Problem 1: Assume that the long run total cost function for each firm in a perfectly competitive industry is LRTC = q3 - 4q2 + 8q and the market demand function is Q = 2000 - 100p. Calculate:
a. Each firm's individual output
b. Equilibrium market price and quantity
c. Number of firms in the industry
d. Profit per firm
Problem 2: If a monopolist charges the same price for all of its output (i.e., it does not price discriminate), total revenue for the firm will be TR = P(Q)Q.
Show that:
a. Total revenue is maximized when prices and quantities are set so that demand elasticity is -1.
b. Explain why a monopolist would never produce at an output level at which demand elasticity is -1 (part 1). Or why a monopolist will always produce an output lower than which would maximize its total revenue? (part 2). (Hint: What is the objective of a monopolist?)