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...
Eisenhower wanted producers of weapons and war-related goods to have influence over fiscal policy decisions
Indicate whether the statement is true or false
An increase in investment, combined with an increase in imports, would have what effect on aggregate demand? a. AD would increase
b. AD would decrease. c. AD would stay the same. d. AD could either increase or decrease, depending on which change was of a greater magnitude.
Which of the following would be most likely to cause an outward shift of the demand curve for electricity?
a. a decrease in the price of electricity b. an increase in the price of air conditioners c. an increase in the price of heating oil d. a decrease in the price of natural gas
In the short run a decrease in the costs of production makes
a) output rise and prices fall. b) output and prices fall. c) output and prices rise. d) output fall and prices rise.