Suppose a firm's total cost curve can be written $T C ( Q ) = Q - .5 Q ^ { 2 } + Q ^ { 3 }$, with marginal cost $M C ( Q ) = 1 - Q + 3 Q ^ { 2 }$. This cost function exhibits:
A) economies of scale
B) diseconomies of scale
C) neither diseconomies nor economies of scale.
D) economies of scale for output levels less than some level, $Q _ { 1 } = 1 / 4$, and diseconomies of scale thereafter.

Question

Quizplus · Accepted Answer

The cost function exhibits economies of scale when marginal cost decreases with an increase in output, and diseconomies of scale when marginal cost increases with an increase in output. In this case, the marginal cost function initially decreases with an increase in output, indicating economies of scale. However, after output level Q = 1/4, the marginal cost function starts increasing with an increase in output, indicating diseconomies of scale. Therefore, the correct answer is D, economies of scale for output levels less than some level, Q1=1/4, and diseconomies of scale thereafter. To determine whether the cost function exhibits economies or diseconomies of scale, we look at the behavior of the marginal cost curve. If the marginal cost curve is decreasing, there are economies of scale; if it is constant, there are constant returns to scale; and if it is increasing, there are diseconomies of scale. In this case, the marginal cost curve is $M C ( Q ) = 1 - Q + 3 Q ^ { 2 }$, which is a quadratic with a positive coefficient on the $Q ^ { 2 }$ term. This means that the marginal cost curve is increasing, so there are diseconomies of scale. However, as we can see from the marginal cost curve, there is a point at which it starts to become less steep -- that is, where the second derivative of the total cost function with respect to Q goes from positive to negative. This point occurs at $Q _ { 1 } = 1 / 4$, which is the output level at which the marginal cost curve is minimized. This means that for output levels less than $Q _ { 1 }$, the firm experiences economies of scale, and for output levels greater than $Q _ { 1 }$, it experiences diseconomies of scale. Thus, the answer is D.

Suppose a Firm's Total Cost Curve Can Be Written TC(Q)=Q−.5Q2+Q3T C ( Q ) = Q - .5 Q ^ { 2 } + Q ^ { 3 }TC(Q)=Q−.5Q2+Q3

Suppose a Firm's Total Cost Curve Can Be Written $T C ( Q ) = Q - .5 Q ^ { 2 } + Q ^ { 3 }$