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Total Costs for a firm are given by: TC=3Q2+11

Economics Dec 07, 2020

Total Costs for a firm are given by: TC=3Q2+11.8TC=3Q2+11.8. Marginal costs for that same firm are given by: MC=2×3QMC=2×3Q. In the long-run, this firm will exit the market if the price falls below what value?

Expert Solution

Firms will produce at the minimum efficient scale, i.e., where average total cost is equal to the marginal cost. Average total cost is

ATC=TC/Q=3Q+11.8/QATC=TC/Q=3Q+11.8/Q

Marginal cost is total cost differentiated with respect to quantity, i.e.,

  • MC=6QMC=6Q

The minimum efficient scale is:

  • 3Q+11.8/Q=6Q11.8/Q=3QQ=23Q+11.8/Q=6Q11.8/Q=3QQ=2

A firm will exit if price is less than average total cost. At Q = 2, average total cost is:

  • 3∗2+11.8/2=11.93∗2+11.8/2=11.9

Hence, the firm will exit if price falls below $11.9.

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