A competitive firm with output y has a production function y = (2x₁ + x₂)^1/2, where x1 and x2 are inputs used in production.The firm produces the output minimizing cost.With input prices w1 and w2, which of the following is true? A)The firm has L-shaped isoquants. B)The firm must use the cheaper input. C)The firm must use only input x₁ if w₁

Question

A competitive firm with output y has a production function y = (2x₁ + x₂)^1/2, where x1 and x2 are inputs used in production.The firm produces the output minimizing cost.With input prices w1 and w2, which of the following is true? A)The firm has L-shaped isoquants. B)The firm must use the cheaper input. C)The firm must use only input x₁ if w₁ < 2w₂. D)The technology has increasing returns to scale. E)More than one of the above is true.

Quizplus · Accepted Answer

The production function shows that the firm has a choice between using input x1 or input x2. The condition for choosing between the two inputs would depend on their relative prices, w1 and w2. If w1₁ F1F1F1S1F1F1F10 2w1₂, then it is cheaper to use input x1. On the other hand, if w1₁ F1F1F1S1F1F1F10 2w1₂, then it is cheaper to use input x2. Therefore, the firm must use only input x1 if w1₁ F1F1F1S1F1F1F10 2w1₂, which means that the isoquant is not L-shaped, but instead has a kink where the firm switches from using one input to the other. The given production function does not explicitly show increasing returns to scale, so option D is not correct.

A Competitive Firm with Output Y Has a Production Function