1 still sets price p for product A (which may differ from what was found in [b.]). e. (0.5 pt) Calculate a consumers' payoff of buying only product A from firm 1 (and therefore don't buy B) when the prices are given by p and PAB f. (0.5 pt) Calculate a consumer's payoff of buying the bundle from firm 2 when the prices are given by på and påB g. (1 pt) When will consumers prefer buying the bundle from firm 2 instead of buying only A from firm 1 (identify a suitable range for PAB). h. (2 pt) What PB will firm 2 set? What på will firm 1 set? i. (0.5 pt) Compared to the first part of Q1, does firm 2 prefer us- ing bundling? What is firm 1's equilibrium profit when firm 2 uses bundles the products? j. (0.5 pt) Calculate the consumer surplus. Are consumers better off compared to under separate selling? Finally, map the model to a situation with one incumbent (firm 2) and one small entrant/start-up (firm 1). Firm 1 has developed this better technology of producing product A and therefore has a lower production cost. However, in order to develop this new technology, firm 1 needs to incur a developing cost. If firm 1 does not develop the technology, it will not enter market A forever, which makes firm 2 a monopolist of both markets in the long run. If firm 1 enters the market, it will stay there forever. Assume there is no future participation from other firms. k. (1 pt) Anticipating firm 2 will use the bundling strategy upon its entry, will firm 1 still want to incur the developing cost? 1. (2 pt) From this long-run perspective which takes into account firm l's innovation incentive, what is the impact of bundling on competition and consumer welfare? There is no calculus involved in this question. Simply give your intuition in words. (Hint: even though firm 2 may not have incentive to use bundling in the short run, but the short-run loss can be more than offset by the benefit of becoming a long-run monopoly)

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a In this scenario firm B sets the price for product B which well denote as pB b Firm 1 and firm 2 engage in Bertrand competition in the market for pr... View the full answer