Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y) = y2 + 1 for y > 0 and c(0) = 0. Suppose that initially the demand curve for this industry is given by D (p) = 52 − p. (The output of a firm does not have to be an integer number, but the number of firms does have to be an integer.)
(a) What is the supply curve of an individual firm? S(p) = ________. If there are n firms in the industry, what will be the industry supply curve? ________.
(b) What is the smallest price at which the product can be sold? ________.
(c) What will be the equilibrium number of firms in the industry)
(d) What will be the equilibrium price? ________. What will be the equilibrium output of each firm? ________.
(e) What will be the equilibrium output of the industry? ________.
(f) Now suppose that the demand curve shifts to D(p) = 52.5 − p. What will be the equilibrium number of firms?
(g) What will be the equilibrium price? Solve 52.5 − p = ________. What will be the equilibrium output of each firm? ________. What will be the equilibrium profits of each firm? ________.
(h) Now suppose that the demand curve shifts to D(p) = 53−p. What will be the equilibrium number of firms? ________. What will be the equilibrium price? ________.
(i) What will be the equilibrium output of each firm? ________. What will be the equilibrium profits of each firm? ________.