Question

In: Economics

Your utility function given by ?(?) = 15√? where ? is net of medical expenses wealth...

Your utility function given by ?(?) = 15√? where ? is net of medical expenses wealth (in thousands of dollars). In a typical year you earn $160,000, but there is a 10 percent chance that you will get sick and incur $70,000 worth of medical expenses (but will lose no wages). a. Explain what it means to buy full insurance in this case. b. How much would you be charged for actuarially fairly priced insurance? Explain why. c. Over the course of the year, the insurer makes negative profits. It turns out the chance of getting sick is 11 percent instead of 10. The insurer raises the price of insurance to $7,700 to reflect the higher risk of paying out. However, you know you’re healthier than everyone else, and that your risk is truly 10%. Would you still buy the insurance at the new premium? Show your work and explain. d. What is the maximum you would be willing to pay for full insurance? Show your work and explain.

Expert Solution

a)

Full insurance in this case means that insurer would pay sum of $70000 i,e. full refund of medical expenses in case one falls sick.

b)

Actuarially fair premium=Risk*Probability of risk=70000*0.10=$7000

Actuarially fair premium is just equal to expected loss. It this stage firm makes no profit.

c)

Probability of falling sick=p=0.10

Wealth in case of being sick=160000-70000=90000

U(90000)=15*(90000)^0.5=4500

Probability of not falling sick=1-p=1-0.10=0.90

Wealth in case of not falling sick=160000

U(90000)=15*(160000)^0.5=6000

Expected utility=p*U(90000)+(1-p)*U(160000)=0.1*4500+0.9*6000=$5850

Let us find the certain income that will give the utility equal to expected utility.Let this amount be X.

U(X)=5850

15*X^0.5=5850

X=(5850/15)^2=$152100

I would be indifferent if my wealth net of medical expenses remains $152100.

Amount that can be given up=160000-152100=$7900

Since amount that can be given up to remain indifferent, is higher than the premium amount of $7700, I would be happy to buy the insurance at $7700.

d)

Maximum willingness for insurance=Amount that can be given up (calculated in part c)=$7900

Rahul Sunny answered 1 year ago

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