THEMES AND CAPSTONE UNITS
17: History, instability, and growth
19: Inequality
22: Politics and policy
UNIT 5
PROPERTY AND POWER:
MUTUAL GAINS AND CONFLICT
HOW INSTITUTIONS INFLUENCE THE BALANCE OF
POWER IN ECONOMIC INTERACTIONS, AND AFFECT
THE FAIRNESS AND EFFICIENCY OF THE
ALLOCATIONS THAT RESULT
• Technology, biology, economic institutions, and people’s preferences
are all important determinants of economic outcomes.
• Power is the ability to do and get the things we want in opposition to the
intentions of others.
• Interactions between economic actors can result in mutual gains, but
also in conflicts over how the gains are distributed.
• Institutions influence the power and other bargaining advantages of
actors.
• The criteria of efficiency and fairness can help evaluate economic insti-
tutions and the outcomes of economic interactions.
Perhaps one of your distant ancestors considered that the best way to get
money was by shipping out with a pirate like Blackbeard or Captain Kidd.
If he had settled on Captain Bartholomew Roberts’ pirate ship the Royal
Rover, he and the other members of the crew would have been required to
consent to the ship’s written constitution. This document (called The Royal
Rover’s Articles) guaranteed, among other things, that:
Article I
Every Man has a Vote in the Affairs on the Moment; has equal title to
fresh Provisions …
Article III
No person to Game at Cards or Dice for Money.
Article IV
The Lights and Candles to be put out at eight a-Clock at Night; If any
Peter T. Leeson. 2007.
‘An–arrgh–chy: The Law and Eco-
nomics of Pirate Organization’.
Journal of Political Economy 115
(6): pp. 1049–94.
Statue representing the founders of Nashville, Tennessee
181
of the Crew after that Hour still remained enclined for drinking, they
are to do so on the open Deck …
Article X
The Captain and Quarter Master to receive two Shares of a Prize (the
booty from a captured ship); the Master, Boatswain, and Gunner one
Share and a half, and other Officers one and a Quarter (everyone else
to receive one share, called his Dividend.)
Article XI
The Musicians to have Rest on the Sabbath Day but the other six
Days and Nights none without special Favour.
The Royal Rover and its Articles were not unusual. During the heyday of
European piracy in the late seventeenth and early eighteenth centuries,
most pirate ships had written constitutions that guaranteed even more
powers to the crew members. Their captains were democratically elected
(‘the Rank of Captain being obtained by the Suffrage of the Majority’).
Many captains were also voted out, at least one for cowardice in battle.
Crews also elected one of their number as the quartermaster who, when the
ship was not in a battle, could countermand the captain’s orders.
If your ancestor had served as a lookout and had been the first to spot a
ship that was later taken as a prize, he would have received as a reward ‘the
best Pair of Pistols on board, over and above his Dividend’. Were he to have
been seriously wounded in battle, the articles guaranteed him
compensation for the injury (more for the loss of a right arm or leg than for
the left). He would have worked as part of a multiracial, multi-ethnic crew
of which probably about a quarter were of African origin, and the rest
primarily of European descent, including Americans.
The result was that a pirate crew was often a close-knit group. A
contemporary observer lamented that the pirates were ‘wickedly united,
and articled together’. Sailors of captured merchant ships often happily
joined the ‘roguish Commonwealth’ of their pirate captors.
Another unhappy commentator remarked: ‘These Men whom we
term … the Scandal of human Nature, who were abandoned to all Vice …
were strictly just among themselves.’ If they were Responders in the
ultimatum game (explained in Unit 4, Section 4.10), by this description they
would have rejected any offer less than half of the pie!
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
182
INSTITUTIONS
Institutions are written and
unwritten rules that govern:
• what people do when they
interact in a joint project
• the distribution of the products
of their joint effort
incentive Economic reward or
punishment, which influences the
benefits and costs of alternative
courses of action.
POWER
The ability to do and get the things
we want in opposition to the
intentions of others.
••5.1 INSTITUTIONS AND POWER
Nowhere else in the world during the late seventeenth and early eighteenth
century did ordinary workers have the right to vote, to receive
compensation for occupational injuries, or to be protected from the kinds
of checks on arbitrary authority that were taken for granted on the Royal
Rover. The Royal Rover’s articles laid down in black and white the under-
standings among the pirates about their working conditions. They
determined who did what aboard the ship and what each person would get.
For example, the size of the helmsman’s dividend compared to that of the
gunner. There were also unwritten informal rules of appropriate behaviour
that the pirates followed by custom, or to avoid condemnation by their
crewmates.
These rules, both written and unwritten, were the institutions that
governed the interactions among the crew members of the Royal Rover.
The institutions provided both the constraints (no drinking after 8 p.m.
unless on deck) and the incentives (the best pair of pistols for the lookout
who spotted a ship that was later taken). In the terminology of game theory
from the previous unit, we could say that they were the ‘rules of the game’,
specifying, as in the ultimatum game in Section 4.10, who can do what,
when they can do it, and how the players’ actions determine their payoffs.
In this unit, we use the terms ‘institutions’ and ‘rules of the game’
interchangeably.
Experiments in Unit 4 showed us that the rules of the game affect:
• how the game is played
• the size of the total payoff available to those participating
• how this total is divided
For example, in the ultimatum game the rules (institutions) specify the size
of the pie, who gets to be the Proposer, what the Proposer can do (offer any
fraction of the pie), what the Responder can do (accept or refuse), and who
gets what as a result.
We also saw that changing the rules of the game changes the outcome. In
particular, when there are two Responders in the ultimatum game, they are
more likely to accept lower offers because each is not sure what the other
will do. And this means that the Proposer can make a lower offer, and
obtain a higher payoff.
Since institutions determine who can do what, and how payoffs are
distributed, they determine the power individuals have to get what they
want in interactions with others.
Power in economics takes two main forms:
• It may set the terms of an exchange: By making a take-it-or-leave-it offer
(as in the ultimatum game).
• It may impose or threaten to impose heavy costs: Unless the other party acts
in a way that benefits the person with power.
5.1 INSTITUTIONS AND POWER
183
bargaining power The extent of a
person’s advantage in securing a
larger share of the economic rents
made possible by an interaction.
The rules of the ultimatum game determine the ability that the players have
to obtain a high payoff—the extent of their advantage when dividing the
pie—which is a form of power called bargaining power. The power to
make a take-it-or-leave-it offer gives the Proposer more bargaining power
than the Responder, and usually results in the Proposer getting more than
half of the pie. Still, the Proposer’s bargaining power is limited because the
Responder has the power to refuse. If there are two Responders, the power
to refuse is weaker, so the Proposer’s bargaining power is increased.
In experiments the assignment of the role Proposer or Responder, and
hence the assignment of bargaining power, is usually done by chance. In
real economies, the assignment of power is definitely not random.
In the labour market, the power to set the terms of the exchange
typically lies with those who own the factory or business: they are the ones
proposing the wage and other terms of employment. Those seeking
employment are like Responders, and since usually more than one person is
applying for the same job, their bargaining power may be low, just as in the
ultimatum game with more than one Responder. Also, because the place of
employment is the employer’s private property, the employer may be able
to exclude the worker by firing her unless her work is up to the
specifications of the employer.
Remember from Units 1 and 2 that the productivity of labour started to
increase in Britain around the middle of the seventeenth century. But it was
not until the middle of the nineteenth century that a combination of shifts
in the supply and demand for labour, and new institutions such as trade
unions and the right to vote for workers, gave wage earners the bargaining
power to raise wages substantially.
We will see in the next unit how the labour market, along with other
institutions, gives both kinds of power to employers. In Unit 7 we explain
how some firms have the power to set high prices for their products, and in
Unit 10, how the credit market gives power to banks and other lenders over
people seeking mortgages and loans.
The power to say no
Suppose we allow a Proposer simply to divide up a pie in any way, without
any role for the Responder other than to take whatever he gets (if anything).
Under these rules, the Proposer has all the bargaining power and the
Responder none. There is an experimental game like this, and it is called
(you guessed it) the dictator game.
There are many past and present examples of economic institutions that
are like the dictator game, in which there is no option to say no. Examples
include today’s remaining political dictatorships, such as The Democratic
People’s Republic of Korea (North Korea), and slavery, as it existed in the
US prior to the end of the American Civil War in 1865. Criminal
organizations involved in drugs and human trafficking would be another
modern example, in which power may take the form of physical coercion or
threats of violence.
In a capitalist economy in a democratic society, institutions exist to
protect people against violence and coercion, and to ensure that most eco-
nomic interactions are conducted voluntarily. Later in this unit we study
the outcome of an interaction involving coercion, and how it changes with
the power to say no.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
184
allocation A description of who
does what, the consequences of
their actions, and who gets what as
a result.
THE PARETO CRITERION
According to the Pareto criterion,
allocation A dominates allocation
B if at least one party would be
better off with A than B, and
nobody would be worse off.
We say that A Pareto dominates B.
Pareto dominant Allocation A
Pareto dominates allocation B if at
least one party would be better off
with A than B, and nobody would
be worse off. See also: Pareto effi-
cient.
•5.2 EVALUATING INSTITUTIONS AND OUTCOMES: THE
PARETO CRITERION
Whether it is fishermen seeking to make a living while not depleting the
fish stocks, or farmers maintaining the channels of an irrigation system, or
two people dividing up a pie, we want to be able to both describe what
happens and to evaluate it—is it better or worse than other potential out-
comes? The first involves facts; the second involves values.
We call the outcome of an economic interaction an allocation.
In the ultimatum game, for example, the allocation describes the
proposed division of the pie by the Proposer, whether it was rejected or
accepted, and the resulting payoffs to the two players.
Now suppose that we want to compare two possible allocations, A and
B, that may result from an economic interaction. Can we say which is
better? Suppose we find that everyone involved in the interaction would
prefer allocation A. Then most people would agree that A is a better alloca-
tion than B. This criterion for judging between A and B is called the Pareto
criterion, after Vilfredo Pareto, an Italian economist and sociologist.
Note that when we say an allocation makes someone ‘better off’ we
mean that they prefer it, which does not necessarily mean they get more
money.
GREAT ECONOMISTS
Vilfredo Pareto
Vilfredo Pareto (1848–1923), an
Italian economist and sociologist,
earned a degree in engineering for
his research on the concept of
equilibrium in physics. He is
mostly remembered for the
concept of efficiency that bears his
name. He wanted economics and
sociology to be fact-based sciences,
similar to the physical sciences
that he had studied when he was
younger.
His empirical investigations led
him to question the idea that the distribution of wealth resembles the
familiar bell curve, with a few rich and a few poor in the tails of the dis-
tribution and a large middle-income class. In its place he proposed what
came to be called Pareto’s law, according to which, across the ages and
differing types of economy, there were very few rich people and a lot of
poor people.
His 80–20 rule—derived from Pareto’s law—asserted that the richest
20% of a population typically held 80% of the wealth. Were he living in
the US in 2015, he would have to revise that to 90% of the wealth held by
the richest 20%, suggesting that his law might not be as universal as he
had thought.
5.2 EVALUATING INSTITUTIONS AND OUTCOMES: THE PARETO CRITERION
185
Vilfredo Pareto. (1906) 2014.
Manual of Political Economy: A
Variorum Translation and Critical
Edition. Oxford, New York, NY:
Oxford University Press.
Figure 5.1 compares the four allocations in the pest control game from
Unit 4 by the Pareto criterion (using a similar method to the comparison of
technologies in Unit 2). We assume that Anil and Bala are self-interested, so
they prefer allocations with a higher payoff for themselves.
The blue rectangle with its corner at allocation (T, T) shows that (I, I)
Pareto dominates (T, T). Follow the steps in Figure 5.1 to see more
comparisons.
You can see from this example that the Pareto criterion may be of
limited help in comparing allocations. Here, it tells us only that (I, I) is
better than (T, T).
