Question

PART II. Problems 1. Suppose the market for canola oil is perfectly competitive. There are 1.000 firms in the market, each of which have a fixed cost of FC = 2 and a marginal cost of MC = 1 + q, where q is the quantity produced by an individual firm. Let s denote the total quantity supplied in the market. The market demand for canola oil is given by Qd = 15, 250 - 250P. a) Find the market supply equation, that is write Q. as a function of price P. b) What is the equilibrium price? What is the equilibrium quantity of canola oil bought and sold? How much profit is a given firm making (if any)? Are firms profit maximizing at this equilibrium? Show your calculations. c) Can you tell whether this is a long-run equilibrium? If not, how would a long-run equilibrium be different? d) How would an increase in demand for canola oil affect the quantity produced by each firm in the short-run? How would it affect their profits in the short-run? Use a supply-and-demand diagram to sup port your answer.

Please show all work.

Answer 1

(a)

Firm supply being the firm MC function,

Firm supply: P = 1 + q

Since there are 1000 firms, Market supply (Qs) = 1,000q

q = Qs/1,000

P = 1 + (Qs/1,000)

1,000P = 1,000 + Qs

Qs = 1,000P - 1,000 [market supply]

(b)

Equating Qd = Qs,

15,250 - 250P = 1,000P - 1,000

1,250P = 16,250

P = 13

Q = (1,000 x 13) - 1,000 = 13,000 - 1,000 = 12,000

q = Q/1,000 = 12,000/1,000 = 12

TR = P x q = 13 x 12 = 156

TC = FC + q x MC = 2 + 12 x (12 + 1) = 2 + 12 x 13 = 2 + 156 = 158

Profit = TR - TC = 156 - 158 = - 2 (loss of 2)

Since firms are making loss, profit is not being maximized.

(c)

In long run equilibrium, profit is zero and loss is zero, so this is not a long run equilibrium.

(d)

Increase in demand will shift market demand curve rightward, increasing market price and increasing market quantity. Since firms are price takers, in short run when number of firms remain unchanged, higher market price and higher market quantity will increase firm profit.

In following graph, left panel shows market equilibrium where demand and supply curves (D0 and S0) intersect at point A with market price P0 and market output Q0. In right panel, firms accept P0 as their own price (which is firm's demand and MR curves) and produces at point B where P0 intersects MC0 with firm output q0. In long run equilibrium, economic profit is zero, so price equals ATC. In the graph, ATC0 intersects P0 and MC0.

Increase in market demand shifts D0 rightward to D1, intersecting S0 at point C with higher market price P1 and higher market quantity Q1. Firms accept P1 as their new price, and new short run equilibrium is at point E where P1 intersects MC with higher firm output q1. Firms earn short run economic profit equal to area P1EFG.

PMR,MC, ATC MC ATC 80 8, vo 1 %