6. Consider two risk averse individuals, Risky Rick and Safe Sal. Rick and Sal both live in an uncertain world. Rick has a family history of cardiovascular problems, while Sal's family history suggest she has little chance of developing such problems. Indeed, Rick's probability of contracting the disease is nr = 50%, while Sal's is just as = 10%. For simplicity, let's assume that Rick and Sal have the same income Y and are otherwise identical, and that developing heart disease is the same as suffering a loss of income L. Thus in the event of disease, net income is Y-L (assumed greater than zero). (i) Draw a diagram with income without heart disease on the horizontal axis, and income with heart disease on the vertical axis, and mark Rick's endowment point. (ii) On the same picture, draw the line along which Rick could trade if he could purchase actuarially fair insurance. What is the slope of this line? (iii) Finally, include Rick's indifference curves and show that he purchases full insurance. (iv) On a separate diagram, repeat steps (i) through (iii) for Sal. (Hint: Sal will have different indifference curves to Rick.) (v) Suppose an insurance company cannot tell who it is selling insurance to, but does know that half the population are like Rick (i.e., have a 50% chance of contracting heart disease) and half are like Sal (i.e., have a 10% chance). Show that the probability that an individual selected from the population at random will contract heart disease is = 30%. (vi) On a new figure, show that if Rick and Sal are offered insurance at a common rate that is actuarially fair on average, then Rick will over-insure (i.e., his income will be higher when he gets the disease than when he doesn't) and Sal will under-insure (i.e., her income will be lower when she gets the disease than when she doesn't). 6. Consider two risk averse individuals, Risky Rick and Safe Sal. Rick and Sal both live in an uncertain world. Rick has a family history of cardiovascular problems, while Sal's family history suggest she has little chance of developing such problems. Indeed, Rick's probability of contracting the disease is nr = 50%, while Sal's is just as = 10%. For simplicity, let's assume that Rick and Sal have the same income Y and are otherwise identical, and that developing heart disease is the same as suffering a loss of income L. Thus in the event of disease, net income is Y-L (assumed greater than zero). (i) Draw a diagram with income without heart disease on the horizontal axis, and income with heart disease on the vertical axis, and mark Rick's endowment point. (ii) On the same picture, draw the line along which Rick could trade if he could purchase actuarially fair insurance. What is the slope of this line? (iii) Finally, include Rick's indifference curves and show that he purchases full insurance. (iv) On a separate diagram, repeat steps (i) through (iii) for Sal. (Hint: Sal will have different indifference curves to Rick.) (v) Suppose an insurance company cannot tell who it is selling insurance to, but does know that half the population are like Rick (i.e., have a 50% chance of contracting heart disease) and half are like Sal (i.e., have a 10% chance). Show that the probability that an individual selected from the population at random will contract heart disease is = 30%. (vi) On a new figure, show that if Rick and Sal are offered insurance at a common rate that is actuarially fair on average, then Rick will over-insure (i.e., his income will be higher when he gets the disease than when he doesn't) and Sal will under-insure (i.e., her income will be lower when she gets the disease than when she doesn't)
