Intermediate Microeconomics, Games and Behaviour – Week 1:
Uncertainty and time
Literature: Week 1 - Uncertainty and Time
Risk Aversion and Incentive Effects → pp. 1644 – 55 (excluding part III and excluding
figures 3-5)
Psychology and Economics → pp. 315 – 372, only section 2.1, Subsections 2.1.1,
2.1.2, and 2.1.9
Debating Climate Economics → pp. 1 – 6
Preliminaries Week 1
Positive versus normative analysis
1. Positive analysis
Analysis describing relationships of cause and effect.
Positive analysis is about what is.
Example: “For non-Giffen goods an increase in price will decrease demand” or “A firm
that sets MR=MC is maximising its profit.”
2. Normative analysis
Analysis examining questions of what ought to be.
Normative analysis is about ought; it always contains a “should”.
Methodological individualism
Economics tries to explain phenomena on a collective level, e.g. on the level of a
market, a country, or the world. Microeconomics is characterised by an approach
that is called methodological individualism. For methodological reasons we descend
to the level of the relevant individual actor. Then we try to explain the behaviour of
this individual actor; to do this we apply rational choice theory (see below).
Eventually, we aggregate, because the problem to explain is on the collective level.
In macroeconomics we do not apply methodological individualism, but try to explain
phenomena on a collective level by directly relating them to other variables on that
level.
So, although several textbooks may suggest otherwise, it is applying or not
methodological individualism that provides the dividing line between
macroeconomics and microeconomics, not whether they analyse phenomena on a
collective level or not. With respect to the latter, they both do.
Rational choice theory
Economics is a special branch of rational choice theory. In rational choice theory
people are assumed to strive for the attainment of certain goals. In their attempt,
they are confronted with restrictions, so they have to make choices. The result of this
choice process is their behaviour.
Method of decreasing abstraction
In economics usually we start in a simple, rather abstract way. Then, step by step, we
make the analysis less abstract by introducing more realistic assumptions. This
approach is called the method of decreasing abstraction.
1
,1.1 Economics of times of climate change
Microeconomics and the (economic, social, ecological) system
→ incentives, trade-offs, interaction, information, time and risk
→ Excessive damage to any one part, ripples back to harm every other part as well
→ Within a system: all economies are closed economies
→ Within a system: there are no externalities
1.2 Uncertain outcomes
Risk and uncertainty
Frank Knight was an economist who formalised a distinction between risk and uncertainty:
→ Uncertainty: likelihood of outcomes unknown
→ Risk: likelihood of outcomes known
What are risky outcomes?
Risk describes any economic activity in which there are uncertain outcomes.
Associated with any uncertain outcome are probabilities.
Probabilities are numbers between zero and one that indicate the likelihood that a
particular outcome will occur.
In the absence of a known probability, economic agents have to estimate; they can
estimate based on frequency or based on subjective probability.
How to compare two options – by calculating the expected values
→ The expected value 𝐸(𝑌): The expected value of an uncertain outcome Y is the sum of the
values of each possible outcome multiplies by the probability it will occur:
𝐸(𝑌) = Pr .𝑦 + Pr .𝑦
1 1 2 2
With:
𝐸(𝑌) = expected value of 𝑌
𝑦 , 𝑦 = payoffs
1 2
Pr , Pr = probabilities of 𝑦 and 𝑦 , respectively
1 2 1 2
Evaluating risky outcomes
→ need to understand the decision maker’s preferences toward risk
→ need to think in terms of utility
2
,→ Utility of the expected value U[𝐸(𝑌)]: The utility of the expected value is the utility an
individual has from receiving a certain amount of money equivalent to the expected value of
an uncertain outcome.
Expected utility theory Von Neumann – Morgenstern (1944)
The first system investigation of preferences regarding risky incomes (lotteries) represented
by the expected value of a payoff function over deterministic outcomes
Rational decision making with risk/uncertainty
A decision maker facing a decision problem with a risky payoff U(Y) is rational if he chooses
an action 𝑎 that maximizes his expected utility.
→ A person’s utility can be expressed as: U ( Y )= √ Y
1.2.1 Risk attitudes
A fair gamble is one where the cost of the gamble is equal to the expected value. e.g. you
pay 10 euros for a ticket to participate in a lottery with the expected value (payout) of 10
euros.
