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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.

Question

  1. (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.
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Solution

(a) June's state-contingent wealth without insurance can be represented as a point (M, M-L) on the graph. The horizontal axis represents her wealth in the state where the truck does not crash (x1 = M), and the vertical axis represents her wealth in the state where the truck does crash (x2 = M-L).

(b) Since June's preferences conform to the theory of Subjective Expected Utility, we can use a utility function of the form U(x1, x2) = p*u(x1) + (1-p)*u(x2) to represent her preferences. Here, p is the probability of the truck not crashing, u(x1) is the utility from wealth in the state where the truck does not crash, and u(x2) is the utility from wealth in the state where the truck does crash.

(c) June is deemed strictly risk averse if she prefers a certain outcome to a risky outcome with the same expected wealth. This implies that her utility function is concave, meaning that the marginal utility of wealth decreases as wealth increases.

In the diagram, this means that her indifference curves are convex to the origin. An indifference curve represents all combinations of x1 and x2 that give June the same level of utility. If June is strictly risk averse, she would prefer to be on a higher indifference curve (representing a higher level of utility). However, given her state-contingent wealth without insurance, she can only achieve a certain level of utility. If she could move to a higher indifference curve (for example, by purchasing insurance), she would prefer to do so.

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