Problem 1:
The locust corporation is composed of a marketing division and a production division. The marginal cost of producing a unit of the firm’s product is $10 per unit, and the marginal cost of marketing it 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 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?
Problem 2:
James Pizzo is president of a firm that is the price leader in the industry; that is, it sets the price and the other firms sell all they want at that price. In other words, the other firms act as perfect competitors. The demand curve for the industry’s product is P=300-Q, where P is the price of the product and Q is the total quantity demanded. The total amount supplied by the firms is equal to Qr, where Qr= 49P. ( P is measured in dollars per barrel; Q,Qr, and Qb are measured in millions of barrels per week.)
a. If Pizzo’s firm’s marginal cost curve is 2.96Qb, where Qb is the output of his firm, at what output level should he operate to maximize profit?
b. what price should he charge?
c. How much does the industry as a whole produce at this price?
d. Is Pizzo’s firm the dominant firm in the industry?