A competitive firm produces its output according to the production function y = min{x2, 100}. Let w be the price of the factor x, and let the price of output be $1.The demand for x, when the price of x is w, is

Question

Quizplus · Accepted Answer

The production function y = min{x^2, 100} implies that output is limited by either the quantity of x or 100, whichever is lower.

Therefore, if the price of x (w) is greater than 10, then it is not profitable for the firm to purchase any x, since the output will be limited by 100. However, if the price of x is less than or equal to 10, the firm will purchase x up to the point where the output is limited by x^2.

Setting x^2 = 100, we get that x = 10. Therefore, the demand for x is 0 if w > 10 and 10 if w ≤ 10.

A Competitive Firm Produces Its Output According to the Production