Question

A monopolist is deciding how to allocate output between two geographically separated markets (market 1 and market 2). Resale between two markets are not possible. Demand functions are p1 (Q1 )=40−2Q1 and p2(Q2 )=30−1,5Q2. The monopolist's total cost is TC=0,5Q2 +10Q+20, where Q=Q1 +Q2.

(A) Calculate the outputs and prices which will be set in the two markets.
(B) Now assume that the monopoly is not allowed to price discriminate. What price will the monopoly charge? What quantity will it sell for each market? Also calculate and compare profits with and without price discrimination.
(C) Show your solution in part (b) graphically.

Answer 1

To allocate output between two markets, the monopolist can calculate the profit-maximizing quantities by setting marginal revenue equal to marginal cost for each market. The prices for each market can be found by substituting the quantities into the demand functions. The total profit can be calculated by subtracting the total cost from the total revenue.

Step-by-step explanation:

Step 1: To determine the outputs and prices set in the two markets, we need to find the profit-maximizing quantities for each market. First, we set the marginal revenue (MR) equal to the marginal cost (MC) for each market separately. The MR equation for market 1 is 40 - 4Q1, and for market 2 it is 30 - 3Q2. The MC equation is 0.5Q2 + 10Q + 20. Solving these equations, we find Q1 = 5 and Q2 = 10. Step 2: Now, let's calculate the prices for each market. We can substitute the quantities into the demand functions to find the prices. For market 1, substituting Q1 = 5 into p1(Q1) = 40 - 2Q1, we get p1 = 30. For market 2, substituting Q2 = 10 into p2(Q2) = 30 - 1.5Q2, we get p2 = 15. Step 3: The total profit can be calculated by subtracting the total cost from the total revenue. The total revenue for market 1 is Q1 * p1 = 5 * 30 = 150, and for market 2 it is Q2 * p2 = 10 * 15 = 150. The total cost is Q * average cost = (Q1 + Q2) * (0.5 * Q2 + 10 * Q + 20). Substituting the quantities, we get TC = 275.