Welfare and state
intervention, taxation
Inequality
Pareto efficiency
The theorems of welfare
Welfare and state intervention, taxation

Welfare theory is a particular aspect of
economics, which attempts to measure and
influence welfare at the level of the
economy, and not the individual



What makes it particular is that it typically
contains normative aspects (value judgments)
Ex: How can you determine a “fair” allocation ?
But it is an important part of economic
theory

And an important part of an economist’s job!
Welfare and state intervention, taxation
Measuring inequality
Pareto efficiency
The theorems of welfare
The effects of taxation
Measuring inequality


Why is inequality an important issue?
Why is it important to be able to measure it?



Inequality is often important from a public
perception point of view
Therefore it is important as a policy issue, so it
needs to be measured properly
From the point of view of positive theory,
inequality is not really the issue, efficiency is

remember the “cool head & warm heart” idea of
Samuelson
Measuring inequality

First, there are different types of inequalities




Income : minimum wage in France 12000 € annually
vs. 6.57million € for the CEO of l’Oreal in 2004 (he’s
worth it…)
Wealth : Bill Gates’ 59 Billion $ vs. an unskilled
labourer (his only asset is the value of his time)
Ability : Zidane, Federer, Eminem vs. adults with
untreated learning disabilities
Not all can be easily measured or modified
by public intervention

The typical focus is on income/wealth inequality
Measuring inequality

The following data gives the distribution of
income over the US population
Share of income by quintiles
Year
Lowest
Second
Middle
Fourth
Highest
1998
3,6
9
15
23,2
49,2
1988
3,8
9,6
16
24,3
46,3
1978
4,3
10,3
16,9
24,8
43,7
1968
4,2
11,1
17,5
24,4
42,8
 Source: US Census Bureau
Measuring inequality

Let’s see what this table says in terms of the
evolution of inequality :
Share of income by quintiles

Year
Lowest
Second
Middle
Fourth
Highest
1998
3,6
9
15
23,2
49,2
1988
3,8
9,6
16
24,3
46,3
1978
4,3
10,3
16,9
24,8
43,7
1968
4,2
11,1
17,5
24,4
42,8
Income inequality has increased over the period
Measuring inequality

There is a much easier way of visualising
this data:


The Lorenz curve
Definition


The Lorenz curve is the plot of the cumulative
share of income
This variable is not really intuitive in a table, but
very useful in a graph
 You can find the share of income of any given
percentage of the population
Measuring inequality

Let’s calculate the cumulative shares for
1998:
Share of income by quintiles
Year
Lowest
Second
Middle
Fourth
Highest
1998
3,6
9
15
23,2
49,2
Cumulative share
1998
3,6
12,6
27,6
50,8
100
Measuring inequality

Plot of the curve :
100
90



The green line is
the even
distribution
The red is the
Lorenz curve
It gives the share
of income of any
given % of the
population
80
70
60
50
Even
40
1998
30
20
10
0
0
20
40
60
80
100
Measuring inequality

Let’s add the
curve for 1968
as a comparison
100
90
80
70
60
50
Even
40
1998
30
20
10
0
0
20
40
60
80
100
Measuring inequality


Let’s add the
curve for 1968
as a comparison
There is less of a
“bulge” in the
Lorenz curve
100
90
80
70
60
Even
50
1998
40

Income was
more equally
distributed in
1968
1968
30
20
10
0
0
20
40
60
80
100
Measuring inequality


Lorenz curve provides an easy, visual way of
identifying changes in the distribution of
income
It also provides a numerical measure of
inequality


The Gini coefficient (or Gini Index)
This coefficient allows us to rank any set of
distributions from the most unequal to the most
equal
Measuring inequality

The Gini coefficient is
calculated as follows:
100
90
80
A
g
A B

It tells us what percentage
of the distribution space
is occupied by the “bulge”
of the Lorenz curve

The higher the
percentage, the more
unequal the distribution
70
60
50
40
A
30
B
20
10
0
0
20
40
60
80
100
Measuring inequality

Extreme case N°1:
100
90

The distribution of
income is perfectly even

A=0
A
g
A B
0
g
0
0 B

The Gini coefficient is 0 if
there is no inequality
80
70
60
50
40
B
30
20
10
0
1
2
3
4
5
6
Measuring inequality

Extreme case N°2:
100
90

The distribution of income
is perfectly uneven

B=0
A
g
A B
A
g
1
A0

The Gini coefficient is 1 if
there is perfect inequality
80
70
60
50
40
A
30
20
10
0
1
2
3
4
5
6
Measuring inequality

Evolution of the Gini coefficient of income
Brazil
Canada
Costa
Rica
Finland
Japan
Nether
-lands
1977
0,60*
0,32
0,5
0,3
0,34
0,28
1981
0,55
0,32
0,48
0,32
0,34
0,27
1984
0,57**
0,33
0,47*
0,31
0,36*
0,28*
1989
0,59
0,28
0,46
0,26*
0,38
0,3
Notes
* 1976
** 1983
*1983
*1991
*1985
*1983

Source: World Bank, K.W. Deininger
Welfare and state intervention, taxation
Measuring inequality
Pareto efficiency
The theorems of welfare
The effects of taxation
Pareto efficiency

Definition of Pareto efficiency (Vilfredo
Pareto) :


A Pareto-improvement:


An allocation is Pareto-efficient if it is not
possible to make an agent better off without
making an other agent worse off
Makes at least one agent better off, all other
agents begin equally well-off as before.
A Pareto efficient allocation is one where
there are no possible Pareto-improvements
Pareto efficiency