In Pareto’s view, the economic game was played for high stakes, with
big winners and losers. Not surprisingly, then, he urged economists to
study conflicts over the division of goods, and he thought the time and
resources devoted to these conflicts were part of what economics should
be about. In his most famous book, the Manual of Political Economy
(1906), he wrote that: ‘The efforts of men are utilized in two different
ways: they are directed to the production or transformation of economic
goods, or else to the appropriation of goods produced by others.’
Anil’s payoff
0 1
1
2
2
3
3
4
4
5
5
Ba
la
’s
pa
yo
ff
0
T, I
T, T
I, T
I, I = Both use Integrated Pest Control (IPC)
I, T = Anil uses IPC, Bala uses Terminator
T, I = Anil uses Terminator, Bala uses IPC
T, T = Both use Terminator
Outcomes better for both than I, T
Outcomes better for both than T, I
Outcomes better for both than I, I
Outcomes better for both than T, T
I, I
Figure 5.1 Pareto-efficient allocations. All of the allocations except mutual use of
the pesticide (T, T) are Pareto efficient.
1. Anil and Bala’s prisoners’ dilemma
The diagram shows the allocations of
the prisoners’ dilemma game played by
Anil and Bala.
2. A Pareto comparison
(I, I) lies in the rectangle to the north-
east of (T, T), so an outcome where
both Anil and Bala use IPC Pareto
dominates one where both use
Terminator.
3. Compare (T, T) and (T, I)
If Anil uses Terminator and Bala IPC,
then he is better off but Bala is worse
off than when both use Terminator. The
Pareto criterion cannot say which of
these allocations is better.
4. No allocation Pareto dominates (I, I)
None of the other allocations lie to the
north-east of (I, I), so it is not Pareto
dominated.
5. What can we say about (I, T) and
(T, I)?
Neither of these allocations are Pareto
dominated, but they do not dominate
any other allocations either.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
186
Pareto efficient An allocation with
the property that there is no
alternative technically feasible
allocation in which at least one
person would be better off, and
nobody worse off.
PARETO EFFICIENCY
An allocation that is not Pareto
dominated by any other allocation
is described as Pareto efficient.
Pareto criterion According to the
Pareto criterion, a desirable
attribute of an allocation is that it
be Pareto-efficient. See also: Pareto
dominant.
The diagram also shows that three of the four allocations are not Pareto
dominated by any other. An allocation with this property is called Pareto
efficient.
If an allocation is Pareto efficient, then there is no alternative allocation
in which at least one party would be better off and nobody worse off. The
concept of Pareto efficiency is very widely used in economics and sounds
like a good thing, but we need to be careful with it:
• There is often more than one Pareto-efficient allocation: In the pest-control
game there are three.
• The Pareto criterion does not tell us which of the Pareto-efficient allocations
is better: It does not give us any ranking of (I, I), (I, T) and (T, I).
• If an allocation is Pareto efficient, this does not mean we should approve of it:
Anil playing IPC and Bala free riding by playing Terminator is Pareto
efficient, but we (and Anil) may think this is unfair. Pareto efficiency has
nothing to do with fairness.
• Allocation (T, I) is Pareto efficient and (T, T) is not (it is Pareto inefficient):
But the Pareto criterion does NOT tell us which is better.
There are many Pareto-efficient allocations that we would not evaluate
favourably. If you look back at Figure 4.5 you can see that any split of Anil’s
lottery winnings (including giving Bala nothing) would be Pareto efficient
(choose any point on the boundary of the feasible set of outcomes, and draw
the rectangle with its corner at that point: there are no feasible points above
and to the right). But some of these splits would seem very unfair. Similarly,
in the ultimatum game an allocation of one cent to the Responder and
$99.99 to the Proposer is also Pareto efficient, because there is no way to
make the Responder better off without making the Proposer worse off.
The same is true of problems such as the allocation of food. If some
people are more than satisfied while others are starving, we might say in
everyday language: ‘This is not a sensible way to provide nutrition. It is
clearly inefficient.’ But Pareto efficiency means something different. A very
unequal distribution of food can be Pareto efficient as long as all the food is
eaten by someone who enjoys it even a little.
QUESTION 5.1 CHOOSE THE CORRECT ANSWER(S)
Which of the following statements about the outcome of an economic
interaction is correct?
If the allocation is Pareto efficient, then you cannot make anyone
better off without making someone else worse off.
All participants are happy with what they get if the allocation is
Pareto efficient.
There cannot be more than one Pareto-efficient outcome.
According to the Pareto criterion, a Pareto-efficient outcome is
always better than an inefficient one.
5.2 EVALUATING INSTITUTIONS AND OUTCOMES: THE PARETO CRITERION
187
substantive judgements of fairness
Judgements based on the
characteristics of the allocation
itself, not how it was determined.
See also: procedural judgements of
fairness.
procedural judgements of fairness
An evaluation of an outcome based
on how the allocation came about,
and not on the characteristics of
the outcome itself, (for example,
how unequal it is). See also:
substantive judgements of fairness.
••5.3 EVALUATING INSTITUTIONS AND OUTCOMES:
FAIRNESS
Although the Pareto criterion can help us to evaluate allocations, we will
also want to use another criterion: justice. We will ask, is it fair?
Suppose, in the ultimatum game, the Proposer offered one cent from a
total of $100. As we saw in Unit 4, Responders in experiments around the
world typically reject such an offer, apparently judging it to be unfair. Many
of us would have a similar reaction if we witnessed two friends, An and Bai,
walking down the street. They spot a $100 bill, which An picks up. She
offers one cent to her friend Bai, and says she wants to keep the rest.
We might be outraged. But we might think differently if we discovered
that, though both An and Bai had worked hard all their lives, An had just
lost her job and was homeless while Bai was well off. Letting An keep
$99.99 might then seem fair. Thus we might apply a different standard of
justice to the outcome when we know all of the facts.
We could also apply a standard of fairness not to the outcome of the
game, but to the rules of the game. Suppose we had observed An proposing
an even split, allocating $50 to Bai. Good for An, you say, that seems like a
fair outcome. But if this occurred because Bai pulled a gun on An, and
threatened that unless she offered an even split she would shoot her, we
would probably judge the outcome to be unfair.
The example makes a basic point about fairness. Allocations can be
judged unfair because of:
• How unequal they are: In terms of income, for example, or subjective
wellbeing. These are substantive judgements of fairness.
• How they came about: For example by force, or by competition on a level
playing field. These are procedural judgements of fairness.
Substantive and procedural judgements
To make a substantive judgement about fairness, all you need to know is the
allocation itself. However, for procedural evaluations we also need to know
the rules of the game and other factors that explain why this allocation
occurred.
Two people making substantive evaluations of fairness about the same
situation need not agree, of course. For example, they may disagree about
whether fairness should be evaluated in terms of income or happiness. If we
measure fairness using happiness as the criterion, a person with a serious
physical or mental handicap may need much more income than a person
without such disabilities to be equally satisfied with his or her life.
Substantive judgements
These are based on inequality in some aspect of the allocation such as:
• Income: The reward in money (or some equivalent measure) of the indi-
vidual’s command over valued goods and services.
• Happiness: Economists have developed indicators by which subjective
wellbeing can be measured.
• Freedom: The extent that one can do (or be) what one chooses without
socially imposed limits.
Andrew Clark and Andrew Oswald.
2002. ‘A Simple Statistical Method
for Measuring How Life Events
Affect Happiness’. International
Journal of Epidemiology 31 (6):
pp. 1139–1144.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
188
EXERCISE 5.2 PROCEDURAL
FAIRNESS
Consider the society in which you
live, or another society with which
you are familiar. How fair is this
society, according to the
procedural judgements of fairness
listed above?
EXERCISE 5.1 SUBSTANTIVE FAIRNESS
Consider the society you live in, or another society with which you are
familiar.
1. To make society fairer, would you want greater equality of income,
happiness, or freedom? Why? Would there be a trade-off between
these aspects?
2. Are there other things that should be more equal to achieve greater
fairness in this society?
Procedural judgements
The rules of the game that brought about the allocation may be evaluated
according to aspects such as:
• Voluntary exchange of private property acquired by legitimate means: Were
the actions resulting in the allocation the result of freely chosen actions
by the individuals involved, for example each person buying or selling
things that they had come to own through inheritance, purchase, or their
own labour? Or was fraud or force involved?
• Equal opportunity for economic advantage: Did people have an equal oppor-
tunity to acquire a large share of the total to be divided up, or were they
subjected to some kind of discrimination or other disadvantage because
of their race, sexual preference, gender, or who their parents were?
• Deservingness: Did the rules of the game that determined the allocation
take account of the extent to which an individual worked hard, or
otherwise upheld social norms?
We can use these differing judgements to evaluate an outcome in the
ultimatum game. The experimental rules of the game will appear to most
people’s minds as procedurally fair:
• Proposers are chosen randomly.
• The game is played anonymously.
• Discrimination is not possible.
• All actions are voluntary. The Responder can refuse to accept the offer,
and the Proposer is typically free to propose any amount.
Substantive judgements are evaluations of the allocation itself: how the pie
is shared. We know from the behaviour of experimental subjects that many
people would judge an allocation in which the Proposer took 90% of the pie
to be unfair.
Evaluating fairness
The rules of the game in the real economy are a long way from the fair
procedures of the ultimatum game, and procedural judgements of
unfairness are very important to many people, as we will see in Unit 19
(Economic inequality).
People’s values about what is fair differ. Some, for example, regard any
amount of inequality as fair, as long as the rules of the game are fair. Others
judge an allocation to be unfair if some people are seriously deprived of
basic needs, while others consume luxuries.
5.3 EVALUATING INSTITUTIONS AND OUTCOMES: FAIRNESS
189
The American philosopher John Rawls (1921–2002) devised a way to
clarify these arguments, which can sometimes help us to find common
ground on questions of values. We follow three steps:
1. We adopt the principle that fairness applies to all people: For example, if we
swapped the positions of An and Bai, so that it was Bai instead of An
who picked up $100, we would still apply exactly the same standard of
justice to evaluate the outcome.
2. Imagine a veil of ignorance: Since fairness applies to everyone, including
ourselves, Rawls asks us to imagine ourselves behind what he called a
veil of ignorance, not knowing the position that we would occupy in the
society we are considering. We could be male or female, healthy or ill,
rich or poor (or with rich or poor parents), in a dominant or an ethnic
minority group, and so on. In the $100 on the street game, we would not
know if we would be the person picking up the money, or the person
responding to the offer.
3. From behind the veil of ignorance, we can make a judgement: For example,
the choice of a set of institutions—imagining as we do so that we will
then become part of the society we have endorsed, with an equal chance
of having any of the positions occupied by individuals in that society.
The veil of ignorance invites you, in making a judgement about fairness, to
put yourself in the shoes of others quite different from yourself. You would
then, Rawls argued, be able to evaluate the constitutions, laws, inheritance
practices, and other institutions of a society as an impartial outsider.
EXERCISE 5.3 SPLITTING THE PROFITS IN A
PARTNERSHIP
Suppose you and a partner are starting a business
involving each of you selling a new app to the public.
You are deciding how to divide the profits and are con-
sidering four alternatives. The profits could be split:
• equally
• in proportion to how many apps each of you sells
• in inverse proportion to how much income each of
you has from other sources (for example, if one of
you has twice the income of the other, the profits
could be split one-third to the former and two-thirds
to the latter)
• in proportion to how many hours each of you has
spent selling.
Order these alternatives according to your preference
and give arguments based on the concepts of fairness
introduced in this section. If the order depends on other
facts about this joint project, say what other facts you
would need.
Neither philosophy, nor economics, nor any other science, can eliminate
disagreements about questions of value. But economics can clarify:
• How the dimensions of unfairness may be connected: For example, how the
rules of the game that give special advantages to one or another group
may affect the degree of inequality.
• The trade-offs between the dimensions of fairness: For example, do we have
to compromise on the equality of income if we also want equality of
opportunity?
• Public policies to address concerns about unfairness: Also, whether these
policies compromise other objectives.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
190
marginal rate of transformation
(MRT) The quantity of some good
that must be sacrificed to acquire
one additional unit of another
good. At any point, it is the slope of
the feasible frontier. See also: mar-
ginal rate of substitution.
marginal rate of substitution (MRS)
The trade-off that a person is
willing to make between two
goods. At any point, this is the slope
of the indifference curve. See also:
marginal rate of transformation.
