Jack makes 50,000 a year, but there is a 20% chance he will get sick, in which c
ID: 1095261 • Letter: J
Question
Jack makes 50,000 a year, but there is a 20% chance he will get sick, in which case his medical bills will effectively lower his income to 40,000. He has a utility function U=In(I) where I = income (net of medical expenses). He is considering buying insurance to pretect against this medical risk, and is deciding between the following plans ( or simply reamining uninsured)
Plan A: 0% coinsurance rate, $14,000 annual premium
Plan B: 20% coinsurance rate. $13,000 annual premium
Plan C: 40% coinsurance rate, $12,000 annual premuim
Plan D: 50% coinsurance rate, $11,000 annual premium
Compute his expected income and expected utility under each of these four plans, as well as under the default option of remaining uninsured. Which option maximizes his expected income? Which option maximizes his expected utility? If they are different, what is the intuition behind this?
Explanation / Answer
Medical expenditure if ill=$10000
A)Exp I=50000-14000=$36000
U=ln(36000)=10.49
B)Exp(I)=50000-13000-0.2*10000=$35000
U=ln(35000)=10.463
C)Exp(I)=50000-12000-0.4*10000=$34000
U=ln(34000)=10.434
D)Exp(I)=50000-11000*0.5*10000=$34000
U=ln(34000)=10.434
Default option.
Exp(I)=$40000
U=ln(40000)=10.60
His income and utility are maximised in the default option clearly.
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