Question

Consider the following production function: x = f(l,k) = Al^bk^bwhere x is the output, l is the labour input, k is the capital input, and A, b are positive constants.

(a) Set up the cost minimization problem and solve for the first order conditions using the Lagrange Method. Let w be the wage rate and r the rental rate of capital.

(b) Using your answer in (a), find how much labour and capital would the firm use to produce x outputs, given wage rate w and rental rate of capital r? What are these functions called?

(c) Using your answer in (b), find the minimum cost it takes to produce x outputs. What is this function called?

(d) Use your answer in (c) to derive the marginal cost function.

(e) Under what conditions does the production function exhibit increasing, constant, and decreasing returns to scale respectively?

Answer 1