Intermediate Microeconomics Notes:
Week 1:
Decisions involving uncertainty:
- (Environmental) Policy
- Investments
- Insurance
- Education
Risk -> likelihood of outcomes known
Uncertainty-> likelihood of outcomes unknown (e.g. climate change-> we do not know the probabilities)
Fair gamble: A fair gamble is one where the cost of the gamble is equal to the expected value.
Expected Value E(Y): The expected value of an uncertain outcome Y is the sum of the values of each
possible outcome multiplied by the probability it will occur.
Example:
Expected value first job: 20.000
Expected value second job: is 0.5(30.000) + 0.5(10.000) = 20.000
So when you compare the jobs they have the same expected value. But are they really equivalent?
You also have to look at the expected utility, not just the expected value.
Utility of the expected value U[E(Y)] : the utility an individual has from receiving a certain amount of
money equivalent to the expected value of an uncertain outcome.
The expected utility E[U(Y)] : the sum of utilities of all possible uncertain outcomes, weighted with
their probability
,Rational Decision Making with Risk:
A risky payoff (𝑌) is rational if he chooses an action 𝒂 that maximizes his expected utility.
Risk Attitudes:
Usually 3 types:
1. Risk averse: E[U(Y)] < U[E(Y)]
Decision maker prefers the option with the certain income over the option with the uncertain
income, given the same expected value.
2. Risk loving (seeking): E[U(Y)] > U[E(Y)]
A person who prefers the gamble to the guaranteed fair payout. Decision maker prefers the
option with the uncertain income over the option with the certain income, given the same
expected value.
3. Risk neutral: E[U(Y)] = U[E(Y)]
A person who is indifferent between the gamble and the fair payout. Decision maker is
indifferent between the option with the certain income and the option with the uncertain
income, given the same expected value.
,Certain equivalent: CE
The certainty equivalent is the certain payoff that generates as much utility as the expected utility of the
gamble.
Risk Premium
The risk premium is the minimum willingness to pay to eliminate risk. It is determined as the difference
between the expected value and the certainty equivalent:
Measures of Risk Aversion:
1. Arrow-Pratt measure of absolute risk aversion (ARA):
2. Arrow-Pratt measure of relative risk aversion (RRA):
, Example:
ARA exhibiting increasing, decreasing or constant?
RRA exhibiting increasing, decreasing or constant?
Week 1:
Decisions involving uncertainty:
- (Environmental) Policy
- Investments
- Insurance
- Education
Risk -> likelihood of outcomes known
Uncertainty-> likelihood of outcomes unknown (e.g. climate change-> we do not know the probabilities)
Fair gamble: A fair gamble is one where the cost of the gamble is equal to the expected value.
Expected Value E(Y): The expected value of an uncertain outcome Y is the sum of the values of each
possible outcome multiplied by the probability it will occur.
Example:
Expected value first job: 20.000
Expected value second job: is 0.5(30.000) + 0.5(10.000) = 20.000
So when you compare the jobs they have the same expected value. But are they really equivalent?
You also have to look at the expected utility, not just the expected value.
Utility of the expected value U[E(Y)] : the utility an individual has from receiving a certain amount of
money equivalent to the expected value of an uncertain outcome.
The expected utility E[U(Y)] : the sum of utilities of all possible uncertain outcomes, weighted with
their probability
,Rational Decision Making with Risk:
A risky payoff (𝑌) is rational if he chooses an action 𝒂 that maximizes his expected utility.
Risk Attitudes:
Usually 3 types:
1. Risk averse: E[U(Y)] < U[E(Y)]
Decision maker prefers the option with the certain income over the option with the uncertain
income, given the same expected value.
2. Risk loving (seeking): E[U(Y)] > U[E(Y)]
A person who prefers the gamble to the guaranteed fair payout. Decision maker prefers the
option with the uncertain income over the option with the certain income, given the same
expected value.
3. Risk neutral: E[U(Y)] = U[E(Y)]
A person who is indifferent between the gamble and the fair payout. Decision maker is
indifferent between the option with the certain income and the option with the uncertain
income, given the same expected value.
,Certain equivalent: CE
The certainty equivalent is the certain payoff that generates as much utility as the expected utility of the
gamble.
Risk Premium
The risk premium is the minimum willingness to pay to eliminate risk. It is determined as the difference
between the expected value and the certainty equivalent:
Measures of Risk Aversion:
1. Arrow-Pratt measure of absolute risk aversion (ARA):
2. Arrow-Pratt measure of relative risk aversion (RRA):
, Example:
ARA exhibiting increasing, decreasing or constant?
RRA exhibiting increasing, decreasing or constant?
