(1) A firm has the production function f(x_1, x_2) = ln(x_1) + ln(x_2). It operates in perfectly com ...

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(1) A firm has the production function f(x_1, x_2) = ln(x_1) + ln(x_2). It operates in perfectly competitive markets, and the output price p and the input prices w_1 and w_2 are all strictly positive. (a) Solve for the input demand functions. (b) Solve for the supply function. (c) Formulate the profit function and apply Hotelling's lemma to check that the supply function in your previous answer was correct. (2) Solve for the conditional demand functions and the cost function of the firm in problem 1. (3) Calculate the conditional input demands and the cost function for the linear production function y = f(x) = the sum over i = 1, ..., m of alpha_i x_i, where alpha_i is a positive constant for all i = 1, 2, ..., m.