Community Rating in the Market for Private Health

Insurance: A simple analysis of why it

can’t work

Community Rating in the Market for Private Health

Insurance: basicA simple analysis of why it

can’t work

Source: Rothschild and Stiglitz, 1976

Consider the following contingent commodities diagrams:

High Risk Individuals

Low Risk Individuals

C2

C1

45°

C2

C1

45°

Consider the following contingent commodities diagrams:

High Risk Individuals

Low Risk Individuals

C2

C1

45°

C2

C1

45°

Consider the following contingent commodities diagrams:

High Risk Individuals

Low Risk Individuals

C2

C1

45°

C2

C1

45°

Consider the following contingent commodities diagrams:

High Risk Individuals

Low Risk Individuals

C2

C1

45°

C2

C1

45°

Consider the following contingent commodities diagrams:

High Risk Individuals

Low Risk Individuals

C2

C1

45°

C2

C1

45°

Insurance companies can fragment the market and offer different risk premiums to different groups.

The slopes of the indifferences curves are:

The slopes of the budget constraints are:

For fair insurancep = r

With two groups this can be a separating equilibrium

ph = rh

pl = rl

p

pMRS

1

r

rMRT

1

C2

C1

45°H

C2

C1

45°H L

C2

C1

45°

L → fair insurance line for low risk people

H→ fair insurance line for high risk people

C2

C1

H L

l

l

p

p

1

h

h

p

p

1

L → fair insurance line for low risk people

H→ fair insurance line for high risk people

A → average of the two

C2

C1

H A L

l

l

p

p

1

a

a

p

p

1

h

h

p

p

1

Mapping the three diagrams together:

C2

C1

Mapping the three diagrams together:

IC1 → indifference curve if high-risk individuals are offered fair insurance

IC1

C2

C1

Mapping the three diagrams together:

IC1 → indifference curve if high-risk individuals are offered fair insurance

IC2 → indifference curve if low-risk individuals are offered fair insurance

IC1

IC2

C2

C1

Mapping the three diagrams together:

A → insurance line for pooled (community rated) contracts

IC1

IC2

A

C2

C1

Mapping the three diagrams together:

A → insurance line for pooled (community rated) contracts

IC1

IC2

C2

C1

Mapping the three diagrams together:

IC3 → indifference curve if high-risk individuals are offered pooled insurance contract

IC1

IC2

IC3

C2

C1

Mapping the three diagrams together:

IC3’ → indifference curve for high-risk who cannot over insure with pooled contract

IC1

IC2

IC3’

C2

C1

Mapping the three diagrams together:

IC3’ → indifference curve for high-risk who cannot over insure with pooled contractIC4 → indifference curve if low-risk individuals are offered pooled insurance contract

IC1

IC2

IC4

IC3’

C2

C1

Mapping the three diagrams together:

We see that:IC3’ > IC1 high-risk people are on a ⇒higher indifference curveIC2 < IC4 low-risk people are on a ⇒higher indifference curve

IC1

IC2

IC4

IC3’

C2

C1

If the market is competitive is this a stable equilibrium?

C2

C1

In a competitive market other firms may enter the market and offer insurance.

Another firm may offer insurance at a different price (insurance line) to the incumbent.

C2

C1

L → fair insurance line for low-risk group

L

C2

C1

Any contract in the shaded area makes low risk people better off but is not attractive to high risk people.

C2

C1

Point X represents a better contract for the low risk individuals if the bad state of the world occurred.

At X the new insurance company will only attract low risk individuals.

X

C2

C1

Point X represents a better contract for the low risk individuals if the bad state of the world occurred.

At X the new insurance company will only attract low risk individuals.

X

C2

C1

The original company will findpa = ra < ph

and will be making a loss.

X

C2

C1

The original company will findpa = ra < ph

and will be making a loss.

To counter this the company may start to charge a higher price.

X

C2

C1

The original company will findpa = ra < ph

and will be making a loss.

To counter this the company may start to charge a higher price.

X

C2

C1

The original company will findpa = ra < ph

and will be making a loss.

To counter this the company may start to charge a higher price.

X

C2

C1

The original company will findpa = ra < ph

and will be making a loss.

To counter this the company may start to charge a higher price.

X

C2

C1

As they have all high risk people this company may increase it price to the fair price for those people.

X

C2

C1

However at this price even high risk people will find contract X attractive and will switch.

X

C2

C1

However at this price even high risk people will find contract X attractive and will switch.This is not what the company the entered the market and offered X wants.

X

C2

C1

C2

C1

As a result of this the company will have to start increasing the price.

C2

C1

As a result of this the company will have to start increasing the price.

This is where we started.

And we already know that this is not a stable equilibrium.

C2

C1

It is not possible to have a stable equilibrium in a competitive insurance market with community rating.

It is not possible to have a stable equilibrium in a competitive insurance market with community rating.

Unless.............