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)