Suppose you are given the following information about a particular perfectly competitive industry:

Q_D=400050P Market Demand

Q_S = 850P Market Supply

C(q) = 100 + 2q²/200 Firm total cost function

MC(q) = 4q/200 Firm marginal cost function

For simplicity, assume that all firms are identical.

a) Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm.

b) How many firms are there in the market?

c) Would you expect to see entry into or exit from the industry in the long run? Explain. What effect would entry or exit have on equilibrium price and quantity? Be specific

d) What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain.

e) What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain.