1. Suppose you are given the following information about a particular industry:
ID: 1203617 • Letter: 1
Question
1. Suppose you are given the following information about a particular industry:
Q^D=6500-100P Market demand
Q^S=1200P Market supply
C(q)=722+q^2/200 Firm total cost function
MC(q)=2q/200 Firm marginal cost function
Assume that all firms are identical, and that the market is competitive.
a. Find the equilibrium market price and quantity, the output supplied by the firm, and firm’s profits.
b. Would you expect to see entry into or exit from the industry in the long-run? Explain. What effect will entry or exit have on market equilibrium?
c. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain.
d.What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain.
Explanation / Answer
a) Given that Q^D=6500-100P is the Market demand and Q^S=1200P is the Market supply
Market price is determined by
Qs = Qd
1200P = 6500 - 100P
1300P = 6500
P = 5, Qd = Qs = 6000
For a typical firm, Profit maximizing level of output is where
MR = P = MC
5 = 2q/200
q = 500 units. Currently there will be 6000/500 or 12 firms operating.
Hence a typical firm supplies 500 units at a price of $5 per unit, bears an average total cost of 722/q + q/200 or (1.444 + 2.5) or $3.944 per unit. Firm's profit is therefore $1.056 per unit or $528 in total
b) One can expect to see entry into the industry in the long-run since there are short run profits. An entry will shift the supply curve to the righet, drive the price down and move the market to a lower price higher quantity equilibrium.
c) The long-run condition for equilibrium is LRATC = P = LRMC, where production point is at the lowest of LRATC. Hence the lowest price at which each firm would sell its output in the long runi sthe minimum of LRTAC curve. Economic rofits are zero at this level.
d)The short-run condition for equilibrium is MR = MC, where production point can be stretched at the lowest level of AVC but not beyond that. Hence the the lowest price at which each firm would sell its output in the short run is Minimum of AVC. There is positive profit at this level
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