Question

A firm's long-run total cost curve is TC(Q) = 40Q - 10Q^2 + Q^3.

a. Over what range of output does the production function exhibit economies of scale?

b. Over what range does it exhibit diseconomies of scale?

c. At what quantity is minimum efficient scale?

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Answer 1

Answer.) Economies of scale occur when MC < AC ; diseconomies of scale occur when MC > AC ; and minimum efficient scale occurs where MC = AC (if MC is increasing at that point). We need to calculate MC and AC :

MC(Q)= 40 - 20Q + 3Q²

AC(Q) = 40 - 10Q + Q²

Economies of scale occur when MC < AC :

40 - 20Q + 3Q² < 40 - 10Q + Q²

2Q² - 10Q < 0

Q( 2Q - 10) <0

Hence, we have economies of scale when Q < 5

Similarly, diseconomies of scale occur when MC > AC . Hence, we have diseconomies of scale when Q > 5.

And finally, since AC is decreasing (economies of scale) for Q < 5 and increasing (diseconomies of scale) for Q > 5, it must be the case that minimum AC occurs at Q = 5. Hence,  the minimum efficient scale is Q = 5.

Q = 5. Hence, the minimum efficient scale is Q = 5.