Risk attitudes
The terms risk attitude, risk appetite, and risk tolerance are often used to describe an
individual’s or an organization’s attitude towards risk-taking.
→ Usually three types:
a) Risk averse
A person who is unwilling to make a fair gamble, i.e. pay the expected value to take
the gamble, is 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.
b) Risk loving (seeking)
A person who prefers the gamble to the guaranteed fair payout is risk loving (risk
seeking): E(U(Y)) > U[E(Y)]
→ Decision maker prefers the option with the uncertain income over the option with
the certain income, given the same expected value.
c) Risk neutral
A person who is indifferent between the gamble and the fair payout is risk neutral:
E(U(Y)) = U[E(Y)]
→ Decision maker is indifferent between the option with the certain income and the
option with the uncertain income, given the same expected value.
3
, The certainty equivalent: CE
The certainty equivalent is the certain payoff that generates as much utility as the expected
utility of the gamble. It is determined by equating the utility function to the expected utility
and solving for the income (or wealth).
Risk premium
The risk premium is the minimum willingness to pay to eliminate risk (or the minimum
willingness to accept as a compensation for the risk). Hence, it is the maximum amount of
money that a risk-averse person will pay to avoid taking a risk. It is determined as the
difference between the expected value and the certainty equivalent.
1.2.2 Measures of risk aversion
A consumer with a von Neumann-Morgenstern utility function can be one of the following:
Risk-averse, with a concave utility function (second derivative = negative)
Risk-neutral, with a linear utility function (second derivative = zero)
Risk-loving, with a convex utility function(second derivative = positive)
→ The degree of risk-aversion a consumer displays is related to the curvature of their utility
function.
Measures of risk aversion (Article by Holt and Laury)
RRA is constant (CRRA) if RRA is not dependent on the level of wealth; RRA is increasing
(IRRA) if RRA is increasing if wealth is increasing; RRA is decreasing (DRRA) if RRA is
decreasing if wealth is increasing. CARA, IARA and DARA are defined in a similar way. These
so-called Arrow-Pratt measures of risk aversion have been introduced in the literature by
Arrow and Pratt in the context of the derivation of a mathematical expression of the risk
premium. Arrow and Pratt considered part of the RHS of the equation as a measure of risk
4
Uncertainty and time
Literature: Week 1 - Uncertainty and Time
Risk Aversion and Incentive Effects → pp. 1644 – 55 (excluding part III and excluding
figures 3-5)
Psychology and Economics → pp. 315 – 372, only section 2.1, Subsections 2.1.1,
2.1.2, and 2.1.9
Debating Climate Economics → pp. 1 – 6
Preliminaries Week 1
Positive versus normative analysis
1. Positive analysis
Analysis describing relationships of cause and effect.
Positive analysis is about what is.
Example: “For non-Giffen goods an increase in price will decrease demand” or “A firm
that sets MR=MC is maximising its profit.”
2. Normative analysis
Analysis examining questions of what ought to be.
Normative analysis is about ought; it always contains a “should”.
Methodological individualism
Economics tries to explain phenomena on a collective level, e.g. on the level of a
market, a country, or the world. Microeconomics is characterised by an approach
that is called methodological individualism. For methodological reasons we descend
to the level of the relevant individual actor. Then we try to explain the behaviour of
this individual actor; to do this we apply rational choice theory (see below).
Eventually, we aggregate, because the problem to explain is on the collective level.
In macroeconomics we do not apply methodological individualism, but try to explain
phenomena on a collective level by directly relating them to other variables on that
level.
So, although several textbooks may suggest otherwise, it is applying or not
methodological individualism that provides the dividing line between
macroeconomics and microeconomics, not whether they analyse phenomena on a
collective level or not. With respect to the latter, they both do.
Rational choice theory
Economics is a special branch of rational choice theory. In rational choice theory
people are assumed to strive for the attainment of certain goals. In their attempt,
they are confronted with restrictions, so they have to make choices. The result of this
choice process is their behaviour.
Method of decreasing abstraction
In economics usually we start in a simple, rather abstract way. Then, step by step, we
make the analysis less abstract by introducing more realistic assumptions. This
approach is called the method of decreasing abstraction.
