Question

A competitive firm has the three-factor production function f (x, y, z) = (x + y)1/2 z 1/2. The factor prices used to be wx = $1, wy = $2, and wz = $3. Suppose that the price of factor y doubled while the other two prices stayed the same. Then the cost of production a. increased by more than 10% but less than 50%. b. increased by 50%. c. doubled. d. stayed the same. e. increased by more than 50% but did not double.

Answer 1

The cost of production increased by more than 50% but did not double when the price of the factory doubled.

Step-by-step explanation:

To determine the effect of the doubled price of the factory on the cost of production, we need to calculate the new cost and compare it to the original cost. The original cost of production can be calculated by plugging in the original factor prices into the production function:

f(x, y, z) = (x + y)^(1/2) × z^(1/2)

To find the new cost of production, we need to double the price of the factory and keep the other prices the same:

wx = $1, wy = $4, and wz = $3

After calculating the new cost of production, we can determine the percentage increase by comparing it to the original cost.

The cost of production increased by more than 50% but did not double, so the correct answer is e. increased by more than 50% but did not double.