Suppose Y Company estimates the following total cost function from cost output data:

Question

TC = $135,000 + $250Q + $1.5Q2.
Find the optimum level of output that makes the company efficient and per unit cost (AC) at the rate of output.

Answer 1

The optimum level of output that makes the company efficient is found by taking the derivative of the total cost function and setting it equal to zero. This gives us:

dTC/dQ = 250 + 3Q = 0

Solving for Q, we get Q = -83.33.

The per unit cost (AC) at the rate of output is found by substituting the optimum level of output into the total cost function and dividing by the output. This gives us:

AC = (135,000 - 83.33*250 + 1.5*(-83.33)2) / -83.33 = $2,917.