Insurance: Reservation Price For this question you have a renter who is considering purchasing tenant's insurance (renter's insurance). They live in a dangerous neighbourhood and have a considerable amount of expensive items they would like to insure. The following provides a distribution of possible losses they could incur: Part A (3 marks): Please compute the expected loss. Part B (8 marks): Please compate the reservation price for each of the following preferences. Le, compute the maximum each type of individual would be willing to pay to fully insure against any possible loss. Each type of individual has isolastic utility, U(W)=3121, but can have different values for and different levels of initial wealth. Warning: You will want to make these calculations in excel, MATLAB, or some other software. There can be many decimal places and any rounding can greatly affect your final answer. Part C (4 marks): Explain why individuals A and B have different reservation prices. Part D (4 marks): Explain why individuals C and D have different reservation prices. Consider an individual who has an isoelastic utility function with =1 and $30,000 in liquid financial eapital (wealth). They are purchasing insurance for their car and are unsure about the size of the deductible. The current value of car is $25,000, and for the sake of simplicity, assume the only kind of accident they can get in results in their car being completely destroyed. Further suppose that the probability this happens is equal to 0.2%. Finally, suppose they are choosing between the following three insurance policies (I repeat some information to help clarify): Policy 1 - Probabality of loss =0.2%. - Loss =$25,000. - Remember, we are assuming they can only purchase full coverage. I.e., they are purchasing 25,000 in coverage. - Deductible =$0 (i.e., no deductible). - Premium =$104. Policy 2 - Probability of loss =0.2%. - toss =$25,000. - For simplicity, assume the estimated probability of loss does not change across insurance prowiders. - Deductible =$750. - Premium = $99. Policy 3 - Probability of loss =0.2% - Los5=$25,000. - Deductible =$1500. - Premium =$94. Part A (3 marks): Please compate the individual's reservation price for Policy 1. Part B (8 marks): Which insurance policy does the individual choose? (Hint: you can do this without computing the reservation prices). Part C ( 4 marks): In general, how will the insurance premium (price charged by the insurance provider) vary with the size of the deductible? Explain by commenting on the basic factors involved in pricing insurance. (Note: This is not a trick question and should be (hopefully is) intuitive.) Part D (3 marks): From a practical perspective, why would it be tnwwise to insure large losses that occur with very high probabilities (hiat: extreme examples can help). Absolute and Relative Risk Aversion For this question, you need to work with the exponential and quadratic utility functions (given below): U(W)=eaWU(W)=a+bWcW2, where a,b, and c are nonegative real numbers. Part A (6 marks): Please compute the absolute and relative risk aversion measures for each vtility function. Part B (6 marks): Please compute, and comment on, the first-order derivative of the ARA and PRA measures for the exponential urilicy function (given in Equation 3.1). Part C (6 marks): Please compute, and comment on, the first-order derivative of the ARA and RRA measures for the quadrutic utility function (given in Equation 3.2). Warning: You must show all steps in the calculations for each part of this question to get full marks, this includes calculating the derivatives
