A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 6, its output will be multiplied by
A) 216.
B) 36.
C) 6.
D) 0.16.
E) The answer depends on the original choice of x, y, and z.

Question

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{  }. If the amount of each input is multiplied by 6, its output will be multiplied by
A) 216. 
B) 36. 
C) 6. 
D) 0.16. 
E) The answer depends on the original choice of x, y, and z.

Quizplus · Accepted Answer

When each input is multiplied by 6, the function becomes f(6x,6y,6z) = min{11(6x), 3(6y)^2, 2(6z)^3}. This simplifies to f(6x,6y,6z) = min{66x, 108y^2, 432z^3}. Since the minimum function only depends on the smallest input, and since multiplying each input by 6 does not change the ranking of the inputs, the output will be multiplied by 36 (6^2) when each input is multiplied by 6.

A Firm Uses 3 Factors of Production