Answer to Question #280953 in Macroeconomics for abeni

Question

3. Suppose that, 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.

i. What is the equilibrium quantity and price in this market given this

Information?

ii. The firm’s MC equation based upon its TC equation is MC = 2q + 1.

Given this information, 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.

Answer 1

Solution:

I) To find the equilibrium set market demand equal to market supply:

$$1000-2Q=100+Q$$

Solving for Q:

$$Q=300$$

Plugging 300 back into either the market demand curve or the market supply curve you get

$$P=400$$

II) 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:

$$400=2Q+1$$

$$Q=199.5$$

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:

R = ($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.