1. Adam, a passionate angler who lives in Kingston, plans to participate in a bass fishing...

 

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1. Adam, a passionate angler who lives in Kingston, plans to participate in a bass fishing tournament next weekend. There are two fishing tournaments scheduled on the next weekend near Kingston: one at Sydenham Lake, and the other one at Charleston Lake. The registration fee for the Sydenham Lake tournament is $S150, and the fee for the Charleston Lake tournament is $200. The winner of each tournament is determined based on the total weight of the five biggest bass that each competitor caught. Winning a tournament requires a combination of skills, experience, and luck. Adam has fished many times for bass on Sydenham Lake, but never on Charleston Lake. He therefore has the following beliefs about winning the tournaments: Sydenham Lake Tournament Prize Probability $5,000 0.1 $1,000 $500 So 1st place 2nd place 3rd place 4th place or lower 0.2 0.2 0.5 Charleston Lake Tournament Prize $10,000 $5,000 $1,000 so 1s place 2nd place 3rd place 4th place or lower Probability 0.05 0.1 0.15 0.7 Adam's preferences can be best described by the utility function U(W) = √W, where W is his wealth. Suppose that Adam's wealth (before participating in a tournament and paying the registration fee) is $4,000. Note: Round your final numbers to 2 decimal places. a) Given his utility function, which bass fishing tournament does Adam prefer? (5 points) b) Adam decided to explore Charleston Lake a bit before making his final decision. He believes that there is a 1 percent chance that he will hit an unmarked shoal, which would destroy the lower unit of his outboard engine. It would cost Adam $3,000 to have the lower unit replaced. Adam therefore considers buying extra insurance for his boat, which would fully cover the cost of replacing a damaged lower unit. Can it be profitable for a risk neutral insurance company to sell Adam such an insurance? To answer this question, (i) Calculate the minimum insurance premium that the insurance company is willing to accept. (ii) Calculate the maximum insurance premium that Adam is willing to pay. (6 points) c) Would your answer to part (b) change if Adam was risk loving? Briefly explain. (Note: No math is required to answer this question.) (3 points) 1. Adam, a passionate angler who lives in Kingston, plans to participate in a bass fishing tournament next weekend. There are two fishing tournaments scheduled on the next weekend near Kingston: one at Sydenham Lake, and the other one at Charleston Lake. The registration fee for the Sydenham Lake tournament is $S150, and the fee for the Charleston Lake tournament is $200. The winner of each tournament is determined based on the total weight of the five biggest bass that each competitor caught. Winning a tournament requires a combination of skills, experience, and luck. Adam has fished many times for bass on Sydenham Lake, but never on Charleston Lake. He therefore has the following beliefs about winning the tournaments: Sydenham Lake Tournament Prize Probability $5,000 0.1 $1,000 $500 So 1st place 2nd place 3rd place 4th place or lower 0.2 0.2 0.5 Charleston Lake Tournament Prize $10,000 $5,000 $1,000 so 1s place 2nd place 3rd place 4th place or lower Probability 0.05 0.1 0.15 0.7 Adam's preferences can be best described by the utility function U(W) = √W, where W is his wealth. Suppose that Adam's wealth (before participating in a tournament and paying the registration fee) is $4,000. Note: Round your final numbers to 2 decimal places. a) Given his utility function, which bass fishing tournament does Adam prefer? (5 points) b) Adam decided to explore Charleston Lake a bit before making his final decision. He believes that there is a 1 percent chance that he will hit an unmarked shoal, which would destroy the lower unit of his outboard engine. It would cost Adam $3,000 to have the lower unit replaced. Adam therefore considers buying extra insurance for his boat, which would fully cover the cost of replacing a damaged lower unit. Can it be profitable for a risk neutral insurance company to sell Adam such an insurance? To answer this question, (i) Calculate the minimum insurance premium that the insurance company is willing to accept. (ii) Calculate the maximum insurance premium that Adam is willing to pay. (6 points) c) Would your answer to part (b) change if Adam was risk loving? Briefly explain. (Note: No math is required to answer this question.) (3 points)

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