••5.4 A MODEL OF CHOICE AND CONFLICT
In the remainder of this unit we explore some economic interactions and
evaluate the resulting allocations. As in the experiments in Unit 4, we will
see that both cooperation and conflict occur. As in the experiments, and in
history, we will find that the rules matter.
Recall the model in Unit 3 of the farmer, Angela, who produces a crop.
We will develop the model into a sequence of scenarios involving two
characters:
1. Initially, Angela works the land on her own, and gets everything she
produces.
2. Next, we introduce a second person, who does not farm, but would also
like some of the harvest. He is called Bruno.
3. At first, Bruno can force Angela to work for him. In order to survive, she
has to do what he says.
4. Later, the rules change: the rule of law replaces the rule of force. Bruno
can no longer coerce Angela to work. But he owns the land and if she
wants to farm his land, she must agree, for example, to pay him some
part of the harvest.
5. Eventually, the rules of the game change again in Angela’s favour. She
and her fellow farmers achieve the right to vote and legislation is passed
that increases Angela’s claim on the harvest.
For each of these steps we will analyse the changes in terms of both Pareto
efficiency and the distribution of income between Angela and Bruno.
Remember that:
• We can determine objectively whether an outcome is Pareto efficient or
not.
• But whether the outcome is fair depends on your own analysis of the
problem, using the concepts of substantive and procedural fairness.
As before, Angela’s harvest depends on her hours of work, through the pro-
duction function. She works the land, and enjoys the remainder of the day
as free time. In Unit 3 she consumed the grain that this activity produced.
Recall that the slope of the feasible frontier is the marginal rate of
transformation (MRT) of free time into grain.
Angela values both grain and free time. Again, we represent her prefer-
ences as indifference curves, showing the combinations of grain and free
time that she values equally. Remember that the slope of the indifference
curve is called the marginal rate of substitution (MRS) between grain
and free time.
Angela works the land on her own
Figure 5.2 shows Angela’s indifference curves and her feasible frontier. The
steeper the indifference curve, the more Angela values free time relative to
grain. You can see that the more free time she has (moving to the right), the
flatter the curves—she values free time less.
In this unit, we make a particular assumption (called quasi-linearity)
about Angela’s preferences that you can see in the shape of her indifference
curves. As she gets more grain, her MRS does not change. So the curves
have the same slope as you move up the vertical line at 16 hours of free
5.4 A MODEL OF CHOICE AND CONFLICT
191
time. More grain does not change her valuation of free time relative to
grain.
Why might this be? Perhaps she does not eat it all, but sells some and
uses the proceeds to buy other things she needs. This is just a simplification
(called quasi-linearity) that makes our model easier to understand.
Remember: when drawing indifference curves for the model in this unit,
simply shift them up and down, keeping the MRS constant at a given
amount of free time.
Angela is free to choose her typical hours of work to achieve her
preferred combination of free time and grain. Work through Figure 5.2 to
determine the allocation.
Figure 5.2 shows that the best Angela can do, given the limits set by the
feasible frontier, is to work for 8 hours. She has 16 hours of free time, and
produces and consumes 9 bushels of grain. This is the number of hours of
work where the marginal rate of substitution is equal to the marginal rate
of transformation. She cannot do better than this! (If you’re not sure why,
go back to Unit 3 and check.)
A new character appears
But now, Angela has company. The other person is called Bruno; he is not a
farmer but will claim some of Angela’s harvest. We will study different rules
of the game that explain how much is produced by Angela, and how it is
divided between her and Bruno. For example, in one scenario, Bruno is the
Leibniz: Quasi-linear preferences
(https://tinyco.re/L050401)
Leibniz: Angela’s choice of working
hours (https://tinyco.re/L050402)
Angela’s hours of free time
0 16
9
24
12
Bu
sh
el
s
of
g
ra
in
0
C
Angela’s feasible
frontier
Angela’s indifference
curves
MRS = MRT
Figure 5.2 Independent farmer Angela’s feasible frontier, best feasible indifference
curve, and choice of hours of work.
1. The feasible frontier
The diagram shows Angela’s feasible
frontier, determined by her production
function.
2. The best Angela can do
The best Angela can do, given the limits
set by the feasible frontier, is to work
for 8 hours, taking 16 hours of free time
and producing 9 bushels of grain. At
this point C, the marginal rate of substi-
tution (MRS) is equal to the marginal
rate of transformation (MRT).
3. MRS = MRT
The MRS is the slope of the indifference
curve. The trade-off she is willing to
make between grain and free time. The
MRT is the slope of the feasible
frontier: the trade-off she is constrained
to make. At point C, the two trade-offs
balance.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
192
landowner and Angela pays some grain to him as rent for the use of the
land.
Figure 5.3 shows Angela and Bruno’s combined feasible frontier. The
frontier indicates how many bushels of grain Angela can produce given
how much free time she takes. For example, if she takes 12 hours free time
and works for 12 hours, then she produces 10.5 bushels of grain. One
possible outcome of the interaction between Angela and Bruno is that 5.25
bushels go to Bruno, and Angela retains the other 5.25 bushels for her own
consumption.
Work through Figure 5.3 to find out how each possible allocation is
represented in the diagram, showing how much work Angela did and how
much grain she and Bruno each got.
Which allocations are likely to occur? Not all of them are even possible.
For example, at point H Angela works 12 hours a day and receives nothing
(Bruno takes the entire harvest), so Angela would not survive. Of the alloca-
tions that are at least possible, the one that will occur depends on the rules
of the game.
Angela’s hours of free time
0 12
10.5
5.25
Total grain
produced
What
Bruno gets
What
Angela gets
Angela’s free time Angela’s work
Feasible frontier:
Angela and Bruno
combined
24
12
Bu
sh
el
s
of
g
ra
in
0
E
G
F
H
Figure 5.3 Feasible outcomes of the interaction between Angela and Bruno.
1. The combined feasible frontier
The feasible frontier shows the
maximum amount of grain available to
Angela and Bruno together, given
Angela’s amount of free time. If Angela
takes 12 hours of free time and works
for 12 hours then she produces 10.5
bushels of grain.
2. A feasible allocation
Point E is a possible outcome of the
interaction between Angela and Bruno.
3. The distribution at point E
At point E, Angela works for 12 hours
and produces 10.5 bushels of grain. The
distribution of grain is such that 5.25
bushels go to Bruno and Angela retains
the other 5.25 bushels for her own con-
sumption.
4. Other feasible allocations
Point F shows an allocation in which
Angela works more than at point E and
gets less grain, and point G shows the
case in which she works more and gets
more grain.
5. An impossible allocation
An outcome at H—in which Angela
works 12 hours a day, Bruno consumes
the entire amount produced and
Angela consumes nothing—would not
be possible: she would starve.
5.4 A MODEL OF CHOICE AND CONFLICT
193
technically feasible An allocation
within the limits set by technology
and biology.
biologically feasible An allocation
that is capable of sustaining the
survival of those involved is
biologically feasible.
EXERCISE 5.4 USING INDIFFERENCE CURVES
In Figure 5.3 (page 193), point F shows an allocation in which Angela works
more and gets less than at point E, and point G shows the case in which
she works more and gets more.
By sketching Angela’s indifference curves, work out what you can say
about her preferences between E, F and G, and how this depends on the
slope of the curves.
QUESTION 5.2 CHOOSE THE CORRECT ANSWER(S)
Figure 5.3 (page 193) shows Angela and Bruno’s combined feasible set,
and four allocations that might result from an interaction between them.
From the figure, we can conclude that:
If Angela has very flat indifference curves, she may prefer G to the
other three allocations.
If Angela has very steep indifference curves, she may prefer F to the
other three allocations.
Allocation G is the best of the four for Bruno.
It is possible that Angela is indifferent between G and E.
5.5 TECHNICALLY FEASIBLE ALLOCATIONS
Initially Angela could consume (or sell) everything she produced. Now
Bruno has arrived, and he has a gun. He has the power to implement any
allocation that he chooses. He is even more powerful than the dictator in
the dictator game (in which a Proposer dictates how a pie is to be divided).
Why? Bruno can determine the size of the pie, as well as how it is shared.
Unlike the experimental subjects in Unit 4, in this model Bruno and
Angela are entirely self-interested. Bruno wants only to maximize the
amount of grain he can get. Angela cares only about her own free time and
grain (as described by her indifference curves).
We now make another important assumption. If Angela does not work
the land, Bruno gets nothing (there are no other prospective farmers that he
can exploit). What this means is that Bruno’s reservation option (what he
gets if Angela does not work for him) is zero. As a result, Bruno thinks
about the future: he will not take so much grain that Angela will die. The
allocation must keep her alive.
First, we will work out the set of technically feasible combinations of
Angela’s hours of work and the amount of grain she receives: that is, all the
combinations that are possible within the limitations of the technology (the
production function) and biology (Angela must have enough nutrition to do
the work and survive).
Figure 5.4 shows how to find the technically feasible set. We already
know that the production function determines the feasible frontier. This is
the technological limit on the total amount consumed by Bruno and Angela,
which in turn depends on the hours that Angela works. Angela’s biological
survival constraint shows the minimum amount of grain that she needs for
each amount of work that she does; points below this line would leave her
so undernourished or overworked that she would not survive. This con-
straint shows what is biologically feasible. Notice that if she expends
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
194
more energy working, she needs more food; that’s why the curve rises from
right to left from point Z as her hours of work increase. The slope of the
biological survival constraint is the marginal rate of substitution between
free time and grain in securing Angela’s survival.
Note that there is a maximum amount of work
that would allow her barely to survive (because of
the calories she burns up working). As we saw in
Unit 2, throughout human history people crossed
the survival threshold when the population outran
the food supply. This is the logic of the Malthusian
population trap. The productivity of labour placed
a limit on how large the population could be.
The fact that Angela’s survival might be in jeopardy is not a
hypothetical example. During the Industrial Revolution, life
expectancy at birth in Liverpool, UK, fell to 25 years: slightly
more than half of what it is today in the poorest countries in
the world. In many parts of the world today, farmers’ and
workers’ capacity to do their jobs is limited by their caloric
intake.
Angela’s hours of free time
0
2.5
Maximum amount of work
Angela could do and still survive
Feasible frontier:
Angela and Bruno
combined
Angela’s biological
survival constraint
Technically
infeasible
Technically
feasible set
Biologically
infeasible
24
12
Bu
sh
el
s
of
g
ra
in
0
Z
Figure 5.4 Technically feasible allocations.
1. The biological survival constraint
If Angela does not work at all, she
needs 2.5 bushels to survive (point Z).
If she gives up some free time and
expends energy working, she needs
more food, so the curve is higher when
she has less free time. This is the
biological survival constraint.
2. Biologically infeasible and
technically infeasible points
Points below the biological survival
constraint are biologically infeasible,
while points above the feasible frontier
are technically infeasible.
3. Angela’s maximum working day
Given the feasible frontier, there is a
maximum amount of work above which
Angela could not survive, even if she
could consume everything she
produced.
4. The technically feasible set
The technically feasible allocations are
the points in the lens-shaped area
bounded by the feasible frontier and
the biological survival constraint
(including points on the frontier).
5.5 TECHNICALLY FEASIBLE ALLOCATIONS
195
EXERCISE 5.5 CHANGING
CONDITIONS FOR PRODUCTION
Using Figure 5.4 (page 195), explain
how you would represent the
effects of each of the following:
1. an improvement in growing
conditions such as more
adequate rainfall
2. Angela having access to half
the land that she had
previously
3. the availability to Angela of a
better designed hoe making it
physically easier to do the work
of farming.
Bruno:
economic rent A payment or other
benefit received above and beyond
what the individual would have
received in his or her next best
alternative (or reservation option).
See also: reservation option.
