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Suppose there is a perfectly competitive industry where all the firms are identical with
identical cost curves. Furthermore, suppose that a representative firm’s total cost is given
by the equation TC = 100 + q2
q where q is the quantity of output produced by the
firm. You also know that the market demand for this product is given by the equation P =
1000 - 2Q where Q is the market quantity. In addition you are told that the market supply
curve is given by the equation P = 100 + Q.
a. What is the equilibrium quantity and price in this market given this information?
To find the equilibrium set market demand equal to market supply: 1000 - 2Q =
100 + Q. Solving for Q, you get Q = 300. Plugging 300 back into either the
market demand curve or the market supply curve you get P = 400.
b. The firm’s MC equation based upon its TC equation is MC = 2q + 1. Given this
information and your answer in part (a), what is the firm’s profit maximizing level
of production, total revenue, total cost and profit at this market equilibrium? Is
this a short-run or long-run equilibrium? Explain your answer.
From part (a) you know the equilibrium market price is $400. You also know that
the firm profit maximizes by producing that level of output where MR = MC.
Since the equilibrium market price is the firm’s marginal revenue you know that
MR = $400. Setting MR = MC gives you 400 = 2q + 1, or q = 199.5. Thus, the
profit maximizing level of output for the firm is 199.5 units when the price is
$400 per unit. Using this information it is easy to find total revenue as the price
times the quantity: TR = ($400 per unit)(199.5 units) = $79,800. Total cost is
found by substituting q = 199.5 into the TC equation: TC = $40,099.75. Profit is
the difference between TR and TC: Profit = TR - TC = 79,800 - 40,099.75 =
$39,700.25. Since profit is not equal to zero this cannot be a long-run equilibrium
situation: it must be a short-run equilibrium situation.
c. Given your answer in part (b), what do you anticipate will happen in this market
in the long-run?
Since there is a positive economic profit in the short run, there should be entry of
firms in the long-run resulting in an increase in the market quantity, a decrease in
the market price, and firms in the industry earning zero economic profit.
d. In this market, what is the long-run equilibrium price and what is the long-run
equilibrium quantity for a representative firm to produce? Explain your answer.
The long-run equilibrium price is that price that results in the representative firm
earning zero economic profit. This will occur when MC = ATC for the
representative firm. ATC is just the TC equation divided by q. Thus, 2q + 1 =
(100 + q2
q)/q. Solving for q, q = 10. Plugging 10 in for q into the ATC
equation yields the following: ATC = (100 + 102
10)/10 = 21. So, when Price
equals MR = min ATC = MC = $21, this firm will break even. To see this
compute TR for the firm when it produces 10 units and sells each unit for $21: TR
= $210. Notice that this is the same as the firm’s TC: thus, the firm earns zero
economic profit.
e. Given the long-run equilibrium price you calculated in part (d), how many units
of this good are produced in this market?
To find this quantity you need to substitute $21 (the long-run equilibrium price)
into the market demand curve to determine the quantity that the market must
produce in order to be in long-run equilibrium. This quantity is equal to 489.5
units.
13 окт 2024
