Lecture 4 –Economics of insurance
Introduction
Discuss other issues, that from a social welfare/economic perspective, are important as well;
Example
Suppose we have 4 different states of the world. You can choose between them ex ante: These
situations show a probability of damage: what is the probability that an accident with a certain
magnitude might occur, and how efficient care and liability rules can prevent this?
State of the world #1: 100% chance that a damage will occur with a magnitude of 1000;
State of the world #2: 10% chance that an accident will occur, with a magnitude of 10.000;
State of the world #3: 1% chance that an accident will occur, with a magnitude of 100.000;
State of the world #4: 0,1% chance that an accident will occur, with a magnitude of 1000.000.
Probabilities and damage are separated in the above. Back in Shavall’s world the probability
and damage are not separated: P x D = expected damage. The expected damage is the
multiplier of the probability and the damage.
Question: in situation 1, there is a 100% probability of losing a 1000 – what is the expected
damage? P x D = (…); 100% x 1000 = 1000.
The four situations are equal in Shavell’s world: the probability of damage multiplied with the
damage is always a 1000. But, in the above we were not interested in the heights of the
probability in relation to the height of the damage. In this lecture we will answer the question
if this matters. Are the four situations the same, because the expected outcome in all four is
the same, namely: a 1000. Or are they different?
You have a big family to take care of. But you only have 50.000 euros. There are 4 situations
of the world. You can choose – and you know the expected damage is always a 1000. But you
get to choose ex ante. Do you want to be in a situation where you have a 100% chance to
loose a 1000? Or 10% chance to loose a 10.000? Etc.
Introduction of the notion of risk
When we care about the high probability and low damage; low probability and high damage.
There are three types of risk attitudes:
1) Risk-aversion
Most people would prefer situation 1, you know in advance what the loss will be. You
know in advance that the housewife would have 49.000 left. Situation 2 would be a
drama, you only have 50.000 – losing 10.000 would mean 20% of your total wealth would
be gone. Situation 3 is really a catastrophe: the probability is 1% - you lose a 100.000 and
would have nothing left! But, situation 4 offers not much difference with situation 3.
There is only 50.000 and gone is gone. However, situation 4 has a lower chance of
happening?
Irrealistic views concerning the likelihood of catastrophes: people think the probability is
low and when it happens they will die anyway. This is extremely dangerous as situation 1,
meaning we don’t take sufficient measures and don’t invest in prevention.
, Many socially desirable project don’t take place because of risk-aversion
We could invest and find the cure for cancer, but there are risk involved. People can lose
everything that is at stake: so risk is a loss to social-welfare.
2) Risk-neutral
Why is Bill Gates risk neutral, and the housewife (and most of the people) risk-averse?
The relationship we have to risk has to do with: 1) magnitude of risk and income, and 2)
our own well-situation: the decreasing marginal utility of money.
What is this?
If you’re homeless, your first 10 euro is worth enormously – and your additional 5 euro as
well. The homeless person can do lots with this. If you have a reasonable good income,
and you receive 10 euro, you may not be aware if you have 10 euro more or less. The
more you have, the marginal value decreases. Economists see the diminishing marginal
utility as the consumer's decreasing willingness to pay more money for the same
incremental increase in units of a product or service. The problem, however, is that our
willingness to pay and consume more should stop at 'satisfactory,' not just diminish.
3) Risk-lovers
They choose situation 4 (casino/lottery).
When you receive an offer, ask yourself if you have a risk-aversion towards this. If so, risk-
aversion causes dis-utility. Because of this dis-utility there is a loss of social welfare, and
therefor we dislike situation 2, 3, and 4.
o We introduced the notion of risk – and most people are risk averse. But society would
be better off if we are all in situation 1 (assuming we are all risk-averse and all have a
limited amount of money).
Can we solve the problem of risk-aversion?
1. Yes, by shifting risks with a risk-sharing agreement
Risk trading: from uncertainty (situation 3) to certainty (situation 1);
Greek example
2000 years ago the problem was, that people made money by sailing. A lot could go wrong on
sea: pirates, bad weather, natural disasters, etc. Suppose that the boat is worth 100.000;
probability 1% of losing ship. That is situation 3 and highly undesirable – the ship is all you
have! Risk-aversion causes loss of social welfare, because people find it too risky and will
decide not to sail. Then it limits economic activity. But, the shipper was not alone. And with
99 others faced the same risk. The ships are all worth the same and the risk is exogenous 1
(comes from external factors). They would like to shift to situation 1.. how to do this?
By creating a risk-sharing agreement (risk-distribution agreement). The decision is made
behind the veil of ignorance (Rawls): made before the sailing. Uncertainty is traded for
certainty: risk-trading is a solution;
When are these agreements suitable?
o Highly complicated risks;
o Catastrophic risk and low probability – high damage;
o Small group of people with low transaction costs;
o Little information on precise probabilities (we often don’t know in reality);
1
Endogenous: You can influence the risk yourself as well.