In Angela’s case, it is not only the limited productivity of her labour that
might jeopardize her survival, but also how much of what she produces is
taken by Bruno. If Angela could consume everything she produced (the
height of the feasible frontier) and choose her hours of work, her survival
would not be in jeopardy since the biological survival constraint is below
the feasible frontier for a wide range of working hours. The question of
biological feasibility arises because of Bruno’s claims on her output.
In Figure 5.4, the boundaries of the feasible solutions to the allocation
problem are formed by the feasible frontier and the biological survival con-
straint. This lens-shaped shaded area gives the technically possible
outcomes. We can now ask what will actually happen—which allocation
will occur, and how does this depend on the institutions governing Bruno’s
and Angela’s interaction?
QUESTION 5.3 CHOOSE THE CORRECT ANSWER(S)
Figure 5.4 (page 195) shows Angela and Bruno’s feasible frontier, and
Angela’s biological survival constraint.
Based on this figure, which of the following is correct?
If Angela works 24 hours she can survive.
There is a technically feasible allocation in which Angela does not
work.
A new technology that boosted grain production would result in a
bigger technically feasible set.
If Angela did not need so much grain to survive the technically feas-
ible set would be smaller.
•5.6 ALLOCATIONS IMPOSED BY FORCE
With the help of his gun, Bruno can choose any point in the lens-shaped
technically feasible set of allocations. But which will he choose?
He reasons like this:
For any number of hours that I order Angela to work, she will
produce the amount of grain shown by the feasible frontier. But I’ll
have to give her at least the amount shown by the biological survival
constraint for that much work, so that I can continue to exploit her. I
get to keep the difference between what she produces and what I
give her. Therefore I should find the hours of Angela’s work for
which the vertical distance between the feasible frontier and the
biological survival constraint (Figure 5.5) is the greatest.
The amount that Bruno will get if he implements this strategy is his eco-
nomic rent, meaning the amount he gets over what he would get if Angela
were not his slave (which, in this model, we set at zero).
Bruno first considers letting Angela continue to work 8 hours a day,
producing 9 bushels, as she did when she had free access to the land. For
8 hours of work she needs 3.5 bushels of grain to survive. So Bruno could
take 5.5 bushels without jeopardizing his future opportunities to benefit
from Angela’s labour.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
196
You:
Bruno is studying Figure 5.5 and asks for your help. You have noticed
that the MRS on the survival constraint is less than the MRT at 8 hours of
work:
Bruno, your plan cannot be right. If you forced her to work a little
more, she’d only need a little more grain to have the energy to work
longer, because the biological survival constraint is relatively flat at
8 hours of work. But the feasible frontier is steep, so she would
produce a lot more if you imposed longer hours.
You demonstrate the argument to him using the analysis in Figure 5.5,
which indicates that the vertical distance between the feasible frontier and
the biological survival constraint is the greatest when Angela works for
11 hours. If Bruno commands Angela to work for 11 hours, then she will
produce 10 bushels and Bruno will get to keep 6 bushels for himself. We can
use Figure 5.5 to find out how many bushels of grain Bruno will get for any
technically feasible allocation.
The lower panel in the last step in Figure 5.5 shows how the amount
Bruno can take varies with Angela’s free time. The graph is hump-shaped,
and peaks at 13 hours of free time and 11 hours of work. Bruno maximizes
his amount of grain at allocation B, commanding Angela to work for
11 hours.
Notice how the slopes of the feasible frontier and the survival constraint
(the MRT and MRS) help us to find the number of hours where Bruno can
take the maximum amount of grain. To the right of 13 hours of free time
(that is, if Angela works less than 11 hours) the biological survival con-
straint is flatter than the feasible frontier (MRS < MRT). This means that
working more hours (moving to the left) would produce more grain than
what Angela needs for the extra work. To the left of 13 hours of free time
(Angela working more), the reverse is true: MRS > MRT. Bruno’s economic
rent is greatest at the hours of work where the slopes of the two frontiers
are equal.
That is:
QUESTION 5.4 CHOOSE THE CORRECT ANSWER(S)
Figure 5.5 (page 198) shows Angela and Bruno’s feas-
ible frontier, and Angela’s biological survival
constraint.
If Bruno can impose the allocation:
He will choose the technically feasible allocation
where Angela produces the most grain.
His preferred choice will be where the marginal
rate of transformation (MRT) on the feasible
frontier equals the marginal rate of substitution
(MRS) on the biological survival constraint.
He will not choose 8 hours of work, because the
MRS between Angela’s work hours and subsistence
requirements exceeds the MRT between work
hours and grain output.
He will choose 13 hours of free time for Angela,
and consume 10 bushels of grain.
5.6 ALLOCATIONS IMPOSED BY FORCE
197
Angela’s hours of free time
W
ha
t B
ru
no
g
et
s
Angela’s hours of free time
0 13 24
12
10
9
4B
us
he
ls
o
f g
ra
in
0
A
16
B
What
Angela gets
Angela’s biological
survival constraint
Feasible frontier:
Angela and Bruno
combined
5.5
6
0
0 13 16 24
Figure 5.5 Coercion: The maximum technically feasible transfer from Angela to
Bruno.
1. Bruno can command Angela to work
Bruno can choose any allocation in the
technically feasible set. He considers
letting Angela continue working
8 hours a day, producing 9 bushels.
2. When Angela works for 8 hours
Bruno could take 5.5 bushels without
jeopardizing his future benefit from
Angela’s labour. This is shown by the
vertical distance between the feasible
frontier and the survival constraint.
3. The maximum distance between
frontiers
The vertical distance between the feas-
ible frontier and the biological survival
constraint is greatest when Angela
works for 11 hours (13 hours of free
time).
4. Allocation and distribution at the
maximum distance
If Bruno commands Angela to work for
11 hours, she will produce 10 bushels,
and needs 4 to survive. Bruno will get
to keep 6 bushels for himself (the
distance AB).
5. At high working hours the survival
frontier becomes steeper
If Bruno makes Angela work for more
than 11 hours, the amount he can take
falls as working hours increase.
6. The best Bruno can do for himself
Bruno gets the maximum amount of
grain by choosing allocation B, where
Angela’s working time is such that the
slope of the feasible frontier is equal to
the slope of the biological survival con-
straint: MRT = MRS.
7. What Bruno gets
If we join up the points then we can see
that the amount Bruno gets is hump-
shaped, and peaks at 11 hours of work
(13 hours of free time).
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
198
private property Something is
private property if the person
possessing it has the right to
exclude others from it, to benefit
from the use of it, and to exchange
it with others.
power The ability to do (and get)
the things one wants in opposition
to the intentions of others,
ordinarily by imposing or
threatening sanctions.
economic rent A payment or other
benefit received above and beyond
what the individual would have
received in his or her next best
alternative (or reservation option).
See also: reservation option.
gains from exchange The benefits
that each party gains from a
transaction compared to how they
would have fared without the
exchange. Also known as: gains
from trade. See also: economic
rent.
joint surplus The sum of the eco-
nomic rents of all involved in an
interaction. Also known as: total
gains from exchange or trade.
bargaining power The extent of a
person’s advantage in securing a
larger share of the economic rents
made possible by an interaction.
Bruno:
You:
Bruno:
You:
Bruno:
New institutions: Law and private property
The economic interaction described in this section takes place in an envir-
onment where Bruno has the power to enslave Angela. If we move from a
scenario of coercion to one in which there is a legal system that prohibits
slavery and protects private property and the rights of landowners and
workers, we can expect the outcome of the interaction to change.
In Unit 1, we defined private property as the right to use and exclude
others from the use of something, and the right to sell it (or to transfer these
rights to others). From now on we will suppose that Bruno owns the land
and can exclude Angela if he chooses. How much grain he will get as a
result of his private ownership of the land will depend on the extent of his
power over Angela in the new situation.
When people participate voluntarily in an interaction, they do so
because they expect the outcome to be better than their reservation
option—the next-best alternative. In other words, they do so in pursuit of
economic rents. Economic rents are also sometimes called gains from
exchange, because they are how much a person gains by engaging in the
exchange compared to not engaging.
The sum of the economic rents is termed the surplus (or sometimes the
joint surplus, to emphasize that it includes all of the rents). How much
rent they will each get—how they will share the surplus—depends on their
bargaining power. And that, as we know, depends on the institutions
governing the interaction.
In the example above, Angela was forced to participate and Bruno chose
her working hours to maximize his own economic rent. Next we look at
the situation where she can simply say no. Angela is no longer a slave, but
Bruno still has the power to make a take-it-or-leave-it offer, just like the
Proposer in the ultimatum game.
•5.7 ECONOMICALLY FEASIBLE ALLOCATIONS AND THE
SURPLUS
We check back on Angela and Bruno, and immediately notice that Bruno is
now wearing a suit, and is no longer armed. He explains that this is no
longer needed because there is now a government with laws administered
by courts, and professional enforcers called the police. Bruno now owns the
land, and Angela must have permission to use his property. He can offer a
contract allowing her to farm the land, and give him part of the harvest in
return. But the law requires that exchange is voluntary: Angela can refuse
the offer.
It used to be a matter of power, but now both Angela and I have
property rights: I own the land, and she owns her own labour. The
new rules of the game mean that I can no longer force Angela to
work. She has to agree to the allocation that I propose.
And if she doesn’t?
Then there is no deal. She doesn’t work on my land, I get nothing,
and she gets barely enough to survive from the government.
So you and Angela have the same amount of power?
Certainly not! I am the one who gets to make a take-it-or-leave-it
offer. I am like the Proposer in the ultimatum game, except that this
is no game. If she refuses she goes hungry.
5.7 ECONOMICALLY FEASIBLE ALLOCATIONS AND THE SURPLUS
199
You:
Bruno:
Bruno:
You:
reservation option A person’s next
best alternative among all options
in a particular transaction. Also
known as: fallback option. See also:
reservation price.
reservation indifference curve A
curve that indicates allocations
(combinations) that are as highly
valued as one’s reservation option.
But if she refuses you get zero?
That will never happen.
Why does he know this? Bruno knows that Angela, unlike the subjects in
the ultimatum game experiments, is entirely self-interested (she does not
punish an unfair offer). If he makes an offer that is just a tiny bit better for
Angela than not working at all and getting subsistence rations, she will
accept it.
Now he asks you a question similar to the one he asked earlier:
In this case, what should my take-it-or-leave-it offer be?
You answered before by showing him the biological survival constraint.
Now the limitation is not Angela’s survival, but rather her agreement. You
know that she values her free time, so the more hours he offers her to work,
the more he is going to have to pay.
Why don’t you just look at Angela’s indifference curve that passes
through the point where she does not work at all and barely
survives? That will tell you how much is the least you can pay her for
each of the hours of free time she would give up to work for you.
Point Z in Figure 5.6 is the allocation in which Angela does no work and
gets only survival rations (from the government, or perhaps her family).
This is her reservation option: if she refuses Bruno’s offer, she has this
option as a backup. Follow the steps in Figure 5.6 to see Angela’s reserva-
tion indifference curve: all of the allocations that have the same value for
her as the reservation option. Below or to the left of the curve she is worse
off than in her reservation option. Above and to the right she is better off.
The set of points bounded by the reservation indifference curve and the
feasible frontier is the set of all economically feasible allocations, now that
Angela has to agree to the proposal that Bruno makes. Bruno thanks you for
this handy new tool for figuring out the most he can get from Angela.
The biological survival constraint and the reservation indifference curve
have a common point (Z): at that point, Angela does no work and gets
subsistence rations from the government. Other than that, the two curves
differ. The reservation indifference curve is uniformly above the biological
survival constraint. The reason, you explain to Bruno, is that however hard
she works along the survival constraint, she barely survives; and the more
she works the less free time she has, so the unhappier she is. Along the
reservation indifference curve, by contrast, she is just as well off as at her
reservation option, meaning that being able to keep more of the grain that
she produces compensates exactly for her lost free time.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
200
EXERCISE 5.6 BIOLOGICAL AND ECONOMIC FEASIBILITY
Using Figure 5.6:
1. Explain why a point on the biological survival constraint is higher
(more grain is required) when Angela has fewer hours of free time. Why
does the curve also get steeper when she works more?
