A competitive firm produces its output according to the production function y = min{ , 10}. Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is

Question

A competitive firm produces its output according to the production function y = min{  , 10}. Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is

Quizplus · Accepted Answer

To determine the demand for factor x, we need to find the firm's profit-maximizing level of input usage. The profit-maximizing condition for a competitive firm is to choose the input level up to the point where the marginal revenue product (MRP) equals the input price. We can find the MRP by taking the derivative of the production function with respect to x: MRP = 11e^{6C}(6C'x) where C'x is the marginal product of x. Setting this equal to the input price w, we get: 11e^{6C}(6C'x) = w Solving for x, we get: x = min{w/(11e^{6C}(6C')), 10} Therefore, the demand for factor x when the factor price is w is: x = min{w/(11e^{6C}(6C')), 10} or x=min{w², 100} so the answer is C.

A Competitive Firm Produces Its Output According to the Production