A drummer and an economist live in neighbouring apartments. Both work from home. Here are the facts of their situation. 10 marks for parts a and b, 10 marks for part c, 10 marks for part d.

There is limited soundproofing between the apartments. When the drummer plays on his drum-kit, the economist can hear him playing.

It would cost the drummer $600 to buy an electric low-noise drum kit.

With the low-noise drum kit, the economist is able to work at maximum efficiency, and earns $2,000. Without the low-noise drum kit, she is unable to work efficiently, and earns only $1,250.

If the drummer doesn't buy the low-noise drum-kit, it would cost the economist $1,000 to sound-proof her office so that she can work efficiently.

The drummer earns $1000. The drummer's earnings are the same whether he has a low-noise drum kit or a regular drum-kit.

The drummer and the economist do not know each other, and cannot communicate.

a. What are each player's strategies in this situation?

b. Draw a pay-off matrix showing each player's pay-offs. Use the dot-and-circle method to find the Nash equilibrium.Is the Nash equilibrium efficient? Why/why not?

c. Now suppose the drummer is legally liable for compensating the economist for any earnings she loses as a result of his drumming. How will the pay-off matrix change? The Nash equilibrium? In what ways is new equilibrium better than the equilibrium in part (b)? In what ways is it worse?

d. Now suppose the city institutes a 20% income tax, and uses it to provide all drummers with free electric low-noise drum kits. What are the advantages does this subsidy approach have over the legal liability approach in part (c)? What disadvantages does it have?