Please provide working.
a. 17.3+ We have illustrated in several settings the role of actuarially fair insurance contracts (b, p) (where b is the insurance benefit in the bad state and p is the insurance premium that has to be paid in either state). In this problem, we will discuss it in a slightly different way that we will later use in Chapter 22. A. Consider again the example, covered extensively in the chapter, of my wife and life insurance on me. The probability of me not making it is d, and my wife's consumption if I don't make it will be 10 and her consumption if I do make it will be 250 in the absence of any life insurance. Now suppose that my wife is offered a full set of actuarially fair insurance contracts. What does this imply for how p is related to d and b? b. On a graph with b on the horizontal axis and p on the vertical, illustrate the set of all actuari- ally fair insurance contracts. Now think of what indifference curves in this picture must look like. First, which way must they slope (given that my wife does not like to pay premiums but she does like benefits)? In which direction within the graph does my wife have to move to become unambiguously better off? We know my wife will fully insure if she is risk averse (and her tastes are state-independent). What policy does that imply she will buy if 8 = 0.25? f. Putting indifference curves into your graph from (b), what must they look like in order for my wife to choose the policy that you derived in (e). What would her indifference map look like if she were risk neutral? What if she were risk-loving? c. d. e. a. 17.3+ We have illustrated in several settings the role of actuarially fair insurance contracts (b, p) (where b is the insurance benefit in the bad state and p is the insurance premium that has to be paid in either state). In this problem, we will discuss it in a slightly different way that we will later use in Chapter 22. A. Consider again the example, covered extensively in the chapter, of my wife and life insurance on me. The probability of me not making it is d, and my wife's consumption if I don't make it will be 10 and her consumption if I do make it will be 250 in the absence of any life insurance. Now suppose that my wife is offered a full set of actuarially fair insurance contracts. What does this imply for how p is related to d and b? b. On a graph with b on the horizontal axis and p on the vertical, illustrate the set of all actuari- ally fair insurance contracts. Now think of what indifference curves in this picture must look like. First, which way must they slope (given that my wife does not like to pay premiums but she does like benefits)? In which direction within the graph does my wife have to move to become unambiguously better off? We know my wife will fully insure if she is risk averse (and her tastes are state-independent). What policy does that imply she will buy if 8 = 0.25? f. Putting indifference curves into your graph from (b), what must they look like in order for my wife to choose the policy that you derived in (e). What would her indifference map look like if she were risk neutral? What if she were risk-loving? c. d. e
