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Homework answers / question archive / Suppose a firm has the following long run cost function: LTC-6000Q-60Q2+Q3 We know that the firm will have economies of scale for Q less than (insert a whole number with no decimal
Suppose a firm has the following long run cost function: LTC-6000Q-60Q2+Q3 We know that the firm will have economies of scale for Q less than (insert a whole number with no decimal.)
TC = 6000Q - 60Q^2 + Q^3
MC = 6000 - 120Q + 3Q^2
Economies of scale means a declining marginal cost, so we need to find marginal of marginal cost
M(MC) = -120 + 6Q
It is negative initially, then zero and then increases. It is zero at -120+6Q = 0, hence Q=120/6 = 20
So before Q=20 MC is declining and beyond Q=20 MC starts to increase. Hence the function shows economies of scale till Q=20
