Sophisticated Monopoly Pricing:
Problem 1: The Locust Corporation is comprised of a marketing division, and production division. The marginal cost of producing a unit of the firm’s product is $10 per unit, and the marginal cost of marketing is $4 per unit. The demand curve for the firm’s product is:
P = 100 – 0.01Q
Where P is the price per unit (in dollars) and Q is the output (in units). There is no external market for the good made by the production division.
a. What is the firm’s optimal output?
b. What price should the firm charge?
c. How much should the production division charge the marketing division for each unit of the product?