1. (20 Total Points) Suppose in the short run a perfectly competitive firm has a fixed cost , F = $147. The firm’s variable cost of production is given by TVC = 3q +3q², where q is the quantity of output that the firm produces. The marginal cost of the firm is given by MC = 3 + 6q. The market demand for the good is given by Q_d = 145 - 2P, where Q_d is the total quantity demanded and P is the price of the good. Also, the market supply is given by Q_s = -50 + 3P.

 

a) (4 points) Calculate the equilibrium price in the market.

 

 

 

 

 

 

b) (4 points) How much output should an individual firm produce in order to maximize profit?

 

 

 

 

 

 

 

 

c) (4 points) How much profit will an individual firm produce?

 

 

 

 

 

d) (4 points) Is this a long run equilibrium?

 

 

 

 

 

 

e) (4 points) Calculate the break even price for this industry.

2. (40 Total Points) Suppose there are two firms operating in a market. The firms produce identical products, and the total cost for each firm is given by C = 10q_i, i = 1,2, where q_i is the quantity of output produced by firm i. Therefore the marginal cost for each firm is constant at MC = 10. Also, the market demand is given by P = 106 –2Q, where Q= q₁+ q₂ is the total industry output.

 

The following formulas will be useful:

 

If market demand is given by P = a –bQ, then

• MR₁ = a – 2bq₁ – bq₂
• MR₂ = a – bq₁ – 2bq₂

 

For parts a-c, assume the firms choose their quantities simultaneously. 

 

a) (4 points) What is firm 1’s reaction function? (Write the equation.)

 

 

 

 

 

 

 

 

 

b) (4 points) Determine the Nash equilibrium in quantities; that is, how much output will each firm 

produce in equilibrium?

 

 

 

 

 

 

 

 

 

 

 

c) (2 points) What will be the market price?

 

 

 

 

 

 

 

 

 

For parts d-g, assume that the two firms decide to collude and act like a monopolist. According to their agreement, they will maximize their total profit and split it. Each firm will produce half of the total output.  

 

d) (4 points) How much output will each firm produce?

 

 

 

 

 

 

e) (2 points) What will the market price be?

 

 

 

 

 

 

 

 

f) (4 points) What is the deadweight loss?

 

 

 

 

 

 

 

 

 

g) (2 points) What is the value of the Lerner Index in this situation?

 

 

 

 

 

 

 

For parts h-j, assume that firm 1 sticks to the agreement and produces the quantity determined in part d). However, Firm 2 decides to cheat on the agreement, and maximizes its profit given the quantity produced by firm 1. 

 

 

h) (4 points) What is the residual demand facing firm 2? (Write the equation.)

 

 

 

 

 

 

 

 

 

 

i) (4 points) How much output will firm 2 produce?

 

 

 

 

 

 

 

 

 

 

 

j) (2 points) What will the market price be?

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