Profit-maximizing price-quantity combination

Question

Question 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?

Question 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.