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Test 2 Solutions.pdf

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University of Toronto Mississauga
Kathleen Wong

ECO204: Solutions to Test 2 1. (20 points total) Daniel Burnham and John Root are the two talented Chicago-based architects that have been given the task of building the 1893 Chicago World’s Fair. In addition to designing and overseeing the construction of the Fair’s buildings, their job also requires them to decide whether they should purchase insurance to protect them against the loss of wealth. If an accident should occur when they are uninsured, it could greatly diminish their wealth because of the liability associated with repairs to the building, as well as medical costs and settlement payments if someone attending the fair should get hurt. Burnham and 4/7 Root’s utility function is described as U(W) = 1.5(W) , where W stands for their wealth (measured in dollars). a. (3 points) If the price is ‘right’, would Burnham and Root be willing to purchase insurance? Explain your answer using two or three sentences. Numerical evidence is not required. Based on their utility function, it is possible to conclude that Burnham and Root are willing to purchase insurance if the price is right because they are risk-averse individuals. Being exposed to risk causes their expected utility to be lower than their guaranteed utility. They are willing to trade-off some of their wealth to purchase the insurance in order to eliminate the possibility of great losses to wealth should an accident occur. b. (10 points) Burnham and Root currently don’t have insurance coverage. Suppose their current wealth is equal to $10 million and there is a 75% chance that their wealth will remain constant if there are no accidents. But if an accident occurs, their remaining wealth will be equal to $2,097,152. When exposed to the risk of being uninsured, calculate how much affects Burnham and Root’s utility level. Hint: For contrast, think of how the risk of being uninsured would affect a risk-neutral individual’s level of utility. Round the change in utility to the nearest whole number. Wealth if no accident = $10 million Probability of no accident = 75% Wealth with an accident = $2,097,152 Probability of accident = 25% This allows us to calculate both the expected wealth and the expected utility. E(W) = (Prob of no accident)(W if no accident) + (Prob of accident)(W with accident) = 0.75($10 million) + 0.25($2,097,152) = $8,024,288 E(U) = (Prob of no accident)(U if W = $10 million) + (Prob of accident)(U if W = $2,097,152) 0.75[1.5($10,000,000) 4/] + 0.25[1.5($2,097,152) )4/7 = 0.75(15,000) + 0.25(6,144) = 11,250 + 1,536 E(U12,786 Names and scenarios described in this test come from the non-fiction novel Devil in the White City Murder, Magic, and Madness at the Fair That Changed America, by Erik Larson. The hint provided tells us to contrast this current scenario with how a risk-neutral individual’s utility would be affected by facing risk: the risk-neutral individual wouldn’t be affected by the risk of being uninsured. Their expected utility will be equal to their actual utility – E(U) = U Since we’ve identified in part (a) that Burnham and Root are risk-averse individuals, we know their U > E(U). This level of expected utility (12,786) will be less than their utility if they were guaranteed a wealth of $8,024,288. 4/7 If guaranteed wealth is equal to $8,024,288, their utility would be equal to 1.5($8,024,288) = 13,227.15. So facing risk will cause Burnham and Root’s utility to decrease by 441 units (= 13,277.15 – 12,786). c. (7 points) Suppose the local insurance agent tells Burnham and Root that the insurance policy to insure against loss of wealth will cost them $450,000. Should Burnham and Root purchase the policy? Explain using two to three sentences. Your explanation must include numerical evidence to support your explanation. Round dollar amounts to two decimal places (example: $0.01). To determine if Burnham and Root should purchase the insurance at a cost of $450,000, we must calculate the risk premium. The risk premium indicates the maximum amount of money they are willing to pay to purchase insurance that will keep their utility constant and eliminate risk that they experience a great loss of wealth should an accident occur. Since their current expected utility is equal to 12,786: 12,786 = 1.5(W) 4/7 4/7 8,524 = 7/4 4/7 (7/4) (8,524) = (W ) W = $7,561,814.54 Based on their current expected wealth of $8,024,288, their risk premium is equal to $462,473.46 (=$8,024,288 – $7,561,814.54). Since their risk premium is greater than the cost of insurance, Burnham and Root will purchase the insurance policy. They will not only eliminate the risk of being uninsured, but will also have an additional $12,473.46 left over ($462,473.46 – $450,000) because the insurance cost less than their risk premium. This extra wealth will cause their U > E(U). 2 2. (20 points total) H.H. Holmes and Benjamin Pitezel are competitors in the perfectly competitive hotel industry. Both hotels are located in Chicago, but Holmes’ hotel is located significantly closer to Jackson Park, the site of the World Fair. So although both hotels incur a fixed cost of $200 and variable costs equal to q+ 20q (where q represents the number of hotel guests), Pitezel has to also pay for shuttle service to transport his guests to Jackson Park. The cost of providing this service is $40 per guest. Holmes’ hotel is located within a block of the Park, so he doesn’t have to incur this cost. The equilibrium market price for a hotel room is $300. Assume each hotel room can accommodate only one guest (there don’t have double-occupancy ro
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