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) 6.
B) 36.
C) 0.16.
D) 216.
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) 6. 
B) 36. 
C) 0.16. 
D) 216. 
E) The answer depends on the original choice of x, y, and z.

Quizplus · Accepted Answer

If the amount of each input is multiplied by 6, we can rewrite the production function as: 
f(6x,6y,6z) = min{ 11(6x), 6(6y), 3(6z)} = min{66x, 36y, 18z}

Therefore, the new output is equal to the minimum value among 66x, 36y, 18z, which is 18 times the minimum value among x, y, z.

Since the minimum value can't increase from 0 to any positive value, the new output can't exceed 18 times the original output. Therefore, the correct answer is B, 36.

A Firm Uses 3 Factors of Production