price theory
Price Theory
Lecture 1: Preferences
Topics for today’s lecture . . .
1. Choice in economics
2. Rationality and preferences
3. Social choice
4. The limitations of social choice
Choice in economics
How would you like to spend your Saturday night?
Imagine that you have to choose what to do with your Saturday night. You have four
options, but you can only choose one:
• Attend a football match.
• Go dancing at a nightclub.
• Watch a movie at the cinema.
• Revise your Price Theory notes at home.
Definition: Preferences
A description of how a decision-maker would rank (compare the desirability of) any two
alternatives, assuming the alternatives are available to the decision-maker at no cost.
In economics we regard preferences as being innate to each individual. Everyone is different,
and no two people share identical preferences.
Ranking two alternatives
There are three ways in which you can rank a pair of alternatives. Consider, for example, the
alternatives ‘attend a football match’ and ‘go dancing at a nightclub’:
• It may be that you prefer the ‘football match’ over the ‘nightclub’. (Written: football match � nightclub)
• Or, it may be that you prefer the ‘nightclub’ over the ‘football match’. (Written: nightclub � football match)
• Finally, you may be indifferent between the ‘football match’ and the ‘nightclub’. (Written: football match ∼ nightclub)
Exercise: Saturday night
• How would you rank the two alternatives ‘attend a football match’, and ‘go dancing at a nightclub’ ?
• How would you rank the two alternatives ‘watch a movie at the cinema’, and ‘revise your Price Theory notes at home’ ?
(Write down your answers, we will use them again later today.)
Definition: Revealed preferences
The preferences a decision-maker reveals through the choices she/he makes.
If you choose option A when option B is available, you reveal that your ranking of the two
alternatives is either A � B or A ∼ B.
Definition: Stated preferences
The preference a decision-maker reports when asked about real situations they might
encounter.
Economists tend to regard revealed preferences as being more reliable than stated preferences
because revealed preferences are derived from actions that affect the welfare of the
decision-maker.
Exercise: Saturday night
• How would you rank the two alternatives ‘attend a football match’, and ‘revise your Price Theory notes at home’ ?
• How would you rank the two alternatives ‘watch a movie at the cinema’, and ‘go dancing at a nightclub’ ?
(Write down your answers, we will use them again later today.)
Your preferences depend on your circumstances
In what way would your answers to the following questions depend on your circumstances?
• “Would you like an aspirin?”
• “Would you prefer a hot drink or a cold drink?”
Your preferences change over time
Have your answers to the following questions changed over time?
• “Would you prefer to play on the swings, or drink a cup of coffee at a cafe?”
• “Do you prefer to get your news from television, news websites, or social media?”
Exercise: Saturday night
• How would you rank the two alternatives ‘attend a football match’, and ‘watch a movie at the cinema’ ?
• How would you rank the two alternatives ‘go dancing at a nightclub’, and ‘revise your Price Theory notes at home’ ?
(Write down your answers, we will use them again later today.)
Rationality and preferences
Definition: Rational preferences
A decision-maker’s preferences are rational if they are complete and transitive.
If a decision-maker’s preferences are not rational, she/he may encounter a situation in which
she/he cannot make a choice from amongst the available alternatives.
Complete preferences
A decision-maker’s preferences are complete if she/he can rank every pair of alternatives.
That is to say, for any two alternatives A and B either,
• A � B, or,
• B � A, or,
• A ∼ B.
Note: The inability to rank two alternatives is not the same as being indifferent between the
two alternatives.
Transitive preferences
A decision-maker’s preferences are transitive if the rankings are consistent in the following
sense: For any three alternatives A, B and C ,
• if A � B,
• and B � C ,
• then A � C .
If a decision-maker’s preferences are complete but not transitive, then there must exist cycles
within the preferences.
Cycles
A
C B
A cycle exists in an individual’s
preferences whenever there are three
alternatives A, B and C such that:
• A � B,
• B � C ,
• C � A.
