2. Suppose you are analyzing a particular market. All consumers in this market have the utility function U(y1, 92) = y2 + 10y1 - yi/2. Suppose that there are many firms producing good 1, and that each of these firms has the production function y1 = 2105 + 4105. Assume good 2 is a composite good with price p2 = 1. (a) Derive a consumer's Marshallian demand for good 1. Assume all consumers can always afford good 1. (b) For the rest of this question, suppose there are 5 consumers in total in the market. What is the aggregate demand for good 1?(c) 'What is the price elasticity of demand for prices p1 = 1, p1 = 5, and p1 = 10? (d) Find the conditional factor demands for L and K for a typical rm producing good 1. (e) Suppose the government forces all rms operating in the market to purchase a $20 operating license. What is the cost function of a rm? (f) For the rest of the question, assume that all input prices are equal to 1. 1What is the supply curve of a rm in this market? (Note: Assume the longrun case, that is, that the supply is zero if prots are negative.) (g) If there was only one rm supplying the market: what would the equilibrium price and quantity be? (Note: do not assume any complicated strategic behaviour. For instance: do not assume that this is a monopoly and that this rm would act like a monopolist; rather: view this as a shortrun case where the rm behaves according to the supply curve you identied in the previous part.) (11) Calculate the prots for this individual rm supplying the market. (i) Assume rms have no barriers to entry or exit. Moreover, assume there are no restrictions on the number of operating licenses issued. In the longrun, how many rms will exist in this market? What will the equilibrium price and quantity be? {j} Compare the shortrun, single rm equilibrium to the longrun equilibrium. \"-"hat are the prices, quantities and average costs of production under each equilibrium? 'What is the producer and consumer surplus under each equilibrium