If you chose to stop playing and take home the $400,000,
you are risk averse. But why?
Well, let's see.
If you choose to keep playing,
you have a 50 percent chance of winning one million dollars,
and a 50 percent chance of taking home nothing.
This is simply a gamble with an expected value of $500,000.
A risk averse person is willing to take home 400,000 in certainty,
rather than a risky bargain that has a value of 500,000.
Put differently, a risk averse person just paid $100,000 to avoid this risk altogether.
In the case of medical care,
risk aversion leads the public to demand health insurance,
that is, pay a premium,
money they forgo in certainty in return for a reduction in
exposure to financial consequences of unexpected negative health shocks.
We turn now to a graphical representation of
the decision making process of a risk averse individuals.
To do so, we will graph the relationship between wealth on the X-axis,
and how much people value that level of wealth on the Y-axis.
When we say how much people value their wealth,
we are referring to a measure of their satisfaction,
or usefulness which economists call utility.
Utility refers to the total satisfaction received from consuming a good,
receiving a service, or accumulating wealth.
The curve illustrates a positive relationship,
but note that it is concave,
representing a diminishing marginal utility.
In other words, incremental changes in wealth
have a smaller effect on utility when the wealth level is high.
For example, if your wealth increased by 50 percent from $50,000 to $75,000,
you'd be very happy about it.
We can see it in the substantial increase in the level of utility.
However, if your wealth increased from 8 million dollars to $8,025,000,
same size increase, the change in utility is barely noticeable.
Using the utility curve,
we can describe risk aversion,
and how its level dictates the magnitude of the insurance premium.
So what we have now is a curve that shows us the level of
utility an individual gets from each additional unit of wealth,
where each additional dollar raises the utility level in smaller and smaller increments.
Let's assume that this individual has a wealth level of $250,000.
This level of wealth corresponds to a utility level, U of 250,000.
That is the level of satisfaction one gets from this level of wealth.
Now assume that this individual has
a 50 percent chance of not requiring any medical care,
and 50 percent chance of needing intense medical care at a cost of $200,000.
This individual faces a substantial risk.
A simple way to think about this risk is to recognize the fact
that if this person experiences a loss of $200,000,
her wealth will fall to $50,000.
In other words, we have a lottery with
a 50 percent chance of keeping the original wealth at $250,000,
and a 50 percent chance of ending up with a wealth level of just $50,000.
The expected wealth is therefore 50 percent times 250,000
plus 50 percent times 50,000 which equals $150,000.
With this information, we can now graph the average utility level,
or expected utility which is simply an average of the utility at 250,000,
and the utility at 50,000.
We can identify the expected utility
graphically by connecting the utility levels with a straight line.
This line allows us to find the expected level of
utility that corresponds with our expected wealth.
So, if we trace a line from our expected wealth of a $150,000,
we get to the expected utility denoted as point A.
This is a way to illustrate the risk faced by a person who is uninsured.
Her wealth may be depleted,
or remain unchanged, a major gamble to be taken.
This uncertainty can largely be avoided by purchasing health insurance.
But how much would this person be willing to pay for insurance?
Since our individual is averse to risk,
we can ask ourselves what would be the wealth level that
would make these individuals exactly indifferent between that amount,
and bearing financial risk.
By keeping the same level of utility,
we make sure that this individual is neither worse off nor better off.
And so, we started to point A,
and move to the left until we hit the utility curve.
We mark this as point B.
This point represent the lowest level of wealth that
this individual is willing to tolerate to avoid uncertainty.
That level of wealth is called the certainty equivalent, or CE.
And it represents the wealth level that people are
willing to have under certainty that is
identical to the expected wealth under uncertainty which is $150,000.
The distance between point A and B,
or between the expected wealth and the certainty equivalent is simply the premium,
or the maximum willingness to pay to avoid the risk.
The more risk averse we are,
the higher will be the premium we would be willing to pay to avoid risk.
The insurer on the other hand can spread risk across a large population of members,
and therefore can be thought of as risk neutral.
In this segment, we assume that
the risks are known to both the individual and the insurer,
which is why by simply paying a premium,
the insurance company can eliminate all financial risk
without requiring additional risk sharing like deductibles,
or copayments, or coinsurance.
However, as we've learned in the previous segment,
insurance plans typically involve deductibles and copayments.
The rationale for these risk sharing arrangements is the topic of our next segment.
Ezekiel J. Emanuel, MD, PhDDiane v.S. Levy and Robert M. Levy University Professor
Guy David, PhDGilbert and Shelley Harrison Associate Professor of Health Care Management
