Suppose that demand for carpet-cleaning services in Nashville is described by the demand function P = 180 - Q. Suppose that there are currently three firms that clean carpets in the area. The unit cost of cleaning a carpet is constant and equal to GHC30 for two firms and is GHC30b for the third firm, where b 2 1. In addition, all firms have fixed overhead costs of $900. Firms in this industry compete in quantities. a) What is the Cournot-Nash equilibrium price and what are the outputs and profits of each firm? What is the upper limit on b for the third firm to be able to survive? - JVVI b) Now suppose that a low-cost firm merges with the high-cost firm. In doing so, the fixed costs of the merged firm become $900a with 1 S a s 2. What is the post-merger equilibrium price? What are the outputs of the non-merged and the merged firms? 3 ) c) Derive a relationship between a and b that is necessary to guarantee that the profit earned by the merged firm is sufficient to compensate all the shareholders/owners who owned