LECTURE 4

WELFARE ECONOMICS

LEARNING OUTCOMES/OBJECTIVES

By the end of this lecture learners should be able to:

 Explain the meaning of welfare economics

 Explain how welfare can be improved using economic policies

 Explain the two fundamental theorems of welfare

 Use the Edgeworthian- box two show how exchange between two individuals improves

the welfare of participating individuals

INTRODUCTION

Welfare economics is a branch of economics concerned with improving human welfare and

social conditions chiefly through the optimum distribution of wealth, the relief or reduction of

unemployment. Traditional welfare economics tends to identify a person's well-being with the

person's command over goods and services. This naturally leads to a focus on income, since a

person's income determines how much he or she can consume. Going a step further, this

approach often views each person as being endowed with a “utility or welfare function,” and

the person's income as an important variable that determines the level of utility that the person

enjoys. Social welfare, according to this approach, is represented by aggregating the utility

levels of all individuals in society.

1
FUNDAMENTAL THEOREMS OF WELFARE

The First Fundamental Welfare Theorem

Asserts that market equilibria are Pareto efficient. In a pure exchange economy, a sufficient

condition for the first welfare theorem to hold is that preferences be locally non satiated. The

first welfare theorem also holds for economies with production regardless of the properties of

the production function. Implicitly, the theorem assumes complete markets and perfect

information. In an economy with externalities, for example, it is possible for equilibria to arise

that are not efficient.

The first welfare theorem is informative in the sense that it points to the sources of inefficiency

in markets. Under the assumptions above, any market equilibrium is tautologically efficient.

Therefore, when equilibria arise that are not efficient, the market system itself is not to blame,

but rather some sort of market failure.

Second Fundamental Theorem of Welfare Economics

Even if every equilibrium is efficient, it may not be that every efficient allocation of resources

can be part of an equilibrium. However, the second theorem states that every Pareto efficient

allocation can be supported as an equilibrium by some set of prices. In other words, all that is

required to reach a particular Pareto efficient outcome is a redistribution of initial endowments

of the agents after which the market can be left alone to do its work. This suggests that the

issues of efficiency and equity can be separated and need not involve a trade-off. The conditions

for the second theorem are stronger than those for the first, as consumers' preferences and

production sets now need to be convex (convexity roughly corresponds to the idea of

2
diminishing marginal rates of substitution i.e. "the average of two equally good bundles is

better than either of the two bundles").

THEORIES IN WELFARE ECONOMICS

1. Pareto Optimality THEORY

We now turn to the concept of Pareto Optimality, named after the economist Vilfredo Pareto. It is a

concept that you will find recurring frequently in the economics literature. The main proposition of

Pareto Optimality can be summed up as follows.

An economy is in a Pareto Optimal state when no further changes in the economy can make

one person better off without at the same time making another worse off.

You may immediately recognise that this is the socially optimal outcome achieved by a perfectly

competitive market referred to above. It can be shown that an economy will be Pareto Optimal when

the economy is perfectly competitive and in a state of static general equilibrium. The intuitive case for

this is based on the fact that prices reflect economic values in a competitive market. If a unit of goods

or services could produce more or bring greater satisfaction in some activity other than its present use,

someone would have been willing to bid up its price, and it would have been attracted to the new use.

When this price system is in equilibrium, the marginal revenue product, the opportunity cost, and the

price of a resource or asset will all be equal. Each unit of every good and service is in its most

3
productive use or best consumption use. No transfer of resources could result in greater output or

satisfaction.

This can be examined more formally in terms of three criteria that have to be met for a market

equilibrium to result in Pareto Optimality. These are that there should be: exchange efficiency,

production efficiency and output efficiency.

Exchange efficiency

Exchange efficiency occurs when, for any given bundle of goods, it is not possible to redistribute

them such that the utility (welfare) of one consumer is raised without reducing the utility (welfare) of

another consumer.

A simple example of this is where there are two individuals, one with a loaf of bread, the other with a

block of cheese. Both can be made better off by exchanging bread for cheese. An efficient exchange

system will allow exchange of bread and cheese to take place until neither party can be made better

off without one of them becoming worse off.

In a multi-product, multi-consumer economy, exchange is far more complex and involves the use of

money to facilitate exchange. However, the principle is the same. So long as products can be

reallocated to make one person better off without making another worse off, the economy is operating

sub-optimally from the point of view of exchange efficiency. In a perfectly competitive market,

exchange will occur until this criterion is met.

