Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s = 0, when there is no smoke in the room, to s = 1, when the room is filled with smoke. Thus, 1 − s measures how “pure,” that is, free of smoke, the air in the room is. Person A cares only about how much she smokes and how much money she owns. (Person A smokes at no cost to her because, sometime ago, she was given a large number of cigarette packs, more than she can ever consume). As the amount of smoke in the room is perfectly and positively correlated to how much Person A smokes, we can write her (“indirect”) utility function as uA (xA, s), where s is the smoke index and xA her amount of money. Person B cares only about the quality of the air he breathes and how much money he owns. His utility function is uB (xB , 1 − s). Both utility functions are increasing in their arguments. Let us denote ωA and ωB Persons A an B’s initial endowments in money.

wa= wb = 30

ua(Xa,s) = 60s + Xa

ub (Xb, 1-s) = (1-s)* Xb

1.Find contra Curve

2.Assume Person B has the legal right to a smoke-free room. If Persons A and B may exchange money for the right to smoke and reach any agreement that would make them both better off, what final combinations of values of the smoke index and allocations of money can occur?

3. Assume Person B has the legal right to a smoke-free room and there exists a market for “emission” or “smoking” rights. Find the Walrasian equilibrium (take the price of money to be 1).

4. Assume Person A has to legal right to fill up the room with smoke. If Persons A and B exchange money for some reduction in smoke and reach any agreement that would make them both better off, what final combinations of values of the smoke index and allocations of money can occur?

5. Assume Person A has the legal right to fill up the room with smoke and there exists a market for smoke “abatements”. Find the Walrasian equilibrium (take the price of money to be 1).