Introduction
Discuss other issues, that from a social welfare/economic perspective, are important as well;
Example
Suppose we have 4 different states of the world. You can choose between them ex ante: These
situations show a probability of damage: what is the probability that an accident with a certain
magnitude might occur, and how efficient care and liability rules can prevent this?
State of the world #1: 100% chance that a damage will occur with a magnitude of 1000;
State of the world #2: 10% chance that an accident will occur, with a magnitude of 10.000;
State of the world #3: 1% chance that an accident will occur, with a magnitude of 100.000;
State of the world #4: 0,1% chance that an accident will occur, with a magnitude of 1000.000.
Probabilities and damage are separated in the above. Back in Shavall’s world the probability
and damage are not separated: P x D = expected damage. The expected damage is the
multiplier of the probability and the damage.
Question: in situation 1, there is a 100% probability of losing a 1000 – what is the expected
damage? P x D = (…); 100% x 1000 = 1000.
The four situations are equal in Shavell’s world: the probability of damage multiplied with the
damage is always a 1000. But, in the above we were not interested in the heights of the
probability in relation to the height of the damage. In this lecture we will answer the question
if this matters. Are the four situations the same, because the expected outcome in all four is
the same, namely: a 1000. Or are they different?
You have a big family to take care of. But you only have 50.000 euros. There are 4 situations
of the world. You can choose – and you know the expected damage is always a 1000. But you
get to choose ex ante. Do you want to be in a situation where you have a 100% chance to
loose a 1000? Or 10% chance to loose a 10.000? Etc.
Introduction of the notion of risk
When we care about the high probability and low damage; low probability and high damage.
There are three types of risk attitudes:
1) Risk-aversion
Most people would prefer situation 1, you know in advance what the loss will be. You
know in advance that the housewife would have 49.000 left. Situation 2 would be a
drama, you only have 50.000 – losing 10.000 would mean 20% of your total wealth would
be gone. Situation 3 is really a catastrophe: the probability is 1% - you lose a 100.000 and
would have nothing left! But, situation 4 offers not much difference with situation 3.
There is only 50.000 and gone is gone. However, situation 4 has a lower chance of
happening?
Irrealistic views concerning the likelihood of catastrophes: people think the probability is
low and when it happens they will die anyway. This is extremely dangerous as situation 1,
meaning we don’t take sufficient measures and don’t invest in prevention.
, Many socially desirable project don’t take place because of risk-aversion
We could invest and find the cure for cancer, but there are risk involved. People can lose
everything that is at stake: so risk is a loss to social-welfare.
2) Risk-neutral
Why is Bill Gates risk neutral, and the housewife (and most of the people) risk-averse?
The relationship we have to risk has to do with: 1) magnitude of risk and income, and 2)
our own well-situation: the decreasing marginal utility of money.
What is this?
If you’re homeless, your first 10 euro is worth enormously – and your additional 5 euro as
well. The homeless person can do lots with this. If you have a reasonable good income,
and you receive 10 euro, you may not be aware if you have 10 euro more or less. The
more you have, the marginal value decreases. Economists see the diminishing marginal
utility as the consumer's decreasing willingness to pay more money for the same
incremental increase in units of a product or service. The problem, however, is that our
willingness to pay and consume more should stop at 'satisfactory,' not just diminish.
3) Risk-lovers
They choose situation 4 (casino/lottery).
When you receive an offer, ask yourself if you have a risk-aversion towards this. If so, risk-
aversion causes dis-utility. Because of this dis-utility there is a loss of social welfare, and
therefor we dislike situation 2, 3, and 4.
o We introduced the notion of risk – and most people are risk averse. But society would
be better off if we are all in situation 1 (assuming we are all risk-averse and all have a
limited amount of money).
Can we solve the problem of risk-aversion?
1. Yes, by shifting risks with a risk-sharing agreement
Risk trading: from uncertainty (situation 3) to certainty (situation 1);
Greek example
2000 years ago the problem was, that people made money by sailing. A lot could go wrong on
sea: pirates, bad weather, natural disasters, etc. Suppose that the boat is worth 100.000;
probability 1% of losing ship. That is situation 3 and highly undesirable – the ship is all you
have! Risk-aversion causes loss of social welfare, because people find it too risky and will
decide not to sail. Then it limits economic activity. But, the shipper was not alone. And with
99 others faced the same risk. The ships are all worth the same and the risk is exogenous 1
(comes from external factors). They would like to shift to situation 1.. how to do this?
By creating a risk-sharing agreement (risk-distribution agreement). The decision is made
behind the veil of ignorance (Rawls): made before the sailing. Uncertainty is traded for
certainty: risk-trading is a solution;
When are these agreements suitable?
o Highly complicated risks;
o Catastrophic risk and low probability – high damage;
o Small group of people with low transaction costs;
o Little information on precise probabilities (we often don’t know in reality);
1
Endogenous: You can influence the risk yourself as well.
