please help to finish the micro economic problem set

please help to finish the micro economic problem set

1 Third-degree price discrimination Adidas, Inc. produces a high-fashion and a low-fashion version of a walking shoe. The estimated inverse demand curves for each of these products are given by: High-fashion version: 𝑃 = 130 − 2𝑄𝐻 , and Low-fashion version: 𝑃 = 80 − 𝑄𝐿 where quantity is measured per thousand pairs of shoes. Assume that the marginal cost of production and sale for each pair (high- or low-fashion) is constant at $30.

(a) Provided that (i) Adidas can design its product such that it successfully segments the high and low-fashion markets and (ii) the two demands are in fact independent, what are the optimal prices for each version?

(b) Given your answers in part (a), determine the profits of Adidas and the amount of consumer surplus realized by each group in equilibrium.

(c) What are the elasticities of demand calculated at each of the optimal prices? Do your answers match your understanding of the relationship between elasticity and price when a firm is segmenting the market? Explain.

(d) Now suppose that Adidas cannot in fact estimate the separate demands for high- vs. lowquality walking shoes but can only estimate the total demand for both types of shoes together. Derive the (ordinary) demand curve faced by Adidas in this case and the price Adidas would charge under this assumption. How does consumer surplus in this case compare to that found in part (b)?

(e) What would be Adidas’s profits if it could identify not only which type of shoe a customer demands but also each shoe buyer’s maximum willingness to pay for the preferred shoe type?

2 Cournot oligopoly and cartels Suppose that a market is characterized by a duopoly where each firm makes the Cournot conjecture (i.e., each believes that regardless of how much it produces, the other firm’s output remains constant). Firm 1’s output is defined as 𝑞1 and firm 2’s as 𝑞2 such that aggregate output is 𝑄 = 𝑞1 + 𝑞2. The (inverse) market demand curve is given by 𝑃(𝑄) = 1000 − 10𝑄 Each firm produces with a marginal cost of zero and incurs no fixed costs of production.

(a) Derive the equations for each firm’s reaction curve and graph these equations on a single well-labeled diagram.

(b) Calculate the Cournot equilibrium output for both firms (𝑞1 ∗ and 𝑞2 ∗ ).

(c) Calculate the equilibrium market price given your answer to part (b).

(d) Suppose the firms form a cartel to maximize joint profits. How much output would be produced and how much profit would each firm make in the cartel? (Assume that the firms would evenly split production between them)? How much more profit does each firm make as a member of the cartel relative to the Cournot equilibrium?

(e) Would you expect the cartel to be more or less likely to breakdown if the demand facing the firms was subject to random fluctuations? Explain.

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