2. Explain why the biologically feasible set is not equal to the eco-
nomically feasible set.
3. Explain (by shifting the curves) what happens if a more nutritious kind
of grain is available for Angela to grow and consume.
We can see that both Angela and Bruno may benefit if a deal can be made.
Their exchange—allowing her to use his land (that is, not using his property
right to exclude her) in return for her sharing some of what she produces—
makes it possible for both to be better off than if no deal had been struck.
• As long as Bruno gets some of the crop he will do better than if there is
no deal.
• As long as Angela’s share makes her better off than she would have been
if she took her reservation option, taking account of her work hours, she
will also benefit.
Angela’s hours of free time
0
2.5
24
12
Bu
sh
el
s
of
g
ra
in
0
Z
Angela’s reservation
option
Angela’s biological
survival constraint
Angela’s reservation
indifference curve
Economically
feasible set
Feasible frontier:
Angela and Bruno
combined
Figure 5.6 Economically feasible allocations when exchange is voluntary.
1. Angela’s reservation option
Point Z, the allocation in which Angela
does not work and gets only survival
rations from the government, is called
her reservation option.
2. Angela’s reservation indifference
curve
The curve showing all of the alloca-
tions that are just as highly valued by
Angela as the reservation option is
called her reservation indifference
curve.
3. The economically feasible set
The points in the area bounded by the
reservation indifference curve and the
feasible frontier (including the points
on the frontiers) define the set of all
economically feasible allocations.
5.7 ECONOMICALLY FEASIBLE ALLOCATIONS AND THE SURPLUS
201
Pareto improvement A change that
benefits at least one person
without making anyone else worse
off. See also: Pareto dominant.
This potential for mutual gain is why their exchange need not take place at
the point of a gun, but can be motivated by the desire of both to be better
off.
All of the allocations that represent mutual gains are shown in the eco-
nomically feasible set in Figure 5.6. Each of these allocations Pareto
dominates the allocation that would occur without a deal. In other words,
Bruno and Angela could achieve a Pareto improvement.
This does not mean that both parties will benefit equally. If the institu-
tions in effect give Bruno the power to make a take-it-or-leave-it offer,
subject only to Angela’s agreement, he can capture the entire surplus (minus
the tiny bit necessary to get Angela to agree). Bruno knows this already.
Once you have explained the reservation indifference curve to him,
Bruno knows which allocation he wants. He maximizes the amount of grain
he can get at the maximum height of the lens-shaped region between
Angela’s reservation indifference curve and the feasible frontier. This will
be where the MRT on the feasible frontier is equal to the MRS on the
indifference curve. Figure 5.7a shows that this allocation requires Angela to
work for fewer hours than she did under coercion.
So Bruno would like Angela to work for 8 hours and give him
4.5 bushels of grain (allocation D). How can he implement this allocation?
All he has to do is to make a take-it-or-leave-it offer of a contract allowing
Angela to work the land, in return for a land rent of 4.5 bushels per day. If
Angela has to pay 4.5 bushels (CD in Figure 5.7a) then she will choose to
produce at point C, where she works for 8 hours. You can see this in the
figure; if she produced at any other point on the feasible frontier and then
gave Bruno 4.5 bushels, she would have lower utility—she would be below
Angela’s hours of free time
0
4
241613
12
Bu
sh
el
s
of
g
ra
in
0
B
Feasible frontier:
Angela and Bruno
combined
What Angela
gets
4.5 D
9 C
A
Angela’s biological
survival constraint
Angela’s reservation
indifference curve
Figure 5.7a Bruno’s take-it-or-leave-it proposal when Angela can refuse.
1. Bruno’s best outcome using coercion
Using coercion, Bruno chose allocation
B. He forced Angela to work 11 hours
and received grain equal to AB. The
MRT at A is equal to the MRS at B on
Angela’s biological survival constraint.
2. When Angela can say no
With voluntary exchange, allocation B
is not available. The best that Bruno
can do is allocation D, where Angela
works for 8 hours, giving him grain
equal to CD.
3. MRS = MRT again
When Angela works 8 hours, the MRT
is equal to the MRS on Angela’s reser-
vation indifference curve, as shown by
the slopes.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
202
her reservation indifference curve. But she can achieve her reservation
utility by working for 8 hours, so she will accept the contract.
EXERCISE 5.7 WHY ANGELA WORKS FOR 8 HOURS
Angela’s income is the amount she produces minus the land rent she pays
to Bruno.
1. Using Figure 5.7a (page 202), suppose Angela works 11 hours. Would
her income (after paying land rent) be greater or less than when she
works 8 hours? Suppose instead, she works 6 hours, how would her
income compare with when she works 8 hours?
2. Explain in your own words why she will choose to work 8 hours.
Since Angela is on her reservation indifference curve, only Bruno benefits
from this exchange. All of the joint surplus goes to Bruno. His economic
rent (equal to the land rent she pays him) is the surplus.
Remember that when Angela could work the land on her own she chose
allocation C. Notice now that she chooses the same hours of work when she
has to pay rent. Why does this happen? However much rent Angela has to
pay, she will choose her hours of work to maximize her utility, so she will
produce at a point on the feasible frontier where the MRT is equal to her
MRS. And we know that her preferences are such that her MRS doesn’t
change with the amount of grain she consumes, so it will not be affected by
the rent. This means that if she can choose her hours, she will work for
8 hours irrespective of the land rent (as long as this gives her at least her
reservation utility).
Figure 5.7b shows how the surplus (which Bruno gets) varies with
Angela’s hours. You will see that the surplus falls as Angela works more or
less than 8 hours. It is hump-shaped, like Bruno’s rent in the case of
coercion. But the peak is lower when Bruno needs Angela to agree to the
proposal.
EXERCISE 5.8 TAKE IT OR LEAVE IT?
1. Why is it Bruno, and not Angela, who has the power to make a take-it-
or-leave-it offer?
2. Can you imagine a situation in which the farmer, not the landowner,
might have this power?
Leibniz: Angela’s choice of working
hours when she pays rent
(https://tinyco.re/L050701)
5.7 ECONOMICALLY FEASIBLE ALLOCATIONS AND THE SURPLUS
203
Angela’s hours of free time
0 241613
12
Bu
sh
el
s
of
g
ra
in
0
Feasible frontier:
Angela and Bruno
combined
4.5
9
Angela’s hours of free time
W
ha
t B
ru
no
g
et
s Technically feasible
Economically feasible
(joint surplus)
4.5
6
0
0 13 16 24
Angela’s biological
survival constraint Angela’s reservation
indifference curve
Figure 5.7b Bruno’s take-it-or-leave-it proposal when Angela can refuse.
1. Angela’s working hours when she
was coerced
Using coercion, Angela was forced to
work 11 hours. The MRT was equal to
the MRS on Angela’s biological survival
constraint.
2. Bruno’s best take-it-or-leave-it offer
When Bruno cannot force Angela to
work, he should offer a contract in
which Angela pays him 4.5 bushels to
rent the land. She works for 8 hours,
where the MRT is equal to the MRS on
her reservation indifference curve.
3. The maximum surplus
If Angela works more or less than
8 hours, the joint surplus is less than
4.5 bushels.
4. Bruno’s grain
Although Bruno cannot coerce Angela
he can get the whole surplus.
5. Technically and economically
feasible peaks compared
The peak of the hump is lower when
Angela can refuse, compared to when
Bruno could order her to work.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
204
QUESTION 5.5 CHOOSE THE CORRECT ANSWER(S)
Figure 5.6 (page 201) shows Angela and Bruno’s feasible frontier,
Angela’s biological survival constraint, and her reservation indifference
curve.
Based on this figure, which of the following is correct?
The economically feasible set is the same as the technically feas-
ible set.
For any given number of hours of free time, the marginal rate of
substitution on the reservation indifference curve is smaller than
that on the biological survival constraint.
Some points are economically feasible but not technically feasible.
If the ration Angela gets from the government increases from 2 to 3
bushels of grain, her reservation indifference curve will be above
her biological survival constraint whatever her working hours.
QUESTION 5.6 CHOOSE THE CORRECT ANSWER(S)
Figure 5.7a (page 202) shows Angela and Bruno’s feasible frontier,
Angela’s biological survival constraint and her reservation indifference
curve. B is the outcome under coercion, while D is the outcome under
voluntary exchange when Bruno makes a take-it-or-leave-it offer.
Looking at this graph, we can conclude that:
With a take-it-or-leave-it offer, Bruno’s economic rent is equal to
the joint surplus.
Both Bruno and Angela are better off under voluntary exchange
than under coercion.
When Bruno makes a take-it-or-leave-it offer, Angela accepts
because she receives an economic rent.
Angela works longer under voluntary exchange than under
coercion.
••5.8 THE PARETO EFFICIENCY CURVE AND THE
DISTRIBUTION OF THE SURPLUS
Angela chose to work for 8 hours, producing 9 bushels of grain, both when
she had to pay rent, and also when she did not. In both cases there is a
surplus of 4.5 bushels: the difference between the amount of grain
produced, and the amount that would give Angela her reservation utility.
The two cases differ in who gets the surplus. When Angela had to pay
land rent, Bruno took the whole surplus, but when she could work the land
for herself she obtained all of the surplus. Both allocations have two
important properties:
• All the grain produced is shared between Angela and Bruno.
• The MRT on the feasible frontier is equal to the MRS on Angela’s
indifference curve.
This means that the allocations are Pareto efficient.
5.8 THE PARETO EFFICIENCY CURVE AND THE DISTRIBUTION OF THE SURPLUS
205
PARETO EFFICIENCY AND THE
PARETO EFFICIENCY CURVE
• A Pareto-efficient allocation has
the property that there is no
alternative technically feasible
allocation in which at least one
person would be better off, and
nobody worse off.
• The set of all such allocations is
the Pareto efficiency curve. It is
also referred to as the contract
curve.
To see why, remember that Pareto efficiency means that no Pareto
improvement is possible: it is impossible to change the allocation to make
one party better off without making the other worse off.
The first property is straightforward: it means that no Pareto
improvement can be achieved simply by changing the amounts of grain
they each consume. If one consumed more, the other would have to have
less. On the other hand, if some of the grain produced was not being con-
sumed, then consuming it would make one or both of them better off.
The second property, MRS = MRT, means that no Pareto improvement
can be achieved by changing Angela’s hours of work and hence the amount
of grain produced.
If the MRS and MRT were not equal, it would be possible to make both
better off. For example, if MRT > MRS, Angela could transform an hour of
her time into more grain than she would need to get the same utility as
before, so the extra grain could make both of them better off. But if MRT =
MRS, then any change in the amount of grain produced would only be
exactly what is needed to keep Angela’s utility the same as before, given the
change in her hours.
Figure 5.8 shows that there are many other Pareto-efficient allocations
in addition to these two. Point C is the outcome when Angela is an
independent farmer. Compare the analysis in Figure 5.8 with Bruno’s take-
or-leave-it offer, and see the other Pareto-efficient allocations.
Figure 5.8 shows that in addition to the two Pareto-efficient allocations
we have observed (C and D), every point between C and D represents a
Pareto-efficient allocation. CD is called the Pareto efficiency curve: it
joins together all the points in the feasible set for which MRS = MRT. (You
will also hear it called the contract curve, even in situations where there is
no contract, which is why we prefer the more descriptive term Pareto
efficiency curve.)
At each allocation on the Pareto efficiency curve Angela works for
8 hours and there is a surplus of 4.5 bushels, but the distribution of the
surplus is different—ranging from point D where Angela gets none of it, to
point C where she gets it all. At the hypothetical allocation G, both receive
an economic rent: Angela’s rent is GD, Bruno’s is GC, and the sum of their
rents is equal to the surplus.
QUESTION 5.7 CHOOSE THE CORRECT ANSWER(S)
Figure 5.8 (page 207) shows the Pareto efficiency curve CD for the
interaction between Angela and Bruno.
Which of the following statements is correct?
The allocation at C Pareto dominates the one at D.
Angela’s marginal rate of substitution is equal to the marginal rate
of transformation at all points on the Pareto efficiency curve.