This can be analysed more intuitively using
an “Edgeworth box”
This is a theoretical tool used to examine
the trading decisions of:



Two agents: 1 and 2
Trading two goods A and B
Main advantage: it is based on consumer
choice theory
Pareto efficiency
Building an Edgeworth box
Agent 1
Agent 2
Good A
Good A
Amax
Amax
Bmax
Good B
Bmax
Good B
Pareto efficiency
Building an Edgeworth box
Agent 1
Agent 2
Good A
Good A
Amax
Amax
Bmax
Good B
Bmax
Good B
Pareto efficiency
Building an Edgeworth box
Good A
Agent 2
Bmax
Good B
Amax
Amax
Agent 1
Bmax
Good A
Good B
Pareto efficiency

Bmax
Agent 2
Amax

Amax
Agent 1
Bmax

Any point within the box
is a possible allocation
It divides the total
amount of goods A and B
available between agents
1 and 2
But how do we determine
which ones are Pareto
efficient, and which ones
are not ?
Pareto efficiency

Agent 2
Bmax

Amax

Y
X
Agent 1
Let’s re-introduce some
indifference curves and
an allocation (X)
Is X Pareto efficient ?
Bmax
Amax

No, because by trading
goods, both agents can
move to a higher
indifference curve !
X → Y is a Paretoimprovement

Y, however, is Pareto
efficient.
Pareto efficiency

Agent 2
Bmax
Amax
Y

X
Agent 1
Amax
So all the points where
the indifference curves
are tangent are Paretoefficient.
Joining them up gives the
set of all the possible
Pareto-efficient
allocations.
Bmax

This is know as the
“Contract Curve”
Welfare and state intervention, taxation
Measuring inequality
Pareto efficiency
The theorems of welfare
The effects of taxation
The theorems of welfare

There are 2 “fundamental theorems of
Welfare”



They are also due to Pareto
They can be analysed using the Edgeworth box
Although they might seem a little “dry” in
their definitions, they are crucial to
understanding :


Why economists see free markets as a social
optimum,
Why there can nevertheless be a role for public
intervention.
The theorems of welfare

The 1st fundamental theorem of welfare



All competitive market equilibria are Paretoefficient.
In other words, a competitive market will exhaust
all the possible gains from trade
This is illustrated by the example we saw in the
Edgeworth box: people are willing to trade until
their indifference curves are tangent and there
are no further gains to trading.
The theorems of welfare

The 1st fundamental theorem of welfare



However, as we saw previously with the contract
curve, this does not tell us anything about the
other desirable properties of the equilibrium
The Pareto-efficient allocation might not be “fair”
Remember, if Agent 1 owns everything and
Agent 2 owns nothing, this is an efficient
allocation, but maybe not a socially desirable
one!
The theorems of welfare

The 2nd fundamental theorem of welfare
 If preferences are convex, there is always a
set of prices such that each Pareto-efficient
equilibrium is a market equilibrium for
appropriate initial endowments


With convex preferences, the Pareto-efficient
allocation is determined by the tangency of 2
indifference curves
Remember basic consumer choice: this slope
will also give the relative prices!!
The theorems of welfare

The 2nd fundamental theorem of welfare
Bmax
Amax
Z
Agent 1
X
∙ Imagine we are at X, But we’d
Agent 2
rather be at Z, in terms of
fairness.
∙ The theorem tells us that
because preferences are
convex, there exists a set of
relative prices (the dotted
line) which supports this
Y
equilibrium
Amax
∙ Z can be achieved simply by
Bmax
redistributing the initial
endowment to Y
The theorems of welfare

Implications of the 2 theorems



1st : Under the assumption of competitive
behaviour, markets with selfish agents can
achieve the highest possible efficiency
2nd : Under the assumption of “well behaved”
preferences, the allocative role of prices
(scarcity) is separate from the distributive role
(the constraint on your level of consumption)
The 2 can be separated: The state can
redistribute the initial endowments, and leave
the market to allocate efficiently
Welfare and state intervention, taxation
Measuring inequality
Pareto efficiency
The theorems of welfare
The effects of taxation
The effects of taxation

The 2nd fundamental theorem of welfare
tells us that we can move to a different
Pareto-efficient allocation by redistributing
the initial endowment


In practice, this would amount to taxing the
initial endowments and redistributing as
necessary
But in reality, there is a problem

What is an “endowment” ? How do we tax it ?
The effects of taxation

For most people, the basis of their
endowment is the amount of labour they
could sell on the market




It is not a simple bundle of goods (as in the
Edgeworth box)
So taxing their income, (the labour they have
sold) affects the relative price of labour (the
wages)
This can in turn affect the decision to sell labour
The tax distorts the relative prices, and there is
an efficiency loss
The effects of taxation

This effect is not too large, as labour supply
decisions are not that sensitive (as we will
see in a few weeks)


But this points out the difficulty of going from
the theoretical results to the practical reality
Another problem is when taxes / subsidies
affect the price of goods directly. (ex, VAT)


The distortion on prices can be very important in
this case
Read about the example of Iraq in Varian, p.306
The effects of taxation
P
Deadweight
loss
S
Pcons.
Unit
Tax
T
Pprod.
D
Q1
Q
The effects of taxation
P
S
Pprod.
Unit
Subsidy
Deadweight
loss
Pcons.
D
Q1
Q