Faced with a choice between A, B and C ,
the decision-maker will be unable to settle
on an alternative.
Money pumps
A
C B
$
$
$
Suppose this individual starts with
alternative A.
The decision-maker would be happy to
swap C for A, and may be willing to pay a
small amount to do so.
But the decision-maker is then willing to
swap B for C .
And then A for B.
Leaving the individual back where she/he
started, but with less money.
Quiz 1
Suppose that Harry is deciding what to do on his holiday. Harry can choose between going
skiing, taking a cruise, and a holiday at the beach. Harry’s preferences over the three
alternatives are:
skiing � cruise, and cruise � beach.
These preferences are,
(a) both complete and transitive.
(b) complete but NOT transitive.
(c) transitive but NOT complete.
(d) NEITHER complete nor transitive.
How many rankings are necessary to complete preferences?
A
B C
3 alternatives
A
B C
D
4 alternatives
A
B C
D E
5 alternatives
Quiz 2
Suppose that Harry is deciding what to do on his holiday. Harry can choose between going
skiing, taking a cruise, and a holiday at the beach. Harry’s preferences over the three
alternatives are:
skiing � cruise, beach � cruise, and beach � skiing.
These preferences are,
(a) both complete and transitive.
(b) complete but NOT transitive.
(c) transitive but NOT complete.
(d) NEITHER complete nor transitive.
Quiz 3
Suppose that Harry is deciding what to do on his holiday. Harry can choose between going
skiing, taking a cruise, and a holiday at the beach. Harry’s preferences over the three
alternatives are:
skiing � cruise, cruise � beach and skiing ∼ beach.
These preferences are,
(a) both complete and transitive.
(b) complete but NOT transitive.
(c) transitive but NOT complete.
(d) NEITHER complete nor transitive.
Using preferences to order alternatives
If preferences are rational, then the alternatives can
be ordered from most-preferred (best), to
least-preferred (worst).
Example 1: Complete and transitive preferences.
B � C , B � A, and C � A
In example 1, B is the most-preferred alternative,
and A is the least-preferred.
A
C
B
Example 1
(Transitive)
Best
Worst
Using preferences to order alternatives
If preferences are not complete and transitive, then
it is not possible to order the alternatives.
Example 2: Complete, non-transitive preferences.
A � B, B � C and A ∼ C .
In example 2, the alternatives cannot be ordered
because C should both lie below B, and at the
same level as A.
B
A
Example 2
(Non-Transitive)
C
C
Exercise: Rational preferences
Using your stated preferences over the alternatives ‘football match’, ‘nightclub’, ‘cinema’ and
‘revise’, that you provided earlier in this lecture:
1. Confirm that your preferences are complete.
2. Determine whether your preferences are transitive.
3. What is your most preferred (best) alternative(s)?
4. What is your least preferred (worst) alternative(s)?
Social choice
Equity versus efficiency
One of the fundamental trade-offs facing society, is the trade-off between equity and
efficiency.
• If a society is equitable, then economic wellbeing is evenly distributed amongst its citizens.
• If a society is efficient, then it is maximising the production of goods and services given its scarce resources.
Policies that increase equity (reduce inequality) tend to reduce economic efficiency. By
redistributing income (or wealth) from rich to poor, they typically reduce the incentive for
hard work.
Visualising the equity-efficiency trade-off
Each point on this line represents
one possible social policy
(equity-efficiency trade-off).
more equitable more efficient
Single-peaked preferences
Each individual in society has preferences over the range of alternative policies. We say that
an individual’s preferences are single peaked if:
• The individual’s preferences are rational (complete and transitive).
• The individual has a single, most-preferred policy.
• If two alternative policies lie on the same side of the most-preferred policy, the individual prefers the policy closest to the most-preferred policy.
Quiz 4
Suppose that Sarah has single-peaked preferences over alternative policies, and that Sarah’s
most preferred policy is policy A. Sarah’s preferences over the policies B and C are:
(a) B � C .