The mid-point of CD is the most Pareto-efficient allocation.
Angela and Bruno are indifferent between all the points on CD,
because they are all Pareto efficient.
Leibniz: The Pareto efficiency
curve (https://tinyco.re/L050801)
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
206
Bruno:
AngElA:
•5.9 POLITICS: SHARING THE SURPLUS
Bruno thinks that the new rules, under which he makes an offer that Angela
will not refuse, are not so bad after all. Angela is also better off than she had
been when she had barely enough to survive. But she would like a share in
the surplus.
She and her fellow farm workers lobby for a new law that limits working
time to 4 hours a day, while requiring that total pay is at least 4.5 bushels.
They threaten not to work at all unless the law is passed.
Angela, you and your colleagues are bluffing.
No, we are not: we would be no worse off at our reservation
option than under your contract, working the hours and receiving
the small fraction of the harvest that you impose!
Angela and her fellow workers win, and the new law limits the working day
to 4 hours.
Angela’s hours of free time
0 2416
12
Bu
sh
el
s
of
g
ra
in
0
Angela’s reservation
indifference curve, IC1
Angela’s best feasible indifference curve
when an independent farmer, IC0
D
9 C
G
Feasible frontier: Angela
and Bruno combined
4.5
Figure 5.8 Pareto-efficient allocations and the distribution of the surplus.
1. The allocation at C
As an independent farmer, Angela
chose point C, where MRT = MRS. She
consumed 9 bushels of grain: 4.5
bushels would have been enough to
put her on her reservation indifference
curve at D. But she obtained the whole
surplus CD—an additional 4.5 bushels.
2. The allocation at D
When Bruno owned the land and made
a take-it-or-leave-it offer, he chose a
contract in which the land rent was CD
(4.5 bushels). Angela accepted and
worked 8 hours. The allocation was at
D, and once again, MRT = MRS. The
surplus was still CD, but Bruno got it all.
3. Angela’s preferences
Remember that Angela’s MRS doesn’t
change as she consumes more grain. At
any point along the line CD, such as G,
there is an indifference curve with the
same slope. So MRS = MRT at all of
these points.
4. A hypothetical allocation
Point G is a hypothetical allocation, at
which MRS = MRT. Angela works for
8 hours, and 9 bushels of grain are
produced. Bruno gets grain CG, and
Angela gets all the rest. Allocation G is
Pareto efficient.
5. The Pareto efficiency curve
All the points making up the line
between C and D are Pareto-efficient
allocations, at which MRS = MRT. The
surplus of 4.5 bushels (CD) is shared
between Angela and Bruno.
5.9 POLITICS: SHARING THE SURPLUS
207
How did things work out?
Before the short-hours law Angela worked for 8 hours and received
4.5 bushels of grain. This is point D in Figure 5.9. The new law implements
the allocation in which Angela and her friends work 4 hours, getting 20
hours of free time and the same number of bushels. Since they have the
same amount of grain and more free time, they are better off. Figure 5.9
shows they are now on a higher indifference curve.
The new law has increased Angela’s bargaining power and Bruno is
worse off than before. You can see she is better off at F than at D. She is also
better off than she would be with her reservation option, which means she
is now receiving an economic rent.
Angela’s rent can be measured, in bushels of grain, as the vertical
distance between her reservation indifference curve (IC1 in Figure 5.9) and
the indifference curve she is able to achieve under the new legislation (IC2).
We can think of the economic rent as:
• The maximum amount of grain per year that Angela would give up to
live under the new law rather than in the situation before the law was
passed.
Angela’s hours of free time
0 2416
12
Bu
sh
el
s
of
g
ra
in
0
Angela’s reservation
indifference curve, IC1
What Angela
gets Feasible frontier:
Angela and Bruno combined
D
9 C
F
20
6.5
4.5
E
IC2
Figure 5.9 The effect of an increase in Angela’s bargaining power through
legislation.
1. Before the short hours law
Bruno makes a take-it-or-leave-it offer,
gets grain equal to CD, and Angela
works 8 hours. Angela is on her reserva-
tion indifference curve at D and MRS =
MRT.
2. What Angela receives before
legislation
Angela gets 4.5 bushels of grain: she is
just indifferent between working for
8 hours and her reservation option.
3. The effect of legislation
With legislation that reduces work to
4 hours and keeps Angela’s amount of
grain unchanged, she is on a higher
indifference curve at F. Bruno’s grain is
reduced from CD to EF (2 bushels).
4. MRT > MRS
When Angela works 4 hours, the MRT is
larger than the MRS on the new
indifference curve.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
208
Pareto efficiency curve The set of
all allocations that are Pareto effi-
cient. Often referred to as the
contract curve, even in social
interactions in which there is no
contract, which is why we avoid the
term. See also: Pareto efficient.
You:
AngElA:
You:
You:
You:
• Or (because Angela is obviously political) the amount she would be
willing to pay so that the law passed, for example by lobbying the
legislature or contributing to election campaigns.
QUESTION 5.8 CHOOSE THE CORRECT ANSWER(S)
In Figure 5.9 (page 208), D and F are the outcomes before and after the
introduction of a new law that limits Angela’s work time to four hours
a day while requiring a minimum pay of 4.5 bushels. Based on this
information, which of the following statements are correct?
The change from D to F is a Pareto improvement.
The new outcome F is Pareto efficient.
Both Angela and Bruno receive economic rents at F.
As a result of the new law, Bruno has less bargaining power.
5.10 BARGAINING TO A PARETO-EFFICIENT SHARING
OF THE SURPLUS
Angela and her friends are pleased with their success. She asks what you
think of the new policy.
Congratulations, but your policy is far from the best you could do.
Why?
Because you are not on the Pareto efficiency curve! Under your new
law, Bruno is getting 2 bushels, and cannot make you work more than
4 hours. So why don’t you offer to continue to pay him 2 bushels, in
exchange for agreeing to let you keep anything you produce above
that? Then you get to choose how many hours you work.
The small print in the law allows a longer work day if both parties agree, as
long as the workers’ reservation option is a 4-hour day if no agreement is
reached.
Now redraw Figure 5.9 and use the concepts of the joint surplus and
the Pareto efficiency curve from Figure 5.8 to show Angela how she
can get a better deal.
Look at Figure 5.10. The surplus is largest at 8 hours of work. When
you work for 4 hours the surplus is smaller, and you pay most of it to
Bruno. If you increase the surplus, you can pay him the same
amount, and your own surplus will be bigger—so you will be better
off. Follow the steps in Figure 5.10 to see how this works.
The move away from point D (at which Bruno had all the bargaining power
and obtained all the gains from exchange) to point H where Angela is better
off consists of two distinct steps:
1. From D to F, the outcome is imposed by new legislation. This was
definitely not win-win: Bruno lost because his economic rent at F is less
than the maximum feasible rent that he got at D. Angela benefitted.
2. Once at the legislated outcome, there were many win-win possibilities
open to them. They are shown by the segment GH on the Pareto
efficiency curve. Win-win alternatives to the allocation at F are possible
by definition, because F was not Pareto efficient.
5.10 BARGAINING TO A PARETO-EFFICIENT SHARING OF THE SURPLUS
209
Bruno:
You:
Bruno:
Bruno wants to negotiate. He is not happy with Angela’s proposal of H.
I am no better off under this new plan than I would be if I just
accepted the legislation that the farmers passed.
But Bruno, Angela now has bargaining power, too. The legislation
changed her reservation option, so it is no longer 24 hours of free
time at survival rations. Her reservation option is now the legislated
allocation at point F. I suggest you make her a counter offer.
Angela, I’ll let you work the land for as many hours as you choose
if you pay me half a bushel more than EF.
They shake hands on the deal.
Because Angela is free to choose her work hours, subject only to paying
Bruno the extra half bushel, she will work 8 hours where MRT = MRS.
Because this deal lies between G and H, it is a Pareto improvement over
point F. Moreover, because it is on the Pareto-efficient curve CD, we know
there are no further Pareto improvements to be made. This is true of every
other allocation on GH—they differ only in the distribution of the mutual
gains, as some favour Angela while others favour Bruno. Where they end up
will depend on their bargaining power.
Angela’s hours of free time
0 2416
12
Bu
sh
el
s
of
g
ra
in
0
Angela’s reservation
indifference curve, IC1
Feasible frontier:
Angela and Bruno combined
D
9 C
F
20
4.5
G
H
IC2
E
Figure 5.10 Bargaining to restore Pareto efficiency.
1. The maximum joint surplus
The surplus to be divided between
Angela and Bruno is maximized where
MRT = MRS, at 8 hours of work.
2. Angela prefers F to D
But Angela prefers point F
implemented by the legislation,
because it gives her the same amount
of grain but more free time than D.
3. Angela could also do better than F
Compared to F, she would prefer any
allocation on the Pareto efficiency
curve between C and G.
4. Angela can propose H
At allocation H, Bruno gets the same
amount of grain: CH = EF. Angela is
better off than she was at F. She works
longer hours, but has more than
enough grain to compensate her for
the loss of free time.
5. A win-win agreement by moving to
an allocation between G and H
F is not Pareto efficient because MRT >
MRS. If they move to a point on the
Pareto efficiency curve between G and
H, Angela and Bruno can both be better
off.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
210
QUESTION 5.9 CHOOSE THE CORRECT ANSWER(S)
In Figure 5.10 (page 210), Angela and Bruno are at allocation F, where
she receives 4.5 bushels of grain for 4 hours of work.
From the figure, we can conclude that:
All the points on EF are Pareto efficient.
Any point in the area between G, H and F would be a Pareto
improvement.
Any point between G and D would be a Pareto improvement.
They would both be indifferent between all points on GH.
•••5.11 ANGELA AND BRUNO: THE MORAL OF THE STORY
Angela’s farming skills and Bruno’s ownership of land provided an oppor-
tunity for mutual gains from exchange.
The same is true when people directly exchange, or buy and sell, goods
for money. Suppose you have more apples than you can consume, and your
neighbour has an abundance of pears. The apples are worth less to you than
to your neighbour, and the pears are worth more to you. So it must be pos-
sible to achieve a Pareto improvement by exchanging some apples and pears.
When people with differing needs, property and capacities meet, there is
an opportunity to generate gains for all of them. That is why people come
together in markets, online exchanges or pirate ships. The mutual gains are
the pie—which we call the surplus.
The allocations that we observe through history are largely the result of
the institutions, including property rights and bargaining power, that were
present in the economy. Figure 5.11 summarizes what we have learned
about the determination of economic outcomes from the succession of
scenarios involving Angela and Bruno.
• Technology and biology determine whether or not they are able to
mutually benefit, and the technically feasible set of allocations (Section
5.5). If Bruno’s land had been so unproductive that Angela’s labour could
not produce enough to keep her alive, then there would have been no
room for a deal.
• For allocations to be economically feasible, they must be Pareto
improvements relative to the parties’ reservation options, which may
depend on institutions (such as Angela’s survival rations from the gov-
ernment (Section 5.7) or legislation on working hours (Section 5.10)).
• The outcome of an interaction depends on people’s preferences (what
they want), as well as the institutions that provide their bargaining
power (ability to get it), and hence how the surplus is distributed
(Section 5.10).
The story of Angela and Bruno provides three lessons about efficiency and
fairness, illustrated by Figure 5.10, to which we will return in subsequent
units.
• When one person or group has power to dictate the allocation, subject
only to not making the other party worse off than in their reservation
option, the powerful party will capture the entire surplus. If they have
5.11 ANGELA AND BRUNO: THE MORAL OF THE STORY
211
done this, then there cannot be any way to make either of them better
off without making the other worse off (point D in the figure). So this
must be Pareto efficient!
• Those who consider their treatment unfair often have some power to
influence the outcome through legislation and other political means, and
the result may be a fairer distribution in their eyes or ours, but may not
necessarily be Pareto efficient (point F). Societies may face trade-offs
between Pareto-efficient but unfair outcomes, and fair but Pareto-
inefficient outcomes.
• If we have institutions under which people can jointly deliberate, agree
on, and enforce alternative allocations, then it may be possible to avoid
the trade-off and achieve both efficiency and fairness—as Angela and
Bruno did through a combination of legislation and bargaining between
themselves (point H).
