econ2 ps#4 answer key

econ2 ps#4 answer key - < Problem Set IV Answer Key >(ECON...

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1 < Problem Set IV: Answer Key > (ECON 2: Spring 2008) ( Market Imperfection and Policies; Prof. Young-Han Kim ) 1. Explain the relationship between three different types of the utility wealth curves of persons, (i.e., concave, convex, and straight line) and their attitude toward risk. (That is, explain the relationship between ‘the diminishing, increasing, and constant marginal utility of wealth ’ of persons, and their attitudes toward risks.) O Diminishing marginal utility of wealth Æ Concave utility of wealth curve Æ Risk averse attitude : To Risk averse people, the utility from an expected wealth under risks is equal to the utility from (much) lower assured wealth without risks. O Constant Marginal utility of wealth Æ linear (straight-line) ‘utility of wealth curve’ Æ Risk neutral attitude: To Risk neutral people, the utility from an expected wealth under risks is equal to the utility from the same level of assured wealth without risks. O Increasing marginal utility of wealth Æ Convex utility of wealth curve Æ Risk loving attitude : To Risk loving people, the utility from an expected wealth under risks is equal to the utility from (much) higher assured wealth without risks. 2. Assume that Gina, our capable TA, bought a car, which values 10,000 dollars. When the car accident happens, the value of the car becomes 0. The probability for a car accident to happen in San Diego region is 20%. Gina is risk averse. So, her utility from the expected wealth under uncertainty (with probability for an accident to be 20%) is 90. However, she gets the same level of utility (90) with assured wealth of $6,000 under no uncertainty. i) When an insurance company provides car insurance guaranteeing a full recovery of wealth from whatever car accident, what would be the ‘minimum cost of insurance”? (Provide your logic using diagrams in addition to the numerical answer.) o The minimum cost of insurance is the difference between the original asset value not under any risks and the expected asset value under risks. That is, the minimum cost of the insurance is the expected cost of insurance guaranteeing the original asset values not under uncertainty. In this example, the minimum cost of insurance is: $10,000 - $8,000 = $2,000.
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