Question

In: Economics

(15) There are two groups of individuals, each with a utility function given by U(M)=√M, where...

(15) There are two groups of individuals, each with a utility function given by U(M)=√M, where M=8,100 is the initial wealth level for every individual. The fraction of group 1 is 3/4 . Each member of group faces a loss of 7,200 with probability 1/2. Each member of group faces a loss of 3,200 with probability 1/2. Assume that the insurance market is perfectively competitive. And the insurance company does not know who belongs to which group.

(5) What is the most a member of each group would be willing to pay to insure against this loss?

(5) Suppose that the insurance market is perfectively competitive. And the insurance company does not know who belongs to which group. What will be the equilibrium level of insurance premium when both groups are expected to purchase the insurance? At this premium, will both groups indeed purchase the insurance? Explain.

(5) Now suppose that the fraction of group 1 is α instead of 3/4. Then find the range of α for which the adverse selection problem does not occur.

Solutions

Expert Solution

In case of group 1,

Expected utility=1/2*(8100)^0.5+1/2*(8100-7200)^0.5=60 utils

WTP for insurance, X, can be determined as under

U(8100-X)=60

(8100-X)^0.5=60

8100-X=3600

X=8100-3600=$4500

In case of group 2,

Expected utility=1/2*(8100)^0.5+1/2*(8100-3200)^0.5=80 utils

WTP for insurance, Y, can be determined as under

U(8100-Y)=80

(8100-Y)^0.5=80

8100-Y=6400

Y=8100-6400=$1700

Equilibrium insurance price=expected WTP=(3/4)*4500+(1/4)*1700=$3800

Since equilibrium insurance price is higher than the WTP of group 2. Group 2 will not buy the insurance.

Only group 1 will buy the insurance.

Equilibrium insurance price is given as

Equilibrium insurance price=expected WTP=*4500+(1-)*1700=4500+1700-1700

Equilibrium insurance price=2800+1700

Equilibrium insurance cost for company for group 1=expected payout=(1/2)*7200=$3600

Equilibrium insurance cost for company for group 2=expected payout=(1/2)*3200=$1600

Problem of adverse selection will not be there if

Equilibrium price3600

2800+17003600

28001900

0.6786

Range of =[0.6786]

Rahul Sunny answered 1 year ago

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