Question

Jane is searching for a job and is considering various job offers. Firm A and Firm B offer her different health insurance plans. The details of each plan are listed below: Firm A: 75% coinsurance policy (insurer pays 25%) Firm B: 25% coinsurance after meeting an $8000 deductible Jane only uses medical care if she is sick. Her demand for care when sick is: Q = 720 – 12P

The market price for medical care is $20/unit. Jane gets sick and demands care with a 20% probability.

a) How many units of care would she demand if uninsured? What is the expected value of her loss when uninsured? b) How much consumer surplus does Jane receive from medical care if she gets sick?

In: Plan A

c) How many units of care will Jane demand in Firm A’s health plan?

d) What is Jane’s AFP for Firm A’s health plan?

e) What is the equation for Jane’s demand for care with coinsurance?

In: Plan B

f) How many units of care will Jane demand in Firm B’s health plan?

g) What is Jane’s AFP for Firm B’s health plan?

Answer 1

A) Jane's demand curve is Q = 720 – 12P. When uninsured, she will get treatment at market price, which is $20/unit. So Quantity Demanded=720-12*20=720-240=480units.

When uninsured, and at this quantity, the cost Jane would incur is 480*20=9600USD. If Jane was insured in plan A, she would've had to pay 75% of it, or 7200. She wouldve benefited 9600-7200=2400USD. So her loss when uninsured is 2400 in plan A. In Plan B, she wouldve had to pay 8000+.25*9600= 8000+2400= 10400. She wouldve had no surplus loss.

Note: This is if we count the deductible too. Not counting it, she will have a surplus loss of USD 2400 in Firm B's case.

B. The maximum price Jane is willing to pay is $20. In Firm A, she pays $15. Her surplus is $5.

In firm B, she pays $5 per unit and $8000 upfront. The per unit cost of the $8000 depends on how much she is sick. Since price P is $5 for firm B, Jane's demand is Q=720-12*5= 720-60=660. At 660, the cost per unit of $8000 comes at= 8000/660=12.12. So total cost is 5+12.12. The surplus becomes 20-17.12= $2.88.

C) The cost for Jane in firm A plan is $15. Hence she will demand Q=720-12*15= 720-180=540units.

D) AFP stands for actuarially fair insurance. This is the insurane where the customer doesnt expect a loss or benefit. This is calculated by using the fact when premium paid=chance of geting sick*permium recieved when sick. Jane has a probability of .2 of getting sick. At firm A price, she will demand 540 units (as discussed above). For these many units, she will have to spend 540*20 (at market price)= 10800USD. She has a probabiliy of .2 of getting sick. Hence, her AFP is 10800*.2= 2160USD.

E) The equation with coinsurance is Q=720-12*Coinsurace*P.

F) Since the cost for Jane is now $5, she will demand Q=720-12*5= 720-60= 660units.

G) At firm B price, she will demand 660 units (as discussed above). For these many units, she will have to spend 660*20 (at market price)= 13200USD. She has a probabiliy of .2 of getting sick. Hence, her AFP is 13200*.2= 2640USD.