Assignment:
1. A monopolist with total cost function c(Q) = 10 + -1/2 Q2, faces a market with two distinct consumer groups with the first group having a demand function of q1(P) = 80 - 5P1 and the second having a demand function of q2(P) = 40 - 2P2.
a) Is this monopolist operating in the short run or the long run? Explain how you know.
b) Calculate the monopolist's profit-maximizing price and quantity sold if the monopolist must engage in uniform pricing. Find the monopolist's profits in this scenario. (Hint: use horizontal aggregation to form the total market demand curve).
c) The monopolist can now engage in third degree price discrimination, setting a different price for each market segment. Calculate the monopolist's optimal prices charged to each market segment, the quantities consumed by each market segment, and the monopolist's profits.
Would the monopolist rather engage in this price discrimination or would they rather set a uniform price?
2. A monopolist with cost function c(Q) = Q2 faces a demand function of QA(P) = 50 - PA in market segment A and QB(P) = 90 - 2PB in market segment B.
a. Suppose the monopolist engages in 3rd degree price discrimination. Calculate monopolist's profit maximizing prices and quantities for each market.
b. Suppose now the monopolist has to engage in uniform pricing. What is the monopolist's profit-maximizing price they should set? How do their profits compare to the profits they earn in part (a) above? (Hint: use horizontal aggregation to form the total market demand
curve).
c. Suppose the monopolist can upgrade their plant so that the cost function becomes:
c(QA, QB) = 3QA2 + QB2. How much should you be willing to pay to get this upgrade?