Question

Suppose you are uncertain about your future healthcare costs. You think that there is a 50/50 shot that in the next year you will need to use $12,000 in health services or $0 in health services. If you buy health insurance, your insurer covers all your health services costs, otherwise you do. Health insurance costs $7,000. Your begin with $16,000 in wealth and your utility is U(W) = sqrt(W).

a)What is the Expected Value (cost) of health services?

b) What is your expected Utility if you do not purchase Health Insurance?

c) What is your expected Utility if you do purchase Health Insurance?

d) Will you choose to Purchase Health Insurance? Why or Why not?

e) What is the most you would have been willing to pay for Health Insurance?

f)What is the minimum amount a health insurer could possibly charge and not go out of business?

Answer 1

a- The expected value (cost) of health services= probalility of using health services * cost of health services + probalility of not using health services * no cost on health services

As given above :

• probability of using health services is 50% = .5
• probability of not using health services is 50% = .5
• cost of using health services is = $12,000
• if no need to use health services than there is no cost = $0

Putting the values in the formula

expected value of health sevices = .5*12000 + .5*0

= 6,000

so the expected value (cost) of health services is $6,000

b- The formula of expected utility if we do not purchase health insurance is = probability of cost of using health services (sqrt of cost of using health services)+probability of not using health services (sqrt of cost of not using health services)

= .5(√12,000) + .5(√0)

= .5(109.54) + 0

= 54.77

So the expected Utility if we do not purchase Health Insurance is 54.77

c-  the formula of expected utility if we purchase health insurance is = probability of cost of health insurance(sqrt of cost of health insurance)+probability of no need to use health insurance(sqrt of no need to use health insurance)

* probability will be same for using health services and health insurance because if we will use health service than only we will need insurance.

= .5(√7000) + .5(√0)

=.5*83.67

=41.835

So the expected utility of purchasing health insurance is 41.835

d- Yes i will choose to purchase health insurance because future is uncertain so we cannot predict that in future if we will need to use health services or not and how much it will cost so if we purchase health insurance the insurer will pay for our health services . It will reduce financial burden and I will not be worry about the costs of using health services.  

e- The most i would be willing to pay for the insurance would be equal to the utility of cost of using health services which i was going to pay in future without health insurance (as given in the question that utility of wealth = sqrt of wealth) that is sqrt of $12,000 = $ 109.54

f- The insurer will make policy as such that so he can get maximum benefit and can survive in the competitive market so he will chagre half of his insurance payment which is $3500 minimum from the customer.