Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y) = y^2+ 1 for y > 0 and c(0) = 0. Suppose that initially the demand curve for this industry is given by D(p) = 52 − p.
(a) What is the supply curve of an individual firm? 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 equi- librium number of firms?
(g) What will be the equilibrium price? 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 equilib- rium number of firm? 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?