1
,1.1 Economics of times of climate change
Microeconomics and the (economic, social, ecological) system
→ incentives, trade-offs, interaction, information, time and risk
→ Excessive damage to any one part, ripples back to harm every other part as well
→ Within a system: all economies are closed economies
→ Within a system: there are no externalities
1.2 Uncertain outcomes
Risk and uncertainty
Frank Knight was an economist who formalised a distinction between risk and uncertainty:
→ Uncertainty: likelihood of outcomes unknown
→ Risk: likelihood of outcomes known
What are risky outcomes?
Risk describes any economic activity in which there are uncertain outcomes.
Associated with any uncertain outcome are probabilities.
Probabilities are numbers between zero and one that indicate the likelihood that a
particular outcome will occur.
In the absence of a known probability, economic agents have to estimate; they can
estimate based on frequency or based on subjective probability.
How to compare two options – by calculating the expected values
→ The expected value 𝐸(𝑌): The expected value of an uncertain outcome Y is the sum of the
values of each possible outcome multiplies by the probability it will occur:
𝐸(𝑌) = Pr .𝑦 + Pr .𝑦
1 1 2 2
With:
𝐸(𝑌) = expected value of 𝑌
𝑦 , 𝑦 = payoffs
1 2
Pr , Pr = probabilities of 𝑦 and 𝑦 , respectively
1 2 1 2
Evaluating risky outcomes
→ need to understand the decision maker’s preferences toward risk
→ need to think in terms of utility
2
,→ Utility of the expected value U[𝐸(𝑌)]: The utility of the expected value is the utility an
individual has from receiving a certain amount of money equivalent to the expected value of
an uncertain outcome.
Expected utility theory Von Neumann – Morgenstern (1944)
The first system investigation of preferences regarding risky incomes (lotteries) represented
by the expected value of a payoff function over deterministic outcomes
Rational decision making with risk/uncertainty
A decision maker facing a decision problem with a risky payoff U(Y) is rational if he chooses
an action 𝑎 that maximizes his expected utility.
→ A person’s utility can be expressed as: U ( Y )= √ Y
1.2.1 Risk attitudes
A fair gamble is one where the cost of the gamble is equal to the expected value. e.g. you
pay 10 euros for a ticket to participate in a lottery with the expected value (payout) of 10
euros.
Risk attitudes
The terms risk attitude, risk appetite, and risk tolerance are often used to describe an
individual’s or an organization’s attitude towards risk-taking.
→ Usually three types:
a) Risk averse
A person who is unwilling to make a fair gamble, i.e. pay the expected value to take
the gamble, is 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.
b) Risk loving (seeking)
A person who prefers the gamble to the guaranteed fair payout is risk loving (risk
seeking): E(U(Y)) > U[E(Y)]
→ Decision maker prefers the option with the uncertain income over the option with
the certain income, given the same expected value.
c) Risk neutral
A person who is indifferent between the gamble and the fair payout is risk neutral:
E(U(Y)) = U[E(Y)]
→ Decision maker is indifferent between the option with the certain income and the
option with the uncertain income, given the same expected value.
3
, The certainty equivalent: CE
The certainty equivalent is the certain payoff that generates as much utility as the expected
utility of the gamble. It is determined by equating the utility function to the expected utility
and solving for the income (or wealth).
Risk premium
The risk premium is the minimum willingness to pay to eliminate risk (or the minimum
willingness to accept as a compensation for the risk). Hence, it is the maximum amount of
money that a risk-averse person will pay to avoid taking a risk. It is determined as the
difference between the expected value and the certainty equivalent.
1.2.2 Measures of risk aversion
A consumer with a von Neumann-Morgenstern utility function can be one of the following:
Risk-averse, with a concave utility function (second derivative = negative)
Risk-neutral, with a linear utility function (second derivative = zero)
Risk-loving, with a convex utility function(second derivative = positive)
→ The degree of risk-aversion a consumer displays is related to the curvature of their utility
function.
Measures of risk aversion (Article by Holt and Laury)
RRA is constant (CRRA) if RRA is not dependent on the level of wealth; RRA is increasing
(IRRA) if RRA is increasing if wealth is increasing; RRA is decreasing (DRRA) if RRA is
decreasing if wealth is increasing. CARA, IARA and DARA are defined in a similar way. These
so-called Arrow-Pratt measures of risk aversion have been introduced in the literature by
Arrow and Pratt in the context of the derivation of a mathematical expression of the risk
premium. Arrow and Pratt considered part of the RHS of the equation as a measure of risk
4
