Please Answer the Question No: 2 Consider a representative consumer with the fol
ID: 1258111 • Letter: P
Question
Please Answer the Question No: 2
Consider a representative consumer with the following quasi-linear utility function over three goods: U{qo, q1q2) = q0 + alpha_1q_1 + alpha_2q_2 - [beta_1q^2_1 + 2 gammaq_1q_2 + beta_2q^2_2]/2 with alpha_i > 0, beta_i > 0, and beta_1beta_2 where q_0 is the numeraire good. Derive the consumer's demands for goods 1 and 2 (both direct and inverse demand systems). Which parameter measures the degree of substitution or complementarity between the two goods? Explain. Derive the consumer's surplus (or indirect utility as a function of prices) (Will it be easier to use matrix notation?).. Suppose two firms produce these two goods at constant marginal cost c_1 and c_2, respectively. Compute the Bertrand-Nash equilibrium when the firms compete by setting prices simultaneously Suppose the two firms merge to become a monopolist over the two products (or collude to maximize their joint profits). Compute the profit-maximizing prices. Compare the prices and consumer's surpluses in the above two market structures. Explain how your results depend on the sign of the paramater gamma.Explanation / Answer
the elasticity of substitution measures the percentage change in factor proportions due to a change in marginal rate of technical substitution. In other words, for our canonical production function, Y = ¦ (K, L), the elasticity of substitution between capital and labor is given by:
s = d ln (L/K)/d ln (¦ K/¦ L)
= [d(L/K)/d(¦ K/¦ L)]·[(¦ K/¦ L)/(L/K)]
The elasticity of substitution was designed as "a measure of the ease with which the varying factor can be substituted for others.