A firm uses only one variable input and faces the following Average Cost function:
AC = Q^2 - 15Q + 48
Calculate the output level (Q) at which diminishing returns set in.
To calculate the output level (Q) at which diminishing returns set in, we need to determine the point at which the marginal cost (MC) starts to increase.
The average cost (AC) equation given is AC = Q^2 - 15Q + 48. To find the marginal cost, we need to calculate the derivative of AC with respect to Q.
MC = dAC/dQ
Differentiating the given AC equation, we get:
MC = 2Q - 15
Now, we can set MC equal to zero and solve for Q:
2Q - 15 = 0
2Q = 15
Q = 15/2
Q = 7.5
Therefore, the output level (Q) at which diminishing returns set in is 7.5 units.