An individual has an initial wealth of $35,000 and might incur a loss of $10,000 with probability p. Insurance is available that charges $gK to purchase $K of coverage
What value of g will make the insurance actuarially fair? If she is risk averse and insurance is fair, what is the optimal amount of coverage?
The insurance company's expected payoff is:
p(gK – K) + (1 – p)(gK)
Fair insurance requires:
p(gK – K) + (1 – p)(gK)=0
Which means the g = p
If she is risk averse, she will purchase full coverage (K = 10,000 ). Formally, she will choose K to maximize her expected utility:
EU = p*U(25,000 + (1 – p)K) + (1 – p)*U(35,000 – pK)
The Necessary Condition for Maximum is:
U'(25000 + (1 - p)K) = U'(35,000 – pK)
which requires that:
25000 + (1 – p)K = 35000 – pK.
Solving yields K = 10,000.
For this to be a maximum (not a minimum), the expected utility function must be concave, which is assured from the fact that the utility function is concave (risk averse).
You might also like to view...
Suppose that the current price of a marketable permit to emit one ton of gunk is $60 . For firm A, the marginal cost of reducing one ton of gunk is $50 . For firm B, the marginal cost of reducing one ton of gunk is $70 . Under a marketable permit system, _____
a. both firms will buy a permit and emit one more ton of gunk b. firm A will buy a permit and emit one more ton of gunk, whereas firm B will reduce its emissions of gunk by one ton c. firm B will buy a permit and emit one more ton of gunk, whereas firm A will reduce its emissions of gunk by one ton d. both firms will reduce their emissions of gunk by one ton e. both firms will go out of business
For any combination or outputs, there is an efficient allocation of income
a. True b. False Indicate whether the statement is true or false