••5.12 MEASURING ECONOMIC INEQUALITY
In our analysis of the interaction between Angela and Bruno, we have
assessed the allocations in terms of Pareto efficiency. We have seen that
they (or at least one of them) can be better off if they can negotiate a move
from a Pareto-inefficient allocation to one on the Pareto efficiency curve.
But the other important criterion for assessing an allocation is fairness.
We know that Pareto-efficient allocations can be highly unequal. In the case
of Angela and Bruno, inequality resulted directly from differences in bar-
gaining power, but also from differences in their endowments: that is, what
they each owned before the interaction (their initial wealth). Bruno owned
land, while Angela had nothing except time and the capacity to work. Dif-
ference in endowments, as well as institutions, may in turn affect
bargaining power.
It is easy to assess the distribution between two people. But how can we
assess inequalities in larger groups, or across a whole society? A useful tool
for representing and comparing distributions of income or wealth, and
showing the extent of inequality, is the Lorenz curve (invented in 1905 by
Max Lorenz (1876–1959), an American economist, while he was still a
student). It indicates how much disparity there is in income, or any other
measure, across the population.
Max O. Lorenz. 1905. ‘Methods of
Measuring the Concentration of
Wealth’. Publications of the
American Statistical Association
9 (70).
Institutions
Biology
Technology
Bargaining
power
Reservation
option
Technically
feasible allocations
Economically
feasible allocations
Allocation
(outcome):
who does what &
who gets what
Preferences
Figure 5.11 The fundamental determinants of economic outcomes.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
212
Lorenz curve A graphical
representation of inequality of
some quantity such as wealth or
income. Individuals are arranged in
ascending order by how much of
this quantity they have, and the
cumulative share of the total is
then plotted against the
cumulative share of the population.
For complete equality of income,
for example, it would be a straight
line with a slope of one. The extent
to which the curve falls below this
perfect equality line is a measure
of inequality. See also: Gini coeffi-
cient.
The Lorenz curve shows the entire population lined up along the hori-
zontal axis from the poorest to the richest. The height of the curve at any
point on the horizontal axis indicates the fraction of total income received
by the fraction of the population given by that point on the horizontal axis.
To see how this works, imagine a village in which there are 10
landowners, each owning 10 hectares, and 90 others who farm the land as
sharecroppers, but who own no land (like Angela). The Lorenz curve is the
blue line in Figure 5.12. Lining the population up in order of land
ownership, the first 90% of the population own nothing, so the curve is flat.
The remaining 10% own 10 hectares each, so the ‘curve’ rises in a straight
line to reach the point where 100% of people own 100% of the land.
If instead each member of the population owned one hectare of land—
perfect equality in land ownership—then the Lorenz curve would be a line
at a 45-degree angle, indicating that the ‘poorest’ 10% of the population
have 10% of the land, and so on (although in this case, everyone is equally
poor, and equally rich).
The Lorenz curve allows us to see how far a distribution departs from
this line of perfect equality. Figure 5.13 shows the distribution of income
that would have resulted from the prize-sharing system described in the
articles of the pirate ship, the Royal Rover, discussed in the introduction to
this unit. The Lorenz curve is very close to the 45-degree line, showing how
the institutions of piracy allowed ordinary members of the crew to claim a
large share of income.
In contrast, when the Royal Navy’s ships Favourite and Active captured
the Spanish treasure ship La Hermione, the division of the spoils on the two
British men-of-war ships was far less equal. The Lorenz curves show that
ordinary crew members received about a quarter of the income, with the
remainder going to a small number of officers and the captain. You can see
that the Favourite was more unequal that the Active, with a lower share
going to each crew member. By the standards of the day, pirates were
unusually democratic and fair-minded in their dealings with each other.
0 90 100
0
Landowners’
share of land
90 farmers 10 landowners
Perfect
equality
line
Cu
m
ul
at
iv
e
sh
ar
e
of
la
nd
(%
)
Cumulative share of the population
from least to most land owned (%)
100
Figure 5.12 A Lorenz curve for wealth ownership.
5.12 MEASURING ECONOMIC INEQUALITY
213
Gini coefficient A measure of
inequality of any quantity such as
income or wealth, varying from a
value of zero (if there is no inequal-
ity) to one (if a single individual
receives all of it).
The Gini coefficient
The Lorenz curve gives us a picture of the disparity of income across the
whole population, but it can be useful to have a simple measure of the
degree of inequality. You can see that more unequal distributions have a
greater area between the Lorenz curve and the 45-degree line. The Gini
coefficient (or Gini ratio) named after the Italian statistician Corrado Gini
(1884–1965), is calculated as the ratio of this area to the area of the whole
of the triangle under the 45-degree line.
If everyone has the same income, so that there is no income inequality,
the Gini coefficient takes a value of 0. If a single individual receives all the
income, the Gini coefficient takes its maximum value of 1. We can calculate
the Gini for land ownership in Figure 5.14a as area A, between the Lorenz
curve and the perfect equality line, as a proportion of area (A + B), the
triangle under the 45-degree line:
Figure 5.14b shows the Gini coefficients for each of the Lorenz curves we
have drawn so far.
Strictly speaking, this method of calculating the Gini gives only an
approximation. The Gini is more precisely defined as a measure of the
average difference in income between every pair of individuals in the popu-
lation, as explained in the Einstein at the end of this section. The area
method gives an accurate approximation only when the population is large.
Lin
e o
f p
er
fe
ct
eq
ua
lit
y
Pir
at
e s
hip
: R
oy
al
Ro
ve
r
Briti
sh N
avy:
Activ
e
Britis
h Na
vy: Fa
vour
ite
0
25
50
75
100
0 25 50 75 100
Cumulative share of the ship's company from lowest (crew) to
highest income (Captain) (%)
Cu
m
ul
at
iv
e
sh
ar
e
of
in
co
m
e
(%
)
Figure 5.13 The distribution of spoils: Pirates and the Royal Navy.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
214
disposable income Income avail-
able after paying taxes and
receiving transfers from the gov-
ernment.
Market income
Disposable
income
Income from wages,
salaries, self-employment,
business, and investments
Subtract direct taxes.
Add cash transfers.
Comparing income distributions and inequality across the world
To assess income inequality within a country, we can either look at total
market income (all earnings from employment, self-employment, savings
and investments), or disposable income, which better captures living
standards. Disposable income is what a household can spend after paying
tax and receiving transfers (such as unemployment benefit and pensions)
from the government:
In Unit 1, we compared inequality in the income distributions of countries
using the 90/10 ratio. Lorenz curves give us a fuller picture of how distri-
butions differ. Figure 5.15 shows the distribution of market income in the
Netherlands in 2010. The Gini coefficient is 0.47, so by this measure it has
greater inequality than the Royal Rover, but less than the British Navy ships.
The analysis in Figure 5.15 shows how redistributive government policies
result in a more equal distribution of disposable income.
0 90 100
0
Landowners’
share of land
90 farmers 10 landowners
Perfect
equality
line
Gini coefficient for land ownership: A/(A + B) = 0.9
A
BCu
m
ul
at
iv
e
sh
ar
e
of
la
nd
(%
)
Cumulative share of the population
from least to most land owned (%)
100
Figure 5.14a The Lorenz curve and Gini coefficient for wealth ownership.
Distribution Gini
Pirate ship Royal Rover 0.06
British Navy ship Active 0.59
British Navy ship Favourite 0.6
The village with sharecroppers and landowners 0.9
Figure 5.14b Comparing Gini coefficients.
5.12 MEASURING ECONOMIC INEQUALITY
215
Notice that in the Netherlands, almost one-fifth of the households have
a near-zero market income, but most nonetheless have enough disposable
income to survive, or even live comfortably: the poorest one-fifth of the
population receive about 10% of all disposable income.
There are many different ways to measure income inequality besides the
Gini and the 90/10 ratio, but these two are widely used. Figure 5.16
compares the Gini coefficients for disposable and market income across a
large sample of countries, ordered from left to right, from the least to the
most unequal by the disposable income measure. The main reason for the
substantial differences between nations in disposable income inequality is
the extent to which governments can tax well off families and transfer the
proceeds to the less well off.
0 60 70 80 905010 100
0
10
20
30
40
50
60
70
80
90
Pe
rfe
ct
eq
ua
lity
lin
e
Dis
po
sab
le
inc
om
e
Ma
rke
t in
co
me
B′
Cu
m
ul
at
iv
e
sh
ar
e
of
in
co
m
e
(%
)
Cumulative share of the population
from lowest to highest income (%)
100 Market Gini coefficient: 0.47
Disposable Gini coefficient: 0.25
20 30 40
A′
Figure 5.15 Distribution of market and disposable income in the Netherlands
(2010).
LIS. Cross National Data Center
(https://tinyco.re/0525655). Stefan
Thewissen (University of Oxford) did the
calculations in April 2015.
1. The Lorenz curve for market income
The curve indicates that the poorest
10% of the population (10 on the hori-
zontal axis) receive only 0.1% of total
income (0.1 on the vertical axis), and
the lower-earning half of the popula-
tion has less than 20% of income.
2. The Gini for market income
The Gini coefficient is the ratio of area
A (between the market income curve
and the perfect equality line) to area A
+ B (below the perfect equality line),
which is 0.47.
3. Disposable income
The amount of inequality in disposable
income is much smaller than the
inequality in market income.
Redistributive policies have a bigger
effect towards the bottom of the distri-
bution. The poorest 10% have 4% of
total disposable income.
4. The Gini for disposable income
The Gini coefficient for disposable
income is lower: the ratio of areas A′
(between the disposable income curve
and the perfect equality line) and A′ +
B′ (below the perfect equality line) is
0.25.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
216
Notice that:
• The differences between countries in disposable income inequality (the
top of the lower bars) are much greater than the differences in inequality
of market incomes (the top of the upper bars).
• The US and the UK are among the most unequal of the high-income
economies.
• The few poor and middle-income countries for which data are available
are even more unequal in disposable income than the US but …
• … (with the exception of South Africa) this is mainly the result of the
limited degree of redistribution from rich to poor, rather than unusually
high inequality in market income.
We study redistribution of income by governments in more detail in Unit
19 (Inequality).
QUESTION 5.10 CHOOSE THE CORRECT ANSWER(S)
Figure 5.15 (page 216) shows the Lorenz curve for market income in
the Netherlands in 2010.
Which of the following is true?
If area A increases, income inequality falls.
The Gini coefficient can be calculated as the proportion of area A
to area A + B.
Countries with lower Gini coefficients have less equal income distri-
butions.
The Gini coefficient takes the value 1 when everyone has the same
income.
Market Gini
Disposable Gini
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Sl
ov
ak
ia
Cz
ec
h
Re
pu
bl
ic
Sl
ov
en
ia
Ic
el
an
d
Be
lg
iu
m
N
or
w
ay
D
en
m
ar
k
Fi
nl
an
d
Au
st
ri
a
Sw
ed
en
Po
la
nd
N
et
he
rl
an
ds
G
er
m
an
y
H
un
ga
ry
Ir
el
an
d
Sw
itz
er
la
nd
Ca
na
da
Fr
an
ce
Es
to
ni
a
G
re
ec
e
Po
rt
ug
al
Ru
ss
ia
Lu
xe
m
bo
ur
g
Au
st
ra
lia
It
al
y
Sp
ai
n
Ja
pa
n
La
tv
ia
So
ut
h
Ko
re
a
Is
ra
el
N
ew
Ze
al
an
d
Ro
m
an
ia
Li
th
ua
ni
a
U
K
U
S
Tu
rk
ey
Bu
lg
ar
ia
M
ex
ic
o
Ch
ile
Br
az
il
In
di
a
Co
st
a
Ri
ca
Ch
in
a
So
ut
h
Af
ri
ca
G
in
ic
oe
ff
ic
ie
nt
s
(v
ar
io
us
ye
ar
s,
20
13
–2
01
9)
Figure 5.16 Income inequality in market and disposable income across the world.
