Your firm is one of 100 identical firms operating in the short run in a perfectl
ID: 1200671 • Letter: Y
Question
Your firm is one of 100 identical firms operating in the short run in a perfectly competitive market. Your total cost function (short run and long run) is C = 800 + 25 q + 0.5 q2, and your marginal cost function is MC = 25 + q. The (short run and long run) market demand curve is given by Q = 2,750 – 5P. a.Find the supply curve for your firm. Show work. Then, find the short-run market supply curve. Show work. b.Find equilibrium price, P*, and quantity, Q*, in the market in the short run.Show work. c.Find the lowest price at which your firm will not exit the market in the long run.Show work. Referring to your answer in part b, should your firm exit the market in the long run if P* in the market does not increase over time?Explain. d.If you choose not to exit, how many firms (including your own) do you expect to be in the market in the long run?Show work, and explain.
Explanation / Answer
a) A firm's short-run supply curve is the marginal cost curve above the shutdown point—the short-run marginal cost curve (SRMC) above the minimum average variable cost). The portion of the SRMC below the shutdown point is not part of the supply curve because the firm is not producing any output.[16] The firm's long-run supply curve is that portion of the long-run marginal cost curve above the minimum of the long run average cost curve.
MC=25+q
p=25+q
q=p-25
since there are 100 firms
S100= 100(p-25)
=100p-2500
b.) equilibrium is attained when demand=supply
2750-5p=100p-2500
2750+2500=100p+5P
5250=105p
p=5250/105
=50
q=100p-2500
100*50-2500
=5000-2500
=2500
thus per firm it will be 2500/100=25
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