(Industry equilibrium when entry is costly) Consider a market with inverse demand function p(Q) = 55 - 2Q, where Q = _ _qi, where N is the number of firms. Firms have constant marginal cost c = 5 per product and fixed cost K = 2 to enter the market. Firms compete by simultaneously choosing quantities. (a) Assume that there are N = 2 firms, and that they play a simultaneous-moves Nash-in-quantities game. Write down expressions for each firm's profits as a function of q, and q2. Use them to find the firms' best response functions and therefore their equilibrium quantities and profits. Calculate also consumer surplus. (b) Now suppose there are N firms in the market. Derive the Nash equilibrium prices, quantities and profits. (c) Suppose now that / is a continuous number and that firms play the following game. (1) They decide whether to enter or not and if so they incur the cost K. (2) Firms which have entered will set quantities. How many firms will enter at equilibrium? (Hint: solve by backward induction!) How would the equilibrium number of firms change if the entry cost K increased