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Homework answers / question archive / Assume that the shoe industry is perfectly competitive
Assume that the shoe industry is perfectly competitive. All firms in the market are identical, with TC=50+2Q+2Q2TC=50+2Q+2Q2, and MC=2+4QMC=2+4Q. The market supply curve is given by P=Q+2P=Q+2 and the market demand curve is P=1000−Q.P=1000−Q.
a) How much will each firm produce?
b) What is the shut-down price for the firm?
c) Are profits positive or negative for a representative firm? Explain.
d) What do you expect to happen in the long-run?
a)
Each firm will produce that output where P=MC
Q+2=1000−Q2Q=998Q=499Q+2=1000−Q2Q=998Q=499
At the market equilibrium, firms will produce 499 shoes units.
b.
Shut down price of the firm is where P< AVC or the average variable cost
TC=50+2Q+2Q2TVC=2Q+2Q2AVC=TVCQ=2Q+2Q2Q=2+2QP=AVC1000−Q=2+2Q998=3QQ=332.67P=1000−332.67P=667.33TC=50+2Q+2Q2TVC=2Q+2Q2AVC=TVCQ=2Q+2Q2Q=2+2QP=AVC1000−Q=2+2Q998=3QQ=332.67P=1000−332.67P=667.33
At this price level p=667.33, price of the firm is having price equal to average variable cost. Hence at the less than price level, firm will shut down in the short run.
c.
Profits:
PF=TR−TC=(1000Q−Q2)−(50+2Q+2Q2)=1000(499)−(499)2−50−2(499)−2(499)2=−249,051PF=TR−TC=(1000Q−Q2)−(50+2Q+2Q2)=1000(499)−(499)2−50−2(499)−2(499)2=−249,051
Firm is incurring losses. This is because equilibrium output is not profit maximizing output. In perfectly competitive market, the profit maximizing output is where price is equal to marginal cost. At this point Q=199.6. This means firm is producing way higher output than its efficiency level.
d.
In the long run, firm may leave the market as it incurring losses. At the long run point P=AC=MC.
AC=50Q+2+2QAC=MC50Q+2+2Q=2+4Q50Q=2Q2Q2=50Q=5AC=50Q+2+2QAC=MC50Q+2+2Q=2+4Q50Q=2Q2Q2=50Q=5
In the long run, at Q=5, AC and MC are equal and minimum. If firm is producing higher output, then firm will exit from the market.