(b) C � B.
(c) B ∼ C .
(d) Cannot be determined.
ABC
more equitable more efficient
Quiz 5
Suppose that Sarah has single-peaked preferences over alternative policies, and that Sarah’s
most preferred policy is policy A. Sarah’s preferences over the policies B and C are:
(a) B � C .
(b) C � B.
(c) B ∼ C .
(d) Cannot be determined.
A BC
more equitable more efficient
Definition: Social preferences
Preferences over policy alternatives that affect society as a whole; constructed by
aggregating the preferences of the individuals within society.
Social preferences are not an innate characteristic of a society. Rather, they are a product of
the method used to aggregate individual preferences.
Majority voting
Policy A defeats policy B in majority voting if more citizens prefer A over B, than prefer B
over A. (The vote is a tie if equal number of citizens prefer each policy.)
Majority voting can be used to construct social preferences as follows:
• Policy A is socially preferred to policy B, if A defeats B in majority voting.
• Policy B is socially preferred to policy A, if B defeats A in majority voting.
• There is social indifference between policies A and B, if A and B are tied in majority voting.
A policy that defeats every other policy in majority voting is called the Condorcet winner. A
Condorcet winner is the socially most-preferred policy.
Majority voting and social preferences
The social preferences derived from majority voting have the following properties:
• The social preferences are complete.
• The social preferences have the Pareto property: If every individual in society prefers policy A over policy B, then A is socially preferred to B.
• The social preferences give equal weight to every individual in society.
• The method for generating the social preferences is not biased towards a particular alternative. (eg. There is no bias towards the status quo.)
Definition: Median voter theorem
A theorem that states: When all individuals in society have single peaked preferences over
policy alternatives, the Condercet winner will be the most-preferred policy of the median
voter.
The median voter theorem is particularly powerful because it requires only that we know each
individual’s most preferred policy.
Finding the Condorcet winner
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median votermore equitable more efficient
Implications of the median voter theorem
Political parties spend a great deal of effort and resources to identify the median voter, and
determine what policies they prefer.
The median voter theorem helps explain why competing political parties, with different
ideologies, often propose very similar policies.
The median voter theorem can also help explain why people who have a strong preference for
either equity or efficiency, tend to feel marginalised by political debates.
Exercise: Voting round 1 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Attend a football match.
(b) Go dancing at a nightclub.
(Record the results of the votes, we will use them in a moment.)
Exercise: Voting round 2 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Watch a movie at the cinema.
(b) Revise your Price Theory notes at home.
(Record the results of the votes, we will use them in a moment.)
Exercise: Voting round 3 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Attend a football match.
(b) Revise your Price Theory notes at home.
(Record the results of the votes, we will use them in a moment.)
Exercise: Voting round 4 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Watch a movie at the cinema.
(b) Go dancing at a nightclub.
(Record the results of the votes, we will use them in a moment.)
Exercise: Voting round 5 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Attend a football match.
(b) Watch a movie at the cinema.
(Record the results of the votes, we will use them in a moment.)
Exercise: Voting round 6 . . .
Using your previously stated preferences, vote on the following alternatives:
(a) Go dancing at a nightclub.
(b) Revise your Price Theory notes at home.
(Record the results of the votes, we will use them in a moment.)
The limitations of social choice
A three-cornered contest
more
equitable more efficient
socially conservative
socially progressive
G
B
R
Three political parties compete in an
election
• The Green party is socially progressive and prefers equity.
• The Blue party is socially conservative and prefers
efficiency.
• The Red party is socially progressive and prefers a balance
between equity and efficiency.
A three-cornered contest
more
equitable more efficient
socially conservative
socially progressive
G
B
R
Three voters have the following
rational preferences over political
parties.
• Tony’s preferences are: B � G , B � R and R � G .
• Tanya’s preferences are: R � G , R � B and G � B.
• Sarah’s preferences are: G � B, G � R and B � R.
