Question
Suppose the wedding dress industry is a perfectly
competitive constant cost industry. Suppose also that market demand for wedding dresses is described by Q = 10,000 – 10P. Suppose individual firms have cost functions of LTC = 20,000+100q+2q2 (LTC = 0 if q = 0) (so that LMC is 100+4q). how many firms are there in the industry in the long run?Solution
In the long run the firm satisfies two conditions. Profit maximization → MR = P = LMC Free Entry → π = 0 → P = LAC Thus at output level of each firm LMC = LAC → 100 + 4q = (20,000 / q ) +100 + 2q → q* = 100, Also, 100 + 4q = P 100+4(100) = 500 = P P* = 500 At P = 500, industry output, from the demand curve, is Q = 10,000 - 10×500 = 5,000 The number of firms is thus 5,000/100 = 50
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