ASSIGNMENT #8 MONOPOLY Q1: (10 points) Suppose a monopolist has the following cost function C(Q) = Q2 (with marginal cost MC(Q) = Q). Suppose they face demand is P = 100 - Q. a) Sketch the market demand, marginal costs, and marginal revenues. b) What is the monopolist's optimal level of output and profits? c) Confirm that demand is elastic at the optimal output. d) Calculate the firm's markup. e) What is the DWL associated with the monopoly output? f) Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output? g) Does the DWL fall or rise?

Q2: (10 points) Price Discrimination. Suppose a monopolist faces two separate markets. Demand in market 1 is P1 = 100 - Q1 and Demand in market 2 is P2 = 80 - Q2. Cost are C(Q) = 10(Q1 + Q2) with marginal cost MC(Q) = 10. a) Suppose the monopolist can charge different prices for each market. What is the profit-maximizing price and quantity in each market (P1, Q1) (P2, Q2)? b) What is the total profit the monopolist receives when it price discriminates? c) Suppose the monopolist must charge the same price in each market. That is, P1 = P2. Sketch the total demand curve and find the equation for the demand. d) What is the profit maximizing price (P) and quantity in each market (Q1, Q2)? e) What total profit does the monopolist receive when it cannot price discriminate? f) Why are profits higher under discrimination? TOTAL: 30 points