Suppose that a particular good, y, is produced according to the following production function y = min(ax₁,bx₂)where x₁and x₂are inputs, and a and b are positive constants. Suppose further that x₁/x₂currently equals b/a. Then: A)an additional unit of x₁or x₂will not increase output. B)the current ratio of input- usage is technically inefficient. C)if a b, the production of any output level requires more x₁than x₂. D)an additional unit of x₁will increase output.

Question

Suppose that a particular good, y, is produced according to the following production function y = min(ax₁,bx₂)where x₁and x₂are inputs, and a and b are positive constants. Suppose further that x₁/x₂currently equals b/a. Then: A)an additional unit of x₁or x₂will not increase output. B)the current ratio of input- usage is technically inefficient. C)if a > b, the production of any output level requires more x₁than x₂. D)an additional unit of x₁will increase output.

Quizplus · Accepted Answer

Given the production function y = min(ax₁, bx₂) and the current input ratio x₁/x₂ = b/a, the production is at an efficient point where both terms inside the min() function are equal. Adding an additional unit of either input will not increase output because the production is determined by the minimum of the two terms, which are currently balanced.

Suppose That a Particular Good, Y, Is Produced According to the Following