Consider a perfectly competitive industry in which the inverse demand is given by p(y)=2001-2y and each firm has the following cost function : c (y)=(1/3)y^3+18 for y>0, c(y)=0 for y=0
(a) In the long-run equilibrium, what price will be charged for the product? What total quantity will be sold? How many firms will operate in this market?
(b) A tax of 6 dollars per unit sold is now imposed on each firm operating in this market. In the long-run equilibrium, what price will be charged for the product? What total quantity will be sold? How many firms will operate in this market?
(c) Suppose instead that a monopolist operates in this market. There is no tax imposed on the monopolist, and he can produce the product at a constant marginal cost of c. What price will the monopolist charge (as a function of c)? Can this price be below the price you found in part a?