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Parallels will be made with the health sector and with the need for government intervention in it

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LECTURE BASED ON

Rothschild, M. and Stiglitz, J. (1976).

“Equilibrium in competitive insurance markets: an essay on the economics of imperfect information”, in: Quarterly Journal of Economics, 90, pp. 629-649.

- First hour: background and intuitions.

- Second hour: numerical example.

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INTRODUCTION

- This article is about insurance market (private market, not specific to the health sector, no government intervention). This lecture is meant to understand how insurance would look like if it was driven by market forces only. Parallels will be made with the health sector and with the need for government intervention in it.

- Observation: the insurance policies specify not only a price as for most market goods, but a price and a quantity (of coverage).

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BASIC INGREDIENTS

1. Uncertainty 2. Risk

3. Asymmetric information on risk

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1. UNCERTAINTY

1.1. Without uncertainty, there is no market for insurance.

2. RISK

2.1. Risk averse individuals are ready to pay something to decrease the risk.

2.2. Without risk aversion, there is no market for insurance.

2.3. With risk aversion, there is a market for insurance.

2.4. Risk discrimination.

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3. ASYMMETRIC INFORMATION ON RISK 3.1. Risk discrimination.

3.2. The good risks are worse off. The bad risks are not better off.

3.3. There is no market for insurance if there are too few bad risk individuals.

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1. UNCERTAINTY

1.1. Without uncertainty, there is no market for insurance.

Example: no market for pregnancy insurance.

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2. RISK

2.1. Risk averse individuals are ready to pay something to decrease the risk.

2.1.1. Why?

A risk averse individual stricly prefers - certainty to uncertainty.

- less uncertainty to more uncertainty.

Therefore, there is a demand for (full/partial) insurance from risk averse individuals.

2.1.2. How much?

It depends on the probability of bad luck, and on the insurance coverage (full/partial).

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2.2. Without risk aversion, there is no market for insurance.

A risk neutral individual is indifferent between - certainty and uncertainty,

- less uncertainty and more uncertainty,

(as long as the expected wealth keeps constant, of course).

Therefore, a risk neutral individual is not ready to pay anything to protect him/herself against uncertainty. Therefore, there is no demand for insurance from risk neutral individuals.

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2.3. With risk aversion, there is a market for insurance.

Supply also exists: Any contract that is demanded and expected to be profitable will be supplied.

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2.4. Risk discrimination.

Risk discrimination: full-insurance with risk-related premium.

Why not one contract for everyone with full-insurance and average risk-related premium (pooling contract)?

- Either low risk individual prefer no insurance to pooling insurance.

- Or another insurer can profitably supply some cheaper partial insurance attracting only low risk individuals.

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3. ASYMMETRIC INFORMATION ON RISK

3.1. Risk discrimination.

No pooling contract for the same reason as in 2.4.

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3.2. The good risks are worse off. The bad risks are not better off.

Risk discrimination:

- full-insurance with high risk-related premium.

- partial insurance with low risk-related premium.

Why not full-insurance with low risk-related premium anymore? Because high risk individual would buy it, which is not profitable for the insurer.

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3.3. There is no market for insurance if there are too few bad risk individuals.

The higher the proportion of low risk individuals, the lower the average risk.

Therefore, a pooling full-insurance contract with a low average risk-related premium would attract both high risk and low risk individuals (discrimination as in 3.2. is not sustainable anymore). However, any (full-insurance) pooling contract is not sustainable either (see 2.4.). Therefore, the insurance market cannot work.

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NUMERICAL EXAMPLE

Wealth 0 10 20 30 40 50 60 70 Corresponding

utility

0 7 13 18 22 25 27 28

- Initial wealth: W = 70

- Loss in case of bad luck: d = 60 - Low risk individuals: pL = 1/3 - High risk individuals: pH = 2/3

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Consider the following contracts:

Insurance contract EU of EP from

Type Premium Coverage Low risk High risk Low risk High risk

(E) 0 0 21 14 0 0

(FL) 20 60 25 25 0 − 20

(FH) 40 60 18 18 +20 0

(FA) 30 60 22 22 +10 − 10

(PI) 10 30 24 21 0 − 10

(PII) 10 20 22.3 17.6 +3.3 − 3.3

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2.1. Risk averse individuals are ready to pay something to decrease the risk.

Consider a low risk individual:

- if , then EW = 50 and EU = 21.

- if , then EW = 50 and EU = 24.

Ready to pay a premium of (more than) 10 for a partial coverage of 30.

- if , then EW = 50 and EU = 25.

Ready to pay a premium of (more than) 20 for a full coverage.

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Consider a high risk individual:

- if , then EW = 30 and EU = 14.

- if , then EW = 30 and EU = 17.

Ready to pay a premium of (more than) 20 for a partial coverage of 30.

- if , then EW = 30 and EU = 18.

Ready to pay a premium of (more than) 40 for a full coverage.

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2.3. With risk aversion, there is a market for insurance.

- A low risk individual is ready to pay a premium of (more than) 10 for a partial coverage of 30.

This is expected to be profitable for the insurer:

EP 10 – (1/3*30) = 0.

- A low risk individual is ready to pay a premium of (more than) 20 for a full coverage.

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This is expected to be profitable for the insurer:

EP 20 – (1/3*60) = 0.

- A high risk individual is ready to pay a premium of (more than) 20 for a partial coverage of 30.

This is expected to be profitable for the insurer:

EP 20 – (2/3*30) = 0.

- A high risk individual is ready to pay a premium of (more than) 40 for a full coverage.

This is expected to be profitable for the insurer:

EP 40 – (2/3*60) = 0.

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2.4. Risk discrimination.

Risk discrimination:

- Contract (FL) for low risk individuals.

- Contract (FH) for high risk individuals.

Why not a pooling contract such as (FA)? Because:

- low risk individuals prefer (PI) to (FA), - high risk individuals prefer (FA) to (PI),

- (PI) is expected to be profitable from low risk individuals,

- (FA) is expected to be non profitable from high risk individuals.

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3.2. The good risks are worse off. The bad risks are not better off.

Risk discrimination:

- Contract (PII) for low risk individuals.

- Contract (FH) for high risk individuals.

These are self-selecting contracts:

- Low risk individuals prefer (PII) to (FH).

- High risk individuals prefer (FH) to (PII).

- Both (PII) and (FH) are profitable when they are self-selected.

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Why not a risk discrimination as in 2.4., with the contracts (FL) and (FH)? Because it is not self-selecting: high risk individuals prefer (FL) to (FH).

Why are the low risks worse off? Because they prefer (FL) to (PII).

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