Question

The goal of this problem is to compare perfect competitive outcome (scenario 1) with monopoly outcome (scenario 2). In both two scenarios, market demand is given by Q=1200-50P.

Scenario 1: Consider a perfectly competitive market with 150 identical firms. Each firm’s marginal costs are given by MC=q+4. (4pts) Determine the equation for market supply curve. Find the equilibrium price and industry output.

1. Determine the equation for market supply curve. Find the equilibrium price and industry output.

2. Plot the demand curve and the supply curve in the same graph. Put quantity on the horizontal axis. Calculate the consumer surplus and producer surplus.

3. Suppose each firm has a standard U-shaped long-run average cost curve that reaches a minimum of $9 at an output level of 5 units, is the market in long run equilibrium? Explain. What is the total profit for each firm?

Scenario 2: Consider instead a monopoly market with only one firm. The firm’s marginal costs are given by MC=1150Q+4.

4. What is the profit-maximizing output and price for this monopolist? Round your answer to the nearest integer.

Answer 1

Q=1200-50P

MC=q+4

150 identical firms

1. For market supply curve:

In perfect competition P=MC

P=q+4

q= P-4

There are 150 identical firms, so

Q=150q= 150(P-4)= 150P-600 (Market supply curve)

2. Equilibiurm price:

Demand = supply

1200-50P=150P-600

1800=200P

P=9

Q= 750

Consumer surplus= 1/2(Pm-P*)(Q*)= 1/2(15)(750)= 5625

Producer surplus= 1/2(P*-Pc)(Q*)= 1/2*5*750= 1875

3. As there are 150 identical firm the total output divided equally:

q=Q/150= 750/150=5

Profit of each firm= (P-AC)q= (9-9)5= 0

4.  MC=1150Q+4

Q=1200-50P

50P=1200-Q

P= (1200-Q)/50=AR

TR= AR*Q= (1200Q-Q2)/50

MR= dTR/dQ= (1200-2Q)/50

For profit maximization:

MR=MC

(1200-2Q)/50=1150Q+4

1200-2Q= 57500Q+200

1000= 57502Q

Q= 0.017

p= (1200-0.017)/50= 23.99=24