There is a market where the consumers have a value v20 that is distributed on the set of non-negative numbers. The consumers have a utility v-p if they buy one unit of the product at price p and otherwise they get zero utility. The probability distribution of v is described by the density function e-v on the set v 0. (a) How many consumers are not willing to buy at the price p? (b) Sketch the demand curve for the product? (c) Suppose the product is supplied by a monopolist with a marginal cost c> 0. Write down its profit as a function of its output. Hence find the monopolist's profit- maximizing output. (d) Now suppose this product is supplied by two firms engaged in quantity competition both firms have marginal cost c>0. Find the quantity each firm wants to supply and the total supply in the market. (e) Hence find the quantity n firms in quantity competition would like to supply. Explain what happens to the market as n gets very large.