What price-quantity combination maximizes firms profits

Question

Problem 1: You are the manager of a monopoly, and your demand and cost functions are given by
                  
P = 200 - 2Q and C(Q) = 2,000 + 3Q², respectively.

a. What price-quantity combination maximizes your firm’s profits?

b. Calculate the maximum profits

c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination?

d. What price-quantity combination maximizes revenue?

e. Calculate the maximum revenues.

f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price-quantity combination?

Problem 2: You are the manager of a firm that produces a product according to the cost function
                        
C(qi )  = 100 +50qi – 4q²i  + q³i  .  Determine the short-run supply function if:

a. You operate a perfectly competitive business.

b. You operate a monopoly.

c. You operate a monopolistically competitive business.