Suppose there are two types of people who need health insurance; high-risk and l

Question

Suppose there are two types of people who need health insurance; high-risk and low-risk consumers. High-risk consumers have a relatively high probability of needing expensive medical care and on average incur $2,000 of medical expenses per year. The high-risk consumers would be willing to pay up to $2,500 for insurance that covers all their medical bills. Low-risk consumers would be willing to pay up to $1,400 for full-coverage insurance and on average would incur on average $1,200 in medical bills. Assume 1/3 of all consumers are high-risk and the remaining 2/3 of consumers are low-risk. Consumers know whether they are high-risk or low-risk. The insurance company knows 2/3 of all consumers are low-risk but cannot identify which consumers are low-risk.

1:nIf all consumers bought insurance, what price must the insurance company charge to break even in expectation? That is, what price must the insurance company charge so that the expected payments equals the premium?

2:Which consumers would purchase insurance at that price?

3:Are there wealth-creating transactions that are not consummated because of the information asymmetry?

4:If the low-risk consumers were willing to pay $1,500 for the insurance, how would your answers to questions 2 and 3 change?

Explanation / Answer

Ans 1

High Risk Consumers

Cost of insurance =

$2500 p.a

Medical Expenses=

$2000 p.a

Low Risk Consumers

Cost of Insurance=

$1400 P.a

Medical Expenses =

$1200 p.a

Let the total no of persons be 100

Premium paid be 66 people (low risk) =

1400*66 = $ 92400

Premium paid be 33 people (high risk) =

2500*34 = $85000

Claim payment Low risk =

120*66 = $79200

Claim payment high risk =

$2000*34 = $68000

Net gain

in $

Premium Collection

177400

Claims paid

147200

Gain (Surplus)

30200

So premium to be charged so that co reaches break even Is $147200/100 = $1472

Ans 2

High risk as well as low risk consumer will purchase insurace at this price of $1472 per person.

Ans3

Yes, wealth creating transaction is there, we can see from above example that excess of $30,200 is there after fulfilling all the obligation

Ans 4

If low risk consumers pay $ 1500 , then following will happen

Low Risk Consumers

Cost of Insurance=

$1500 P.a

Medical Expenses =

$1200 p.a

Let the total no of persons be 100

Premium paid be 66 people (low risk) =

1500*66 = $ 99000

Premium paid be 33 people (high risk) =

2500*34 = $85000

Total Premium Collection=

$184000

Claim payment Low risk =

120*66 = $79200

Claim payment high risk =

$2000*34 = $68000

Net gain

in $

Premium Collection

184000

Claims paid

147200

Gain (Surplus)

36800

Cost of Insurance to each person

$147200/100 = $ 1472 per person

Still cost of insurance per person is $ 1472 is not changed as medical expenses are same only premium paying capacity has been increased.

Now there is excess/gain of $36800 which is $ (36800- 30200) = $ 6600 more than the previous one.

So wealth creating transaction wil be there if we increase the premium paying capacity of low risk consumers.

Ans 1

High Risk Consumers

Cost of insurance =

$2500 p.a

Medical Expenses=

$2000 p.a

Low Risk Consumers

Cost of Insurance=

$1400 P.a

Medical Expenses =

$1200 p.a

Let the total no of persons be 100

Premium paid be 66 people (low risk) =

1400*66 = $ 92400

Premium paid be 33 people (high risk) =

2500*34 = $85000

Claim payment Low risk =

120*66 = $79200

Claim payment high risk =

$2000*34 = $68000

Net gain

in $

Premium Collection

177400

Claims paid

147200

Gain (Surplus)

30200

So premium to be charged so that co reaches break even Is $147200/100 = $1472

Ans 2

High risk as well as low risk consumer will purchase insurace at this price of $1472 per person.

Ans3

Yes, wealth creating transaction is there, we can see from above example that excess of $30,200 is there after fulfilling all the obligation

Ans 4

If low risk consumers pay $ 1500 , then following will happen

Low Risk Consumers

Cost of Insurance=

$1500 P.a

Medical Expenses =

$1200 p.a

Let the total no of persons be 100

Premium paid be 66 people (low risk) =

1500*66 = $ 99000

Premium paid be 33 people (high risk) =

2500*34 = $85000

Total Premium Collection=

$184000

Claim payment Low risk =

120*66 = $79200

Claim payment high risk =

$2000*34 = $68000

Net gain

in $

Premium Collection

184000

Claims paid

147200

Gain (Surplus)

36800

Cost of Insurance to each person

$147200/100 = $ 1472 per person

Still cost of insurance per person is $ 1472 is not changed as medical expenses are same only premium paying capacity has been increased.

Now there is excess/gain of $36800 which is $ (36800- 30200) = $ 6600 more than the previous one.

So wealth creating transaction wil be there if we increase the premium paying capacity of low risk consumers.

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