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 monopolistic 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 monopolistic would ever never produce at an output level at which demand elasticity is -1 (part I). Or why a monopolist will always produce an output lower than that which would maximize its total revenue? (Part II). (Hint: What is the objective of a monopolist?)