Consider a market with demand given by Q = 12p^( −4) . A firm has a constant MC = 3 > 0 with no fixed costs. Answer the following questions. (You don’t need to set the maximization problem)
a) (3 points) Derive the price elasticity of quantity demand by the notation.
b) (2 points) Write the definition of Lerner’s index by the given notation and the answer from a).
c) (10 points) Suppose the government grants this firm an exclusive monopoly in this market. Find the profit maximizing price(market price) by a) and b). Suppose that, in addition to the firm’s output, the government also produces QG = 2p −4 , where p is the price charged by the firm.
d) (10 points) Obtain the firm’s residual demand (very easy) and show that the presence of the government in the market does not change either the market price nor the aggregate market quantity. e) (5 points) Calculate HHI measure in this market(Monopolist and Government) and report the degree of market concentration from the Department of Justice.