Consider a health insurance market. The market has many insurers so that each insurance company offers insurance at the fair insurance premium. Each consumer has utility function, U(X)=√√X and has an initial wealth of $100. Consumers have access to a (magical) gym that reduces their probability of needing to go to the doctor from 90% to 10%. A gym membership costs $10. A trip to the doctor costs $75. Suppose insurance companies charge the fair insurance premium which assumes all consumers go to the gym. This fair insurance premium is $ ✓and the insurance company makes a profit of $ ✓ per consumer. Suppose insurance companies continue to charge the fair insurance premium that assumes all consumers go to the gym, but now charges a copay of $13 for a doctor's visit. The insurance company now makes a profit of $ ✓per consumer. By implementing a copay, the insurance company ✓ the ✓ problem.

Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) du' (c) consumption and u"(c) (which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc dc2 1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.

An individual is offered a choice of either $50 or a lottery which may result in $0 or $100, each with equal probability 1/2. If the individual has a utility function u(w) = w, which one would they choose? If the individual has a utility function u(w) =sqr(w)?

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, where there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is UA(XA,S)=XA+In(1+s), where xA is the amount of money Person A owns. Person B's utility function is uB(XB,1s)%3D3XB+2(1-s), where Xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Persch B has the legal right to a smoke-free room and there is a market for "emission right." At the Walrasian equilibrium, what will be the (per unit of smoke index) price p of the emission rights if the price of money is 1? O a. None of the other answers. O b. p=2/3 O c. p=1 O d. p=3/2 О е. р31/6