Kindly solve these for me
2. Consider a firm that produces output using only labor input, E, and capital input, K, using the production technology f(E, K) = E"KB. The firm is a price taker in input markets, where w is the per unit price of labor and r is the per unit price of capital. The firms sells its output in a competitive product market at price p. c. What two conditions hold if the firm chooses the (E,K) bundle that produces output level y at minimum long run cost? d. Use the conditions in (c) to find the firm's conditional (i.e., output constant) demand functions for labor and capital. What is the wage elasticity of conditional labor demand? What is the output elasticity of conditional labor demand? e. Find the firm's long run total cost and marginal cost functions, given the conditional input demand functions that you found in (d). f. Find the firm's profit-maximizing output level, given the long run total cost function that you found in (e). What is the wage elasticity of output supply? g. Use your answers to (d) and (f) to find the firm's unconditional (i.e., not holding output constant) demand functions for labor and capital. What is the wage elasticity of unconditional labor demand? answer a-g5. Suppose N has mean 3 and variance {. Suppose )' has mean S and Variance 9. Let Z - 6X + 7Y. Suppose the covariance between X and ) is 2 (a) Compute the mean of Z [b) Compute the variance of Z (e) Compute the variance of 6X - TY (d) Com inmor between X and Z2. Suppose that X has mean fx and variance of, and suppose that Y has mean by and variance of. Suppose the correlation between X and Y is p. Let U = ax +b and V = cy + d where a, b, c, d are constants. (a) Find Covariance(U. V) in terms of a, b. c, d, ux. ox, ur. of, and p. (Note: some of these parameters might not appear in the answer.) (b) Find Corr(U. V) in terms of a, b. c, d, ux. ox. My, or, and p. (Note: some of these parameters might not appear in the answer.) (c) Suppose that W and V are two random variables with Var(W) = 4 Var(V) = 9, and Cov(W. V ) = 2. Find Var(-4W + 3V - 2). (d) Suppose that X and Y are random variables with cov(X, Y) = 3 Find cov(2X - 4, 3 - 5Y)Consider a pure exchange economy with two consumers and two goods. Each consumer has the following utility function: Exchange Economy Consider a pure exchange economy with two consumers, i=1,2 and two goods. The consumers' utility functions are given by U(x,,x, )=(Xi-)(x; ) and endowments are given by wi=(a;, b; ) for i=1, 2. Let p denote the relative price of good 1 in terms of good 2 al Compute the excess demand function for this economy. b) Define a competitive equilibrium for this economy. c) Find the equilibrium price ratio
