Simon has current wealth of $36, including $20 in cash. With probabil- ity Simon's money will...

  

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Simon has current wealth of $36, including $20 in cash. With probabil- ity Simon's money will be stolen (contingency 1), leaving him with only $16 to spend on consumption, and with probability his cash will not be stolen (contingency 2) so he can spend the entire $36 on consumption. Simon has utility function u (.02) = 5 + where c is consumption spending in contingency i. (a) What is the expected value of Simon's contingent consumption? (b) What is the expected utility of Simon's contingent consumption? (c) What is Simon's MRS at his current contingent consumption bun- dle? (d) An insurance company offers to fully insure Simon against the risk of theft for a premium (price) of SP. That is, if Simon pays SP to the insurance company, then the insurer will replace Simon's $20 in contingency 1. If Simon buys the insurance his contingent consumption bundle is therefore (36-P, 36-P). i. What is Simon's MRS at the fully insured contingent con- sumption bundle? ii. At what value of P would the insurer make zero expected profit were Simon to buy the insurance? iii. Would Simon buy the insurance at the price you identified in (ii)? Be sure to explain your answer. iv. At what value of P would Simon be indifferent about buying the insurance or not? What is the insurer's expected profit at this premium? v. Draw a CC diagram showing Simon's contingent consump- tion without insurance and his contingent consumption with insurance at the premium you computed in (iv). Sketch Si- mon's indifference curve through each point. Be as accurate as possible, and make sure your diagram is consistent with your answers to the previous parts of this question. 2 Simon has current wealth of $36, including $20 in cash. With probabil- ity Simon's money will be stolen (contingency 1), leaving him with only $16 to spend on consumption, and with probability his cash will not be stolen (contingency 2) so he can spend the entire $36 on consumption. Simon has utility function u (.02) = 5 + where c is consumption spending in contingency i. (a) What is the expected value of Simon's contingent consumption? (b) What is the expected utility of Simon's contingent consumption? (c) What is Simon's MRS at his current contingent consumption bun- dle? (d) An insurance company offers to fully insure Simon against the risk of theft for a premium (price) of SP. That is, if Simon pays SP to the insurance company, then the insurer will replace Simon's $20 in contingency 1. If Simon buys the insurance his contingent consumption bundle is therefore (36-P, 36-P). i. What is Simon's MRS at the fully insured contingent con- sumption bundle? ii. At what value of P would the insurer make zero expected profit were Simon to buy the insurance? iii. Would Simon buy the insurance at the price you identified in (ii)? Be sure to explain your answer. iv. At what value of P would Simon be indifferent about buying the insurance or not? What is the insurer's expected profit at this premium? v. Draw a CC diagram showing Simon's contingent consump- tion without insurance and his contingent consumption with insurance at the premium you computed in (iv). Sketch Si- mon's indifference curve through each point. Be as accurate as possible, and make sure your diagram is consistent with your answers to the previous parts of this question. 2

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a Expected value of Simons contingent consumption Ptheft 05 Consumption if ... View the full answer