Classwork 3

Property Rights, the Coase Theorem, and the Environment

Question 1. Property Rights and Coasian Bargaining

Consider a society with just two people. Person 1 enjoys playing loud music for \(h\) hours, while Person 2 dislikes the noise. Both are self-interested and care only about their own payoff.

• Person 1’s marginal benefit (in dollars) from music is:
  \(MB(h) = 4 - 2h\).
  
• Person 2’s marginal cost (in dollars) from music is:
  \(MC(h) = 2h\).

Note

Here, \(MB(h)\) and \(MC(h)\) are functions of \(h\).
Transfers \(T\) (in dollars) are lump-sum payments between the two people.

a. Market outcome

If the decision is left entirely to Person 1, what level of music \(h_M\) will she choose?

b. Socially efficient outcome

What is the socially optimal level \(h^*\)?

c. Person 1 has the right to play

Suppose the government gives Person 1 the legal right to play as much as she wants (\(h=h_M\)).
Person 2 may then “bribe” Person 1 to reduce music in exchange for a lump-sum transfer \(T\) (in dollars).
Assume there are no transaction costs in bargaining.

• Show how bargaining can still lead them to agree on the socially optimal level \(h^*\).
  • Identify the possible range of transfers \(T\) (in dollars), paid from Person 2 to Person 1, that makes both better off compared to their initial legal entitlement (\(h=h_M, T=0\)).

d. Person 2 has the right to silence

Now suppose the government gives Person 2 the legal right to silence (\(h=0\)).
Person 1 may then “bribe” Person 2 to allow some music in exchange for a lump-sum transfer \(T\) (in dollars).
Assume there are no transaction costs in bargaining.

• Show how bargaining can still lead them to agree on the socially optimal level \(h^*\).
  • Identify the possible range of transfers \(T\) (in dollars), paid from Person 1 to Person 2, that makes both better off compared to their initial legal entitlement (\(h=0, T=0\)).