Chapter 9: Uncertainty Flashcards
A probability distribution
A probability distribution is a depiction of all possible payoffs in a lottery and their associated probabilities.
It is the procentage posability of an outcome.
The expected value (EV)
The expected value is a measure of the average payoff that a lottery will generate. It is the average payoff you would get from the lottery if the lottery were repeated many times.
the variance
The riskiness of a lottery can be characterized by its variance:
- The variance is the sum of the probability-weighted squared deviations of the possible outcomes of the lottery
the standart deviation
The standard deviation is the square root of the variance and is another measure of risk.
The higher the variance or standard deviation, the riskier the investment.
the contingent consumption plan
contingent consumption plan is a specification of what will be consumed in each different state of nature.
People have preferences over different plans of consumption, just like they have preferences over actual consumption.
states of nature
Let us think of the different outcomes of some random event as being different states of nature.
(Contingent consumption)
- what consumption or wealth you will get in each possible outcome of some random event.
independence assumption.
This implies that the utility function for contingent consumption has to be additive across the different contingent consumption bundles.
risk averse
A consumer is risk averse if the utility of expected wealth is greater than the expected utility of wealth.
A risk averse consumer prefers to have the expected value of his wealth rather than face a gamble.
risk loving
A consumer is risk loving if she prefers a gamble to the expected value of the
gamble.
risk neutral
A consumer is risk neutral if the expected utility of wealth is the utility of its
expected value. In this case, the consumer only cares about the expected value
of wealth.
risk premium
The risk premium is the minimum difference between the expected value of a lottery and the payoff of a sure thing that would make the decision maker
indifferent between the lottery and the sure thing.
A probability distribution has the following characteristics:
- The probability of any particular outcome is between 0 and 1 (or between 0% and 100%).
- The sum of the probabilities of all possible outcomes is 1 (or 100%).
most humans are risk averse
Expected utility incorportates the fact that they will not take gambles even with small positive expected value. The way economists capture this is through expected utility theory.
- Individuals do not maximize expected value.
- Individuals maximize expected utility.
(Given the indifference curves for consumption in each state of nature, we can
look at the choice of how much insurance to purchase. This will be characterized by)
a tangency condition:
the marginal rate of substitution between consumption in each state of nature should be equal to the price at which you can trade off consumption in those states.
use of utility function
If the consumer has reasonable preferences about consumption in different circumstances, then we will be able to use a utility function to describe these preferences.
what depends on the probability?
In general, how a person values consumption in one state as compared to another will depend on the probability that the state in question will actually occur.
A positive affine transformation
v(u) = au + b, with a > 0 is a monotonic transformation that keeps the expected utility property.
An expected utility function is unique up to a positive affine transformation.
Why is expected utility a reasonable objective for choice under uncertainty?
- Only 1 of the outcomes is actually going to occur.
- In choice under uncertainty, there is a natural kind of independence between the different outcomes because they must be consumed separately.
- The choices that people plan to make in one state of nature should be independent from the choices that they plan to make in other states of nature.
when is the independence assumption satisfied?
If c1, c2, and c3 are the consumptions in different states of nature, and π1, π2, and π3 are the probabilities that these three different states of nature materialize.
A risk averse decision maker might prefer a gamble to a sure thing if
the expected payoff from the gamble is sufficiently larger than the payoff from the sure thing
With uncertain outcomes, individuals want to
smooth their consumption across outcomes. That is, they would like consumption in one eventuality to be as similar as possible to consumption in another eventuality.
