Question

3. Using Grossman’s pure consumption model of the demand for
health, consider the impact of the following on the optimal stock
of health, the optimal amount of health inputs to purchase, and the
optimal spending on all other goods and services other than on
health inputs:

?a. An increase in education that only increases productive
efficiency (i.e. education ?only increases the marginal product of
health inputs)?

?b. Suppose that the increase in education in part a was
simultaneously associated with ?with an increase in the persons
daily wage rate.

?c. How does changing the person’s tastes and preferences
toward health and away from ?other goods and services affect the
answers to a and b above?

4) Jack’s income is $16,900. There is a 30% chance Jack will
get sick during the next year. If Jack gets sick, he will incur a
loss of $4,800. His utility function is U(I)=I0.5 (that is, utility
equals the square root of Income). (4 pts)

a) What is Jack’s expected income?

b) What is Jack’s expected loss?

c) What is Jack’s expected utility?

d) What is the maximum amount of money Jack is willing to pay
for insurance? What is the pure premium? What is the risk
premium?

e) Show part d) using a diagram.

Answer #1

4.

Jack’s income = I = $16,900

The probabilty of being sick is 0.3. If Jack gets sick, he will
incur a loss of $4,800. His utility function is
U(I)=I^{0.5}

a) Jack’s expected income is

E(I) = 0.3*(16900 - 4800) + 0.7*(16900)

= .3* 12100 + .7 * 16900

= 3630 + 11830

= $15460

b) Jack’s expected loss is

E(L) = 0.3*4800 + 0.7*0

=480*3

= $1440

c) Jack’s expected utility

E(U) = 0.3*(16900 - 4800)^{0.5} +
0.7*(16900)^{0.5}

= .3* 12100^{0.5} + 0.7*(16900)^{0.5}

= .3 * 110 + .7 * 130

=33 + 91

=124

d) Its certainty equivalent is

124 = I^{0.5}

I = (124)^{2}

I = $15376

The maximum amount of money Jack is willing to pay for insurance = current income - CE

= 16900 - 15376

= $1524

His pure premium is 1524.

risk premium = maximum amount paid by him as insurance - the expected loss

= 1524 - 1440

= $84

Note: 1 question at a time with 4 sub-parts

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