Ringo and Paul are roommates. Ringo plays the drums, but the noise annoys Paul. In addition, they both prefer having more money to less. Ringo’s utility function is Ur(d, mr) = 2/3mr + 1/3d, where d is the number of hours he gets to play the drums and mr is the amount of money he has. Paul’s utility function is Up(d, mp) = 2/3mp −1/72d^2, where d is still the amount of time Ringo spends playing the drums and mp is the amount of money Paul has. They each start with $500 and spend 100 hours per week in the house together. Their landlord has no restriction on noise, and so Ringo spends all 100 hours per week playing the drums.

(a) Draw an Edgeworth Box with Ringo’s origin in the bottom left and hours spent drumming on the horizontal axis. Note, in this Edgeworth Box, Paul’s horizontal axis measures his hours of quiet moving from right to left. Show the endowment in the Edgeworth Box. Is the initial outcome Pareto efficient? Why or why not? If the endowment is not Pareto efficient, find an outcome, any outcome, that is a Pareto improvement for both Ringo and Paul.

(b) Solve for and graph the contract curve.

(c) Suppose we establish a market in which Ringo has the right to play drums, but Paul can pay Ringo not to do so on an hourly basis. What will be the equilibrium outcome? That is, how many hours does Ringo spend playing the drums and how much does Paul pay him? You’ll need to use the first-order conditions from both individuals’ maximization problems.

(d) Suppose we again create a market as in part (c), but this time, Paul has the right to a quiet house. That is, if Ringo wants to spend an hour playing drums, he must pay Paul. Once again, find the same equilibrium outcome under this property rights regime.

(e) Based on your answers to parts (c) and (d) compute each individual’s utility for each allocation of property rights. In what respects are the outcomes the same? In what respects are they different? Are either, or both, efficient?