problem 1: A firm has segmented its market into the following demand functions:
P1 = 500 – 50Q, P2 = 500 – 20Q with a cost function: MC = AC = 20
a) Determine the profit maximizing price and quantity and corresponding economic profits if the firm charges all customers the same price.
b) Determine the profit maximizing prices and quantities and corresponding economic profits if it practices third-degree price discrimination.
c) What are the conditions necessary for price discrimination to succeed?
problem 2: A firm has a demand function P = 200 – 5Q and cost function: AC = MC = 10 and a potential entrant has a cost function: AC = MC = 20.
a) Determine the optimal price, quantity and economic profit for the firm in the short run.
b) If the firm wants to preclude all entry into the market what price, quantity and profit will it choose?
c) What price, quantity, and corresponding profit occur if this a purely competitive market?
d) Assuming the demand function is identical for all buyers, determine the two-part tariff that maximizes profit for the firm.
e) Determine the optimal price, quantity and economic profit for the firm if it is a pure monopolist.
problem 3: If a firm targets a 25 % rate of return on sales, and has unit costs of production of $100, what price should it charge if it uses cost-plus pricing? If the firm has a demand function P = 10000 – 20Q is the cost-plus price the profit-maximizing price? If not, determine the profit-maximizing price, quantity and corresponding profit. Is the target rate of return the profit-maximizing r.o.r.? why or why not? What important economic considerations, does cost-plus pricing ignore?
problem 4: Use the following production function and budget constraint to answer the problems below.
Q = L + K
1000 = 2L + 4K
a) Determine the returns to scale property of the production function.
b) Determine the returns property to each factor.
c) Determine the optimal quantities of labor and capital
d) Determine the maximum quantity that can be produced.
e) Determine the production relationship between labor and capital.
problem 6: Discuss a typical firm’s preferred market structure and pricing policy for maximizing its economic profit potential.