Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firms 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.
What is the equilibrium quantity and price in this market given this information?
The firms MC equation based upon its TC equation is MC = 2q + 1. Given this information and your answer in part (a), what is the firms 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.
Given your answer in part (b), what do you anticipate will happen in this market in the long-run?
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.
Given the long-run equilibrium price you calculated in part (d), how many units of this good are produced in this market?
a. 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. 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 firms 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. 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…
he industry earning zero economic profit. d. 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. 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 firms TC: thus, the firm earns zero economic profit. e. 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.