Tom and Jerry are roommates. They spend a total of 80 hours a week together in their room. Tom likes loud music, even when he sleeps. His utility function is UT (CT,M) = CT + M, where CT is the number of cookies he eats per week and M is the number of hours of loud music per week that is played while he is in their room. Jerry hates all kinds of music. His utility function is U(CJ,M) = CJ − M2/12. Every week, Tom and Jerry each get two dozen chocolate chip cookies sent from home. They have no other source of cookies. We can describe this situation with a box that looks like an Edge worth box. The box has cookies on the horizontal axis and hours of music on the vertical axis. Since cookies are private goods, the number of cookies that Tom consumes per week plus the number that Jerry consumes per week must equal 48. But music in their room is a public good. Each must consume the same number of hours of music, whether he likes it or not. In the box, let the height of a point represent the total number of hours of music played in their room per week. Let the distance of the point from the left side of the box be “cookies for Tom” and the distance of the point from the right side of the box be “cookies for Jerry.”
(a) Suppose the dorm’s policy is that you must have your roommate’s permission to play music. The initial endowment in this case denotes the situation if Tom and Jerry make no deals. There would be no music, and each person would consume 2 dozen cookies a week. Mark this initial endowment on the box above with the label A. Use red ink to sketch the indifference curve for Tom that passes through this point, and use blue ink to sketch the indifference curve for Jerry that passes through this point. Use blue ink to shade in the points representing situations that would make both roommates better off than they are at point A.
(b) Suppose, alternatively, that the dorm’s policy is “rock-n-roll is good for the soul.” You don’t need your roommate’s permission to play music. Then the initial endowment is one in which Tom plays music for all of the 80 hours per week that they are in the room together and where each consumes 2 dozen cookies per week. Mark this endowment point in the box above and label it B. Use red ink to sketch the indifference curve for Tom that passes through this point, and use blue ink to sketch the indifference curve for Jerry that passes through this point. Given the available resources, can both Tom and Jerry be made better off than they are at point B?