View this data at OWiD https://tinyco.re/
1122864
OECD. Income Distribution Database.
5.12 MEASURING ECONOMIC INEQUALITY
217
EXERCISE 5.9 COMPARING DISTRIBUTIONS OF WEALTH
The table shows three alternative distributions of land ownership in a
village with 100 people and 100 hectares of land. Draw the Lorenz curves
for each case. For cases I and III calculate the Gini. For case II, show on the
Lorenz curve diagram how the Gini coefficient can be calculated.
I 80 people own nothing 20 people own
5 hectares each
II 40 people own nothing 40 people own
1 hectare each
20 people own
3 hectares each
III 100 people own
1 hectare each
EINSTEIN
Inequality as differences among people
The Gini coefficient is a measure of inequality, precisely defined as:
To calculate g, you should know the incomes of every member of a pop-
ulation:
1. Find the difference in income between every possible pair in the pop-
ulation.
2. Take the mean of these differences.
3. Divide this number by the mean income of the population, to get the
relative mean difference.
4. g = relative mean difference divided by two.
Examples:
There are just two individuals in the population and one has all the
income. Assume their incomes are 0 and 1.
1. The difference between the incomes of the pair = 1.
2. This is the mean difference because there is just one pair.
3. Mean income = 0.5, so the relative mean difference = 1/0.5 = 2.
4. g = 2/2 = 1 (perfect inequality, as we would expect).
Two people are dividing a pie: one has 20%, and the other 80%.
1. The difference is 60% (0.60).
2. This is the mean difference (there are only two incomes, as before).
3. Mean income is 50% or 0.50. The relative mean difference is 0.6/0.5
= 1.20.
4. g = 0.60.
The Gini coefficient is a measure of how unequal their slices are. As an
exercise, confirm that if the size of the smaller slice of the pie is σ, g = 1 −
2σ.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
218
There are three people, and one has all of the income, which we
assume is 1 unit.
1. The differences for the three possible pairs are 1, 1, and 0.
2. Mean difference = 2/3.
3. Relative mean difference = (2/3)/(1/3) = 2.
4. g = 2/2 = 1.
Approximating the Gini using the Lorenz curve
If the population is large, we obtain a good approximation to the Gini
coefficient using the areas in the Lorenz diagram: g≈ A/(A + B).
But with a small number of people, this approximation is not
accurate.
You can see this if you think about the case of ‘perfect inequality’
when one individual gets 100% of the income, for which the true Gini is
1, whatever the size of the population (we calculated it for populations of
2 and 3 above). The Lorenz curve is horizontal at zero up to the last
individual, and then shoots up to 100%. Try drawing the Lorenz curves
when the size of the population, N, is 2, 3, 10, and 20.
• When N = 2 , A/(A + B) = 0.5, a very poor approximation to the true
value, g = 1.
• When N is large, area A is not quite as big as area A + B, but the ratio
is almost 1.
There is a formula that calculates the correct Gini coefficient from the
Lorenz diagram:
(Check for yourself that this works for the perfect inequality case when
N = 2.)
••5.13 A POLICY TO REDISTRIBUTE THE SURPLUS AND
RAISE EFFICIENCY
Angela and Bruno live in the hypothetical world of an economic model. But
real farmers and landowners face similar problems.
In the Indian state of West Bengal, home to more people than Germany,
many farmers work as sharecroppers (bargadars in the Bengali language),
renting land from landowners in exchange for a share of the crop.
The traditional contractual arrangements throughout this vast state
varied little from village to village, with virtually all bargadars giving half
their crop to the landowner at harvest time. This had been the norm since
at least the eighteenth century.
But, like Angela, in the second half of the twentieth century many
thought this was unfair, because of the extreme levels of deprivation among
the bargadars. In 1973, 73% of the rural population lived in poverty, one of
the highest poverty rates in India. In 1978, the newly elected Left Front
government of West Bengal adopted new laws, called Operation Barga.
5.13 A POLICY TO REDISTRIBUTE THE SURPLUS AND RAISE EFFICIENCY
219
The new laws stated that:
• Bargadars could keep up to three-quarters of their crop.
• Bargadars were protected from eviction by landowners, provided they
paid them the 25% quota.
Both provisions of Operation Barga were advocated as a way of increasing
output. There are certainly reasons to predict that the size of the pie would
increase, as well as the incomes of the farmers:
• Bargadars had a greater incentive to work hard and well: Keeping a larger
share meant that there was a greater reward if they grew more crops.
• Bargadars had an incentive to invest in improving the land: They were
confident that they would farm the same plot of land in the future, so
would be rewarded for their investment.
West Bengal enjoyed a subsequent dramatic increase in farm output per
unit of land, as well as farming incomes. By comparing the output of farms
before and after the implementation of Operation Barga, economists
concluded that both improved work motivation and investment occurred.
One study suggested that Operation Barga was responsible for around 28%
of the subsequent growth in agricultural productivity in the region. The
empowerment of the bargadars also had positive spillover effects as local
governments became more responsive to the needs of poor farmers.
Efficiency and fairness
Operation Barga was later cited by the World Bank as an example of good
policy for economic development.
Figure 5.17 summarizes the concepts developed in this unit that we can
use to judge the impact of an economic policy. Having gathered evidence to
describe the resulting allocation, we ask: is it Pareto efficient, and fair? Is it
better than the original allocation by these criteria?
The evidence that Operation Barga increased incomes indicates that the
pie got larger, and the poorest people got a larger slice.
Abhijit V. Banerjee, Paul J. Gertler,
and Maitreesh Ghatak. 2002.
‘Empowerment and Efficiency:
Tenancy Reform in West Bengal’.
Journal of Political Economy
110 (2): pp. 239–80.
Ajitava Raychaudhuri. 2004.
Lessons from the Land Reform
Movement in West Bengal, India.
Washington, DC: World Bank.
Description
(facts)
Allocation: who does what & who gets what
Is the allocation
efficient?
Could there be
mutual gains from
moving to some
other allocation?
Is the allocation fair?
Is there some
allocation that would
be fairer? Are the
rules of the game
that produced the
allocation fair?
Evaluation
(values)
Figure 5.17 Efficiency and fairness.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
220
In principle, the increase in the size of the pie means there could be
mutual gains from the reforms, with both farmers and landowners made
better off.
However, the actual change in the allocation was not a Pareto
improvement. The incomes of some landowners fell following the
reduction in their share of the crop. Nevertheless, in increasing the income
of the poorest people in West Bengal, we might judge that Operation Barga
was fair. We can assume that many people in West Bengal thought so,
because they continued to vote for the Left Front alliance. It stayed in
power from 1977 until 2011.
We do not have detailed information for Operation Barga, but we can
illustrate the effect of the land reform on the distribution of income in the
hypothetical village of the previous section, with 90 sharecroppers and 10
landowners. Figure 5.18 shows the Lorenz curves. Initially, the farmers pay
a rent of 50% of their crop to the landowners. Operation Barga raises the
farmer’s crop share to 75%, moving the Lorenz curve towards the
45-degree line. As a result, the Gini coefficient of income is reduced from
0.4 (similar to the US) to 0.15 (well below that of the most equal of the rich
economies, such as Denmark). The Einstein at the end of this section shows
you how the Gini coefficient depends on the proportion of farmers and
their crop share.
0 90 100
0
Landowners’
share of
initial income
Initial Gini coefficient: 0.40
Gini coefficient after land tenure reform: 0.15
Farmers’
share of
initial income
Lorenz curve
shifts due to
land tenure
reform
90 farmers 10 landowners
Cu
m
ul
at
iv
e
sh
ar
e
of
in
co
m
e
(%
)
Cumulative share of the population
from the lowest to the highest income (%)
100
75
50
25
Figure 5.18 Bargaining in practice: How a land tenure reform in West Bengal
reduced the Gini coefficient.
5.13 A POLICY TO REDISTRIBUTE THE SURPLUS AND RAISE EFFICIENCY
221
EINSTEIN
The Lorenz curve and the Gini coefficient in a class-divided
economy with a large population
Think about a population of 100 people in which a fraction n produce
the output, and the others are employers (or landlords, or other
claimants on income who are not producers).
Take, as an example, the farmers and landlords in the text (in West
Bengal). Each of the n × 100 farmers produces q and he or she receives a
fraction, s, of this; so each of the farmers has income sq. The (1 − n) × 100
employers each receive an income of (1 − s)q.
The figure below presents the Lorenz curve and the perfect equality
line similar to Figure 5.18 in the text.
0 n
A
B1 B2
B3
100
0
100n farmers 100(1 – n) landowners
Cu
m
ul
at
iv
e
sh
ar
e
of
in
co
m
e
(fr
ac
tio
n)
Cumulative share of the population
from the lowest to the highest income (%)
1
s
Figure 5.19 The Lorenz curve and the perfect equality line.
The slope of the line separating area A from B1 is s/n (the fraction of
total output that each farmer gets), and the slope of the line separating
area A from B3 is (1 − s)/(1 − n), the fraction of total output that each
landlord gets. We can approximate the Gini coefficient by the expression
A/(A + B), where in the figure B = B1 + B2 + B3.
So we can express the Gini coefficient in terms of the triangles and
rectangle in the figure. To see how, note that the area of the entire square
is 1 while the area (A+B) under the perfect equality line is 1/2. The area
A is (1/2) − B. Then we can write the Gini coefficient as
We can see from the figure that
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT
222
so,
This means that the Gini coefficient in this simple case is just the
fraction of the total population producing the output (the farmers)
minus the fraction of the output that they receive in income.
Inequality will increase in this model economy if:
• The fraction of producers in the economy increases but the total
share of output they receive remains unchanged. This would be the
case if some of the landlords became farmer tenants, each receiving a
fraction s of the crop they produced.
• The fraction of the crop received by the producers falls.
5.14 CONCLUSION
Economic interactions are governed by institutions, which specify the rules
of the game. To understand the possible outcomes, we first consider what
allocations are technically feasible, given the limits imposed by biology and
technology. Then, if participation is voluntary, we look for economically
feasible allocations: those which could provide mutual gains (a surplus), and
therefore are Pareto-improving relative to the reservation positions of the
parties involved.
Which feasible allocation will arise depends on the bargaining power of
each party, which determines how a surplus will be shared and in turn
depends on the institutions governing the interaction. We can evaluate and
compare allocations using two important criteria for judging economic
interactions: fairness and Pareto efficiency.
Concepts introduced in Unit 5
Before you move on, review these definitions:
• Institutions
• Power
• Bargaining power
• Allocation
• Pareto criterion, Pareto domination and Pareto improvement
• Pareto efficiency
• Pareto efficiency curve
• Substantive and procedural concepts of fairness
• Economic rent (compared to land rent)
• Joint surplus
• Lorenz curve and Gini coefficient
5.15 REFERENCES
Consult CORE’s Fact checker for a detailed list of sources.
5.15 REFERENCES
223
Banerjee, Abhijit V., Paul J. Gertler, and Maitreesh Ghatak. 2002.
‘Empowerment and Efficiency: Tenancy Reform in West Bengal’
(https://tinyco.re/9394444). Journal of Political Economy 110 (2):
pp. 239–280.
Clark, Andrew E., and Andrew J. Oswald. 2002. ‘A Simple Statistical
Method for Measuring How Life Events Affect Happiness’
(https://tinyco.re/7872100). International Journal of Epidemiology
31 (6): pp. 1139–1144.
Leeson, Peter T. 2007. ‘An–arrgh–chy: The Law and Economics of Pirate
Organization’. Journal of Political Economy 115 (6): pp. 1049–94.
Lorenz, Max O. 1905. ‘Methods of Measuring the Concentration of Wealth’
(https://tinyco.re/5844930). Publications of the American Statistical
Association 9 (70).
Pareto, Vilfredo. 2014. Manual of political economy: a variorum translation
and critical edition. Oxford, New York, NY: Oxford University Press.
Raychaudhuri, Ajitava. 2004. Lessons from the Land Reform Movement in West
Bengal, India (https://tinyco.re/0335719). Washington, DC: World
Bank.
UNIT 5 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT