Question

Suppose in Pakistan, all the firms are identical with identical cost curves which mean
industry is perfectly competitive. Now please consider this following information about the
industry: 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?
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.
c. Given your answer in part (b), what do you anticipate will happen in this market in the
long-run?
d. In this market, what is the long-run equilibrium price (breakeven or MC=ATC) and what
is the long-run equilibrium quantity for a representative firm to produce? Explain your
answer?
e. Given the long-run equilibrium price you calculated in part (d), how many units of this
good are produced in this market?

Answer 1

a). Market equilibrium condition is reached where demand is equal to supply. Market demand equation is P = 1000 - 2Q and market supply equation is P = 100 +Q. Therefore in equilibrium 1000 - 2Q = 100 +Q , or, 3Q = 900, or, Q = 900/3 =300. Putting Q =300, we get, P = 100+300 = 400. Therefore market equilibrium price is P = 400 and quantity Q = 300.

b). MC equation is MC = 2q +1, Market equilibrium price is 400. As it is competitive market price is given for the firm and here given market price is 400. For a typical firm in competitive market equilibrium take place at P = MC, therefore 400 = 2q +1, or 2q = 400 -1 =399, or, q = 399/2 = 199.5. Firm's profit maximising level of output is q = 199.5.

Total revenue for firm is p*q = 400*199.5 = 79,800.

Total cost function of firm is TC = 100 + q^2 + q , putting q =199.5, we get TC = 100 + 199.5^2 + 199.5 = 40,099.75.

Total profit in short run for the firm is TR - TC = 79,800 - 40,099.75 = 39,700.25. This is a short run equilibrium as firm is getting positive profit.

c). This is a short run equilibrium because firm is getting supernormal profit and in the short run firm is enjoying profit. Due to this supernormal profit more firm will get attraction to enter into this firm and in the long run more firm will enter in this market. In the long run firm will get only normal profit and this means in the long run there will be TR = TC. In the long run firm will enter in this market as long as it reaches to break-even condition i.e TR =TC.

d). In the long run price will be equal to MC = Minimum of ATC. TC = 100 + q^2 + q , ATC = TC/q = 100/q + q + 1 , for ATC minimum we take first order condition of ATC function. At ATC minimum FOC of ATC is 0. Therefore dATC/dq = d/dq(100/q + q +1) = 0, or , -100/q^2 + 1 = 0, or, -100/q^2 = -1, or q^2 = 100, or, q = 10, as q= -10 is not possible. So at q=10, ATC is minimum. At q =10 , ATC = 100/10 +10 +1 =21. In the long run price will be 21 and marginal cost and average cost will be also equal to 21. It means in the long run, P = Min ATC = MC = 21 and long run quantity q =10. In the long run TR = TC. TR = p*q = 21*10 =210. TC = 100 +q^2 +q = 100 +10^2 +10 = 210. So at q=10 and p =21 there will be breakeven i.e TR = TC = 210.

e). In the long run the firm will produce 10 units of output.