A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by A) 0.30. B)3 C)9 D)27 E) The answer depends on the original choice of x, y, and z.

Question

Quizplus · Accepted Answer

Given the production function, f(x, y, z) = min{ 11e6, y, 11e6 }

If we increase the amount of each input by 3, the new production function becomes,
f(3x, 3y, 3z) = min{ 11e6*3, y*3, 11e6*3 }
f(3x, 3y, 3z) = min{ 33e6, 3y, 33e6 }

As we can see, the minimum of the three values is now much higher than before. This means that the output has increased by a factor of 9 when the inputs are multiplied by 3.

Hence, the answer is C) 9.

A Firm Uses 3 Factors to Produce Its Output