Illustrate on your diagram from part (a) her state-contingentwealth bundles corresponding to the set of choices going from zero cov-erage (that is, C = 0) to full coverage (that is, C = L). [Hint: eachadditional dollar of coverage reduces Juneís wealth by q dollars in theevent the truck does not crash and increases it by q + 1 in the eventthe truck crashes.
Question
Illustrate on your diagram from part (a) her state-contingentwealth bundles corresponding to the set of choices going from zero cov-erage (that is, C = 0) to full coverage (that is, C = L). [Hint: eachadditional dollar of coverage reduces Juneís wealth by q dollars in theevent the truck does not crash and increases it by �q + 1 in the eventthe truck crashes.
Solution
-
To illustrate June's state-contingent wealth bundles corresponding to the set of choices going from zero coverage (C = 0) to full coverage (C = L), we need to plot a line on the diagram from part (a) that represents all possible insurance policies she could purchase.
-
If June does not take out any insurance (C = 0), her wealth in the state where the truck does not crash (x1) will be W, and her wealth in the state where the truck does crash (x2) will be W - L. This is the point we plotted in part (a).
-
If June takes out full insurance (C = L), her wealth in both states will be W - qL. This is because she pays the premium qL in both states, but in the state where the truck crashes, she also receives a payout of L from the insurance company, so her net loss is zero. This point will be on the 45-degree line, which represents equal wealth in both states.
-
For any level of coverage between zero and full, June's wealth in the state where the truck does not crash will be W - qC, and her wealth in the state where the truck does crash will be W - qC + L - C. This is because she pays the premium qC in both states, but in the state where the truck crashes, she receives a payout of C from the insurance company, so her net loss is L - C.
-
These points will all lie on a line that slopes upward from the point without insurance to the point with full insurance. The slope of this line is (1 - q), which represents the net gain in wealth in the state where the truck crashes for each additional dollar of coverage.
-
The line will be below the 45-degree line if the insurance is actuarially unfair (q > 1/2), on the 45-degree line if the insurance is actuarially fair (q = 1/2), and above the 45-degree line if the insurance is actuarially favorable (q < 1/2).
-
The optimal insurance for June will be the point on this line that gets her on the highest possible indifference curve, given her risk aversion. This will typically involve full insurance if the insurance is actuarially fair or favorable, and partial insurance if the insurance is actuarially unfair.
Similar Questions
Let (x1; x2) (0; 0) denote Juneís state-contingent wealth,where x1 0 is her wealth in the state in which the truck does notcrash and x2 0 is her wealth in the state in which the truck doescrash. Draw a graph with the horizontal axis measuring the quantityx1 and the vertical axis measuring the quantity x2 and plot Juneísstate-contingent wealth if she does not take out any insurance.Suppose Juneís preferences over state-contingent wealth bundles (x1; x2)conform to the theory of Subjective Expected Utility
Without needing to know anything more about Juneís at-titude toward risk (except that she is strictly risk averse), explain whyif June believes the insurance is actuarially unfair, that is q is strictlygreater than her subjective probability that the truck will crash, thenJune will not fully insure, that is, she will choose C < L. Illustrateyour your answer by drawing appropriate indi§erence curves for Juneon your diagram from part (d)
Suppose now June can purchase insurance for the transport of her householde§ects at a price of q 2 (0; 1) per dollar of coverage. That is, if she chooses apolicy that covers a maximum of C in the event of a loss, she pays qC to theinsurance company and they agree to pay her in the event of a loss, the valueof her loss up to the agreed maximum cover of C. So, in particular, if she3takes out a policy with the maximum coverage of L, then she will be fullyinsured in the event of the truck crashing since her state-contingent wealthwill be M qL in the event the truck does not crash and M qL L + L =M qL in the event the truck crashes.(d) (5 points) Illustrate on your diagram from part (a) her state-contingentwealth bundles corresponding to the set of choices going from zero cov-erage (that is, C = 0) to full coverage (that is, C = L). [Hint: eachadditional dollar of coverage reduces Juneís wealth by q dollars in theevent the truck does not crash and increases it by q + 1 in the eventthe truck crashes.]
Draw a diagram showing Lucy’s optimal bundle, clearly depicting her budget set and the indifference curve where the optimal bundle lies.
2. (50 points) June is relocating from Canberra to Sydney and hasengaged a removalist company to bring her household goods by truck fromher house in Canberra to her new residence in Sydney. Suppose she faces thefollowing uncertainty, either the truck makes the journery from Canberrato Sydney without incident and unloads her household goods in Sydneywith nothing lost and nothing damaged, or, the truck crashes and all herhousehold goods are damaged beyond repair. Let M denote her overall(money) wealth in the event that nothing is lost and M L denote herwealth in the event the truck carrying her household goods crashes. AssumeM > L > 0.(a) (5 points) Let (x1; x2) (0; 0) denote Juneís state-contingent wealth,where x1 0 is her wealth in the state in which the truck does notcrash and x2 0 is her wealth in the state in which the truck doescrash. Draw a graph with the horizontal axis measuring the quantityx1 and the vertical axis measuring the quantity x2 and plot Juneísstate-contingent wealth if she does not take out any insurance.Suppose Juneís preferences over state-contingent wealth bundles (x1; x2)conform to the theory of Subjective Expected Utility.(b) (5 points) Explain what type of utility function this means we canuse to represent her preferences.(c) (15 points) Explain what it means for June to be deemed strictly riskaverse and what this implies for the utility function from your answerto part (b). Illustrate in your diagram from part (a) what this meansfor her indi§erence curves.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.