Welfare and state intervention, taxation Inequality Pareto efficiency The theorems of welfare.

Welfare and state intervention, taxation

InequalityPareto efficiency

The theorems of welfare


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!


Measuring inequality

Pareto efficiency


The effects of taxation


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


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


The following data gives the distribution of income over the US population

Source: US Census Bureau

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




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


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


Let’s calculate the cumulative shares for 1998:



1998 3,6 9 15 23,2 49,2

Cumulative share

1998 3,6 12,6 27,6 50,8 100


Plot of the curve :

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


Let’s add the curve for 1968 as a comparison


Let’s add the curve for 1968 as a comparison

There is less of a “bulge” in the Lorenz curve

Income was more equally distributed in 1968


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


The Gini coefficient is calculated as follows:

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

AB

BA

Ag


Extreme case N°1:

The distribution of income is perfectly even

A=0

The Gini coefficient is 0 if there is no inequality

BBA

Ag

00

0

Bg


Extreme case N°2:

The distribution of income is perfectly uneven

B=0

The Gini coefficient is 1 if there is perfect inequality

ABA

Ag

10

A

Ag


Evolution of the Gini coefficient of income

Source: World Bank, K.W. Deininger

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



Pareto efficiency



Pareto efficiency

Definition of Pareto efficiency (Vilfredo Pareto) : An allocation is Pareto-efficient if it is not

possible to make an agent better off without making an other agent worse off

A Pareto-improvement: 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

Good A Good A

Building an Edgeworth box

Agent 1 Agent 2

Good BGood B

Amax

Bmax

Amax

Bmax

Pareto efficiency

Good A Good A


Agent 1 Agent 2

Good BGood B

Amax

Bmax

Amax

Bmax

Pareto efficiency

Good A

Good A


Agent 1

Agent 2

Good B

Good BAmax

Bmax

Amax

Bmax

Pareto efficiency

Agent 1

Agent 2

Amax

Bmax

Amax

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 1

Agent 2

Amax

Bmax

Amax

Bmax

Let’s re-introduce some indifference curves and an allocation (X)

Is X Pareto efficient ? No, because by trading

goods, both agents can move to a higher indifference curve !

X → Y is a Pareto-improvement Y, however, is Pareto

efficient.

Y

X

Pareto efficiency

Agent 1

Agent 2

Amax

Bmax

Amax

Bmax

So all the points where the indifference curves are tangent are Pareto-efficient.

Joining them up gives the set of all the possible Pareto-efficient allocations.

This is know as the “Contract Curve”

Y

X



Pareto efficiency




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 1st fundamental theorem of welfare All competitive market equilibria are Pareto-

efficient.

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 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 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 2nd fundamental theorem of welfare

Agent 1

Agent 2

Amax

Bmax

Amax

Bmax

∙ Imagine we are at X, But we’d 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 equilibrium

∙ Z can be achieved simply by redistributing the initial endowment to Y

Y

XZ


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



Pareto efficiency




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 problemWhat is an “endowment” ? How do we tax it

?


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


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


P

QQ1

Pcons.

Pprod.

TUnit Tax

Deadweight loss

S

D


P

QQ1

Pcons.

Pprod.

Unit Subsidy

Deadweight loss

S

D

Welfare and state intervention, taxation Inequality Pareto efficiency The theorems of welfare.

Documents

income inequality

incomewealth inequality

measuring inequality

evolution of inequality

lorenz curve income

comparison slide

theorems of welfare

cumulative share of