2. Consider the problem of a manufacturer of sunglasses (firm M) and a retailer

Question

2. Consider the problem of a manufacturer of sunglasses (firm M) and a retailer (firm R). The manufac- turer produces sunglasses at an unit cost of S30, and sells them to the retailer for pu each. The retailer then resells the sunglasses to consumers. The retailer has no marginal cost other than the price pu paid to the manufacturer. The consumer's inverse demand for sunglasses is given by pr150-q where q is the volume of sunglasses sold by the retailer and pr is the retail price. (a) Assume that the manufacturer and the retailer are jointly owned. The wholesale price Pu and the quantity q are set to maximize the joint profits of the firms. Argue that pu does not affect these joint profits. Please find the equilibrium q. What are the joint profits of the firms? (b) Now assume that the order of events is as follows: Firm M first sets pu. Having observed pu, firm R decides the quantity q of sunglasses to be sold to consumers. Each firm maximizes its own profits. Please find pu, Pr and q in the subgame perfect Nash equilibrium of this game. What are the profits for the manufacturer and the retailer? We now consider a slightly different scenario. There is still one manufacturer, which has a marginal cost of $30. But there are two retailers, firms R1 and R2. The manufacturer sells the sunglasses to R1 and R2 for a wholesale price pu (the same for the two retailers). The retailers then resell the glasses to consumers. The retailers have no cost besides the wholesale price pu. Assume that the order of events is as follows: The manufacturer sets Pu and then the retailers compete à la Cournot. Specifically, firms R1 and R2 set quantities qi and q2, respectively, and the retail price is determined by the inverse demand p, 150-q1 - g2 (c) Please find pw, Pr, q1 and q2 in the SPNE of this game. What are the profits for the manufacturer and the retailers? (d) Please compare the joint profits for the firms in the scenarios considered in parts (a), (b) and (c) In words, explain how competition among the retailers affects the double marginalization problenm in this particular vertical relationship.

Explanation / Answer

Market demand is defined as the total amount of purchases of a product or family of products within a specified demographic. The demographic may be based on factors such as age or gender, or involve the total amount of sales that are generated in a particular geographic location.

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