Question

1. Assume that a monopolist has MC=20 and and no fixed costs; the monopolist faces a downward sloping demand curve of P=100-4Q. Calculate the deadweight loss (DWL).
2. B) Why is there no deadweight loss in the equilibrium of a perfectly discriminating monopolist?
3. Consider the scenario below: Two firms are merging into a larger company and must select a computer system for daily use. In the past, the players have used different systems I and A; each firm prefers the system it has used in the past. They will both be better off by using the same computer system than if they use different systems. The payoff matrix for the two players is given below:

4. Player 2

   I

   A

   Player 1

   I

   2,1	0,0
   0,0	1,2

   A

   Find the Nash equilibria of this game by considering all possibilities. Explain your answer fully.

Answer 1

The monopolist sets MC=MR for profit maximization

MC=20

MR = 100-8Q

MC=MR

100-8Q =20

80=8Q

Q= 80/8 = 10

P = 100-4(10) = 60

Whereas setting P=MC, the firm will produce 100-4Q=20

Q= 20

P = 20

So, DWL = 0.5*(20-10)*(60-20) = 5*40 = 200

b):- The monopoly pricing strategy makes a deadweight loss since it produces a lower quantity at a more significant expense than the efficient quantity.

A perfect price discriminating monopolist would set P = MC and capture all the consumer surplus and the deadweight loss by producing the efficient quantity and as there is no adjustment in the efficient quantity, there would be no deadweight loss in the market.

Condition 1:

If player 1 chooses I, then player 2 will choose I as it gives him a higher pay-off of 1 as compared to 0.

Condition 2:

If player 1 chooses A, then player 2 will choose A as it gives him a higher pay-off of 2 as compared to 0.

Condition 3:

If player 2 chooses I, then player 1 will choose I as it gives him a higher pay-off of 2 as compared to 0.

Condition 4:

If player 2 chooses A, then player 1 will choose A as it gives him a higher pay-off of 1 as compared to 0.

So, (2,1) and (1,2) are the nash equilibrium in this case.