Question

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 revenue is given by the equation TR = q.p; where q is the quantity of output produced by the firm and p the market price (=P).

The market demand for this product is given by the equation P = 5000 – 9Q where Q is the market quantity.

In addition you are told that the market supply curve is given by the equation P = 1000 + Q.

a. What is the equilibrium quantity and price in this market given this information?

b. The firm’s MC equation based upon its TC equation is MC = 5q + 4. 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.

c. Given your answer in part (b), what do you anticipate will happen in this market in the long-run?

Answer 1

a)

Market demand P = 5000 - 9Q  

Market supply P = 1000 + Q

Demand = supply  

5000 - 9Q = 1000 + Q

5000 - 1000 = Q + 9Q

4000 = 10Q  

Q = 400

P = 1000 + 400 = 1400  

b) MC = 5q + 4  

P = 1400

Profit maximising rule P = MC  

1400 = 5q + 4  

1400 - 4 = 5q  

5q = 1396

q = 279.2

TR = Pq

= 1400(279.2)

= 390,880

TC =

=  (5q + 4) dq

TC = 5q2/2  + 4q + FC

TC =  5q2/2 + 4q + FC

= q(5q/2 + 4) + FC

= 279.2(5279.2/2 + 4 ) + FC

= 195,998.4 + FC

since we do not have any information regarding FC , we assume FC = 0 for simplicity

Therefore TC = 195,998.4

Profit = TR - TC  

= 390,880 - 195,998.4

= 194,881.6

c) This is short run equilibrium because in short run market demand equals market supply and P = MC

d) Since firms are making a positive profit of 194,881.6 in short run therefore firms will enter in the market in the long run.