Given the cost function C(x)=30000+100xC(x)=30000+100x for producing xx auto body frames

A)

The average cost is the total cost divided by the number of units produced. Therefore the average cost of producing 500 units are:

C(500)500=30000+100∗500500=160C(500)500=30000+100∗500500=160

Thus, the average cost is $160.

B)

For this part, we need to first find the marginal average cost function. The marginal average cost function is the first derivative of the average cost function. The average cost function will be:

AC=C(x)x=30000x−1+100∴MAC=−30000x−2The marginal average cost at production level of 500 units will be:MAC=−0.12AC=C(x)x=30000x−1+100∴MAC=−30000x−2The marginal average cost at production level of 500 units will be:MAC=−0.12

The average costs of the firm fall by $0.12 with the production of the 500th unit.