Question

Question #4

A perfectly competitive firm is currently producing 10 units of output. Its current total
cost is $85 and its cost curves have the usual shapes. If the firm increased output to 12
units, total cost would rise to $87. The firm’s fixed cost is $15. Is Q = 10 the short-run profit-maximizing level of output for this firm? Why or why not? Show your work and explain clearly your reasoning. If you just show an answer with no work, you will not receive full credit.

Answer 1

Q1 = 10

TC1 = $85

Q2=12

TC2 = $87

TFC = $15

Hence, TVC1 = TC1 - TFC = $85 - $15 = $70

TVC2 = TC2 - TFC = $87 - $15 = $72

MC = (TC2 - TC1)/(Q2-Q1) = ($87 - $85)/(12-10) = $1

In Perfect competition, for profit-maximization in the short-run, the equilibrium condition observed is: P = MC = MR

AC1 = TC1/Q1 = $85/10 = $8.50

AC2 = TC2/Q2 = $87/12 = $7.25

AVC1 = TVC1/Q1 = $70/10 = $7

AVC2 = TVC2/Q2 = $72/12 = $6

It shall be noted that as output increases from 10 to 12 units, the AVC, as well as AC both decreases - AVC decreases from $7 to $6 and AC, decrease from $8 to $7.25

Hence, Q = 10 is not the short-run profit-maximizing level of output for this firm.

Because for the short-run equilibrium to hold at a given quantity , say X unit, the MC would increase for an additional unit of quantity beyond this X unit such that AVC and AC curve are both increasing.

But, in this case, the AC and AVC both are decreasing as Q increases from 10 unit to 12 unit.

Thus, Q = 10 is not the short-run profit-maximizing level of output for this firm.