Answer both parts (a) and (b) of this question. (a) A firm produces output, q, using...

 

Transcribed Image Text:

Answer both parts (a) and (b) of this question. (a) A firm produces output, q, using only capital, k, bought at a price 0 < r < 1. The price of output is assumed to be 1. The production technology is such that the capital k needed to produce q is k = with 0 <k < 1. (i) [10 marks] Suppose that the firm seeks to maximize profits. Write the max- imization program of the firm. (ii) [6 marks] Compute and solve the first order conditions to obtain the firm's demand for k as a function of r. (iii) [4 marks] Obtain the second order condition. Is the solution to the first order condition a solution to the maximization program of the firm? (iv) [5 marks] Compute the firm's profit as a function of r. (v) [5 marks] Use the envelope theorem to evaluate the marginal effect of a rise in r on the profit , that is r (b) Suppose now that the firm uses both capital K and labor L. The production function is q=g(K)log(L) with g'(K) > 0 and g" (K) < 0. Capital is employed at a given rental rate r per unit, the wage rate is w and the price of output p. The firm's profit, 7, can be written as: =pg(K)log (L) - wL-rK. (i) [10 marks] Obtain the first and second order derivatives of the firm's profit with respect to K and L. (ii) [10 marks] State the necessary first order conditions for profit maximiza- tion. Obtain the second order sufficient condition for profit maximisation in terms of g, g'. g" and L. Answer both parts (a) and (b) of this question. (a) A firm produces output, q, using only capital, k, bought at a price 0 < r < 1. The price of output is assumed to be 1. The production technology is such that the capital k needed to produce q is k = with 0 <k < 1. (i) [10 marks] Suppose that the firm seeks to maximize profits. Write the max- imization program of the firm. (ii) [6 marks] Compute and solve the first order conditions to obtain the firm's demand for k as a function of r. (iii) [4 marks] Obtain the second order condition. Is the solution to the first order condition a solution to the maximization program of the firm? (iv) [5 marks] Compute the firm's profit as a function of r. (v) [5 marks] Use the envelope theorem to evaluate the marginal effect of a rise in r on the profit , that is r (b) Suppose now that the firm uses both capital K and labor L. The production function is q=g(K)log(L) with g'(K) > 0 and g" (K) < 0. Capital is employed at a given rental rate r per unit, the wage rate is w and the price of output p. The firm's profit, 7, can be written as: =pg(K)log (L) - wL-rK. (i) [10 marks] Obtain the first and second order derivatives of the firm's profit with respect to K and L. (ii) [10 marks] State the necessary first order conditions for profit maximiza- tion. Obtain the second order sufficient condition for profit maximisation in terms of g, g'. g" and L.

Answer rating: 100% (QA)

a i The maximization program of the firm can be written as Maximize pq rk subject to k 01 Where Prof... View the full answer