Question

You are given the following information about the current conditions of a particular perfectly competitive industry with identical firms:

Market demand: QD = 1, 410 − 40P
Market supply: QS = 30P − 60
Firm total cost function: T C(q) = 50 + 2q + 2q2

(a) (5 points) What is the current equilibrium price and quantity in the market?

(b) (10 points) What is the supply curve of each firm (This should be a function of price: qS = f(P))? What is the amount of output supplied by each firm? How many firms are there in the market? Are individual firms making a profit?

(c) (10 points) Is the equilibrium you just calculated the long-run equilibrium in the market? If yes, explain why. If not, calculate the long-run equilibrium price and quantity in the market and for each firm. Assume the cost function given applies in the long run.

(d) (5 points) How many firms are there in the long run? What is the market supply in the long run (This should be a function of price: QS = f(P))?

Answer 1

Market demand: QD = 1, 410 − 40P

Market supply: QS = 30P – 60. Firm total cost function: T C(q) = 50 + 2q + 2q2

(a) The current equilibrium price and quantity in the market are determined by

Qd = Qs

1410 – 40P = 30P – 60

1470 = 70P

P = 21 and Q = 30*21 – 60 = 630 – 60 = 570 units.

(b)  Supply function of a single firm is the marginal cost function MC = 2 + 4q or P = 2 + 4q. This becomes

qS = (P – 2)/4 or qS = 0.25P – 0.5. At a price of 21, each firm supplies qS = 0.25*21 – 0.5 = 4.75 units. This implies that there are n = 575/4.75 = 120 firms. ATC is TC/Q = (50 + 2*4.75 + 2*(4.75)^2)/4.75 = 22.03. Since P < ATC, firms are making economic losses.

(c)  No, the equilibrium we just calculated is not the long-run equilibrium in the market. It is when ATC = MC

(50 + 2q + 2q2)/q = 2 + 4q

50/q + 2 + 2q = 2 + 4q

50/q = 2q

q^2 = 25

q = 5. This is the long run output per firm. Long run price = MC = 2 + 4*5 = $22.

(d)  In the market, at P = 22, the quantity demanded is 1410 – 40*22 = 530. Number of firms are 530/5 = 106 in the long run. Long run market supply is

106qS = QS new = 106*(P – 2)/4 = 26.5P – 53.