Red versus Blue
Tony’s preferences
Blue � Green
Blue � Red
Red � Green
Blue � Red
Tanya’s preferences
Red � Green
Red � Blue
Green � Blue
Red � Blue
Sarah’s preferences
Green � Blue
Green � Red
Blue � RedBlue � Red
The Blue party defeats the Red party.
Blue versus Green
Tony’s preferences
Blue � Green
Blue � Red
Red � Green
Blue � Green
Tanya’s preferences
Red � Green
Red � Blue
Green � BlueGreen � Blue
Sarah’s preferences
Green � Blue
Green � Red
Blue � Red
Green � Blue
The Green party defeats the Blue party.
Green versus Red
Tony’s preferences
Blue � Green
Blue � Red
Red � GreenRed � Green
Tanya’s preferences
Red � Green
Red � Blue
Green � Blue
Red � Green
Sarah’s preferences
Green � Blue
Green � Red
Blue � Red
Green � Red
The Red party defeats the Green party.
The Condorcet paradox
If we use the results of the majority voting to construct social preferences, we get,
• Blue is socially preferred to Red,
• Red is socially preferred to Green, and,
• Green is socially preferred to Blue.
Even though each individual’s preferences are rational, the social preferences produced
through majority voting are not transitive (they contain a cycle).
The Condorcet paradox is possible in any situation where the preferences of individual voters
are not single peaked.
Exercise: Constructing social preferences for the class
Using the results of the six rounds of voting, construct social preferences for the class.
1. Are the social preferences complete?
2. Are the social preferences transitive?
3. Which alternative(s) are socially most-preferred?
4. Which alternative(s) are socially least-preferred?
Thinking about social preferences another way . . .
Instead of starting with a method, and investigating what properties the resulting social
preferences possess, we could start with a list of desirable properties and use these to design
an appropriate method.
Economists tend to agree that the following properties are desirable:
• Rationality.
• The Pareto property.
• Independence from irrelevant alternatives.
(Independence from irrelevant alternatives requires that the social ranking of two
alternatives is only affected by the way in which individuals rank the two alternatives.)
Definition: Arrow’s impossibility theorem
A theorem that states: In general, the only method for constructing social preferences that
are rational, have the Pareto property, and are independent of irrelevant alternatives, is
dictatorial.
A dictatorial mechanism selects one individual in society, and dictates that social preferences
match her/his preferences. Any individual selected in this way is called a dictator.
Implications of Arrow’s impossibility theorem
The theorem shows us that any form of collective decision-making is unlikely to have the
coherence of individual decision-making.
• This is important to keep in mind during your studies: It is common for us to treat firms, governments and nations, as individual decision-makers.
The theorem illustrates the importance of institutional structures: For example, the choice of
voting system can, sometimes, determine the outcome of a vote.
The theorem warns us to be aware of the hidden assumptions in any empirical research that
aggregates the preferences of many individuals.
A warning: The theorem should not be interpreted as stating that democracy is impossible, or
as advocating for dictatorship.
Questions?
Key concepts from today’s lecture
You can use these concepts (as search terms) to conduct further research into the topics
covered in today’s lecture:
• Preferences
• Rationality
• Completeness
• Transitivity
• Cycles
• Ordering alternatives
• Social preferences
• Single peaked preferences
• Majority voting
• Median voter theorem
• Condorcet paradox
• Arrow’s impossibility theorem
Further reading
The further readings provide additional context to the lecture material, and reinforce core
concepts. All readings can be found in Microeconomics 5th edition, by Besanko and
Braeutigam.
• Chapter 3, section 3.1.
• Mathematical appendix, sections A.1–A.3.
Where the readings and lecture materials differ, the lecture materials take precedence.
Quiz solutions
Quiz 1 (d)
Quiz 2 (a)
Quiz 3 (b)
Quiz 4 (a)
Quiz 5 (d)
- Choice in economics
- Rationality and preferences
- Social choice
- The limitations of social choice
- Appendix