< Problem Set IV:
(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
O Diminishing marginal utility of wealth
Concave utility of wealth curve
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
linear (straight-line) ‘utility of wealth curve’
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
Convex utility of wealth curve
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
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.
ii) If the insurance firm is a monopoly firm, and exercises the market leadership perfectly, what would be the