Chapter 9: Uncertainty

Question 1

A probability distribution

Answer 1

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.

Question 2

The expected value (EV)

Answer 2

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.

Question 3

the variance

Answer 3

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

Question 4

the standart deviation

Answer 4

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.

Question 5

the contingent consumption plan

Answer 5

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.

Question 6

states of nature

Answer 6

Let us think of the different outcomes of some random event as being different states of nature.

Question 7

(Contingent consumption)

Answer 7

1. what consumption or wealth you will get in each possible outcome of some random event.

Question 8

independence assumption.

Answer 8

This implies that the utility function for contingent consumption has to be additive across the different contingent consumption bundles.

Question 9

risk averse

Answer 9

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.

Question 10

risk loving

Answer 10

A consumer is risk loving if she prefers a gamble to the expected value of the
gamble.

Question 11

risk neutral

Answer 11

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.

Question 12

risk premium

Answer 12

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.

Question 13

A probability distribution has the following characteristics:

Answer 13

• 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%).

Question 14

most humans are risk averse

Answer 14

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.

Question 15

(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:

Answer 15

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.

Question 16

use of utility function

Answer 16

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.

Question 17

what depends on the probability?

Answer 17

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.

Question 18

A positive affine transformation

Answer 18

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.

Question 19

Why is expected utility a reasonable objective for choice under uncertainty?

Answer 19

• 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.

Question 20

when is the independence assumption satisfied?

Answer 20

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.

Question 21

A risk averse decision maker might prefer a gamble to a sure thing if

Answer 21

the expected payoff from the gamble is sufficiently larger than the payoff from the sure thing

Question 22

With uncertain outcomes, individuals want to

Answer 22

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.