Question

# 1. Suppose Bob has income of \$18,000. There is a 20% chance that Bob will get...

1. Suppose Bob has income of \$18,000. There is a 20% chance that Bob will get sick and have to spend \$10,000 of his income on a treatment. Suppose Bob’s income-utility relationship is given by:

Where I is Bob’s income.

U(I) = square root I

Complete the table below to find Bob’s total certain utility for various levels of wealth, along his marginal utility associated with increases in his wealth.

 Wealth Certain Utility Marginal Utility = change in utility per extra \$2,000 0 0.0 2000 44.7 22.36 4000 63.2 9.26 6000 77.5 8000 89.4 10000 100 12000 109.5 14000 118.3 16000 126.5 18000 134.2 20000 141.42 22000 148.3

a. What is Bob’s expected income, given that he faces a chance of illness? What is the actuarially fair premium for Bob’s circumstance?

b. How happy is Bob if he doesn’t buy any insurance? (Hint: expected utility!) Compare this to how happy Bob is if he can buy insurance at the actuarially fair premium.

a. Bob's income=\$18,000

probablity of illness=0.2

probablity of being healthy=0.8

expenses during illness=\$10,000

Bob's expected income=0.2*(\$18,000-\$10,000)+0.8*(\$18,000)

= 0.2*\$8,000+0.8*\$18,000

= \$1,600+\$14,400

=\$16,000

b. Bob's expected utility with insurance=0.2 sqrt18000-2000 +0.8sqrt18000

=0.2* sqrt16000 + 0.8sqrt18000

=0.2*126.5+0.8*134.2=132.66

Bob's expected utility with no insurance=0.2*sqrt8000 + 0.8sqrt18000

=0.2*89.4+0.8*134.2

=125.24

As Bob's expected utility is more when he takes insurance of fair premium so, he should take insurance policy.

thanx

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