Consider a competitive industry with a large number of firms, all of which have identical cost functionsc(y) =y2+ 1 fory >0 andc(0) = 0. Suppose that initially the demand curve for this industry is given byD(p) = 52p. (The output of a firm does not have to be an integer, but the number of firms does have to be an integer.)

(1) What is the supply curve of an individual firm? (Construct an expression forS(p).) If therenfirms in the industry, what will be the industry supply curve?

(2) What is the smallest price at which the product can be sold?

(3) What will be the equilibrium number of firms in the industry? (Hint: Take a guess at what the industry price will be and see if it works.)

(4) What will be the equilibrium price? What will be the equilibrium output of each firm?

(5) What will be the equilibrium output of the industry?

(6) Now suppose that the demand curve shifts toD(p) = 52.5p. What will be the equilibrium number of firms? (Hint: Can a new firm enter the market and make non-negative profits?)

(7) What will be the equilibrium price, the equilibrium output of each firm, and the equilibrium profits of each firm?

(8) Now suppose that the demand curve shifts toD(p) = 53p. What will be the equilibrium number of firms and the equilibrium price?

(9) What will be the equilibrium output of each firm, and the equilibrium profits of each firm?