Question

In: Economics

Partial Insurance: An individual has $2000 in physical assets, and $600 in cash initially. This person...

Partial Insurance: An individual has $2000 in physical assets, and $600 in cash initially. This person faces the following loss distribution to the wealth. Full insurance is available at $600

Probability

Loss

0.5

0

0.1

200

0.2

400

0.1

1000

0.1

2000

The Individual can also buy partial insurance with i. a $200 deductible, or ii. 75% coinsurance, or iii. Upper limit on coverage, with the limit being $1000. The premium on each partial coverage policy is $450. Provide a ranking of the four types of policies for the individual, in terms of preference if the preference function is given by U(FW) = LN(1+FW), where FW is final wealth of the individual.

Solutions

Expert Solution

Probability Loss $ Loss forecast $
P L P X L
0.5 0 0
0.1 200 20
0.2 400 80
0.1 1000 100
0.1 2000 200
1.00 Toal 400

FW (no insurance) = Physical assets + cash - Total loss forecast = 2000 + 600 - 400 = $ 2200 [ RANK 1]

FW ( full insurance) = Physical assets + cash - Insurance Premium = 2000 + 600 - 600 = $ 2000 [RANK 2]

FW (partial insurance with $200 deductible) = Physical assets + cash - Insurance Premium (i.e., $450)- Deductible = $1950 [RANK 3]

FW (partial insurance with 75% co-payment) = Physical assets + cash - Insurance Premium (i.e., $450)- copayment ( i.e., 75% of total loss forecast) = 2000 + 600 - 450 - 300 = $1850 [RANK 4]

FW (partial insurance with $ 1000 limit) = Physical assets + cash - Insurance Premium (i.e., $450)- forecast value of expected loss of $ 2000 = 2000 + 600 - 450 - 200 = $1950 [ RANK 3]

Ranks for consumer are juxtaposed above as the utility function is based on LN (natural logarithm) of FW. In other words more the FW, higher the utility.

Rahul Sunny answered 1 year ago
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