Exchange efficiency alone does not necessarily result in Pareto Optimality. This is because it relates

only to a specific bundle of goods. It may be possible to make one or more individuals even better off

- without making any one else worse off - by altering the bundle of goods produced in the economy.

4
This could involve raising the total volume of goods produced, as well as altering the combination of

goods produced.

Production efficiency

Production efficiency occurs when the available factors of production are allocated between products

in such a way that it is not possible to reallocate the production factors so as to raise the output of one

product without reducing the output of another product.

This is analogous to technical or production efficiency at the level of the firm. What is being said here

is that there are many situations in which it is possible to raise the total output in an economy by

simply reallocating factors of production at no additional cost. This is because factors of production

are more productive in some uses than they are in others. In a competitive economy, producers bid for

factors of production until they are reallocated to their most productive use.

For example, if there is a lot of unproductive, low-wage labour employed in the agricultural sector

and labour shortages in the industrial sector where labour productivity is potentially high, factory

owners will bid up the price of labour and draw labour from the agricultural sector into the industrial

sector. This could significantly raise output in the industrial sector without having a negative impact

on output in the agricultural sector. So long as factors of production can be redistributed in a way that

increases the output of one product without reducing the output of others, the economy is operating

sub-optimally in terms of production efficiency.

Output efficiency

Output efficiency occurs where the combination of products actually produced is such that there is no

alternative combination of products that would raise the welfare of one consumer without reducing

the welfare of another.

5
Both the exchange efficiency and the production efficiency criteria must hold in order for this

criterion to be met. The combination of outputs produced according to this criterion is distributed

between consumers according to the exchange efficiency criterion, and the economy is operating with

production efficiency.

Pareto Optimality is the result of rational economic behaviour on the part of producers, consumers

and owners of factors of production in a perfectly competitive economy. Although we don't have the

scope to examine the underlying theory here it can be shown that Pareto Optimality will be achieved

if all markets are perfectly competitive and in equilibrium.

It is important to realise that, whilst Pareto Optimality is the outcome in an economy that meets each

of the three efficiency criteria listed earlier, this does not mean that there is only one 'optimal'

allocation of resources. A Pareto efficient economy results in the maximisation of aggregate

economic welfare for a given distribution of income and a specific set of consumer preferences. A

shift in income distribution changes the incomes of individual consumers. As their incomes change,

so too will their preferences, as their demand curves for various products shift to the left or right. This

will result in a different equilibrium point in the various markets that make up the economy. Every

alternative distribution of income or set of preferences is characterised by a different Pareto Optimum.

Thus, since there is an infinite number of different ways in which income can be distributed, there is

also an infinite number of different Pareto Optimal equilibriums.

Obviously, in practice, no economy can be expected to attain the Pareto Optimum position.

Moreover, the Pareto principle is of little practical use as a policy tool since it is rarely possible to

devise a policy that makes someone better off without making someone else worse off. Nevertheless,

it is an important concept in the neo-classical tradition of economics and integrates much of the

theory. It is also a standard against which economists can explore the real world, where making one

person better off almost invariably means making someone else worse off.

6
USING EDGEWORTH BOX TO SHOW PARETO OPTIMALITY

Edgeworth diagram is divided into two types. The horizontal side of the box measures a fixed

total output of good 1 and the vertical side measures a fixed total output of good 2. Individual

1’s consumption of good 1 is measured horizontally from the origin at o 1. His/ her consumption

of good 2 is vertical from o1. In the diagram, consumption of individual 2 is measured from the

origin at o2. The Edgeworth box diagram assumed that there is non-satiation of consuming

commodities.

It means that it cannot be efficient to have total consumption of any good which is less than the

output of the good. Therefore we need to restrict attention to consumption bundles for the

individuals. It will add up to the total output of the two goods. In the Edgeworth box diagram,

a single point is defined as the consumption bundle of both individuals. The allocation A0 has

individual 1’s allocation and he is getting the consumption bundle (x011, x012).

The individual 2 is getting (x021, x022) the consumption bundle. If we assume that the individual

labour supply is constant then we need to draw different indifference curve. We can draw

another indifference curve for two commodities. Such indifference curves are drawn for two

commodities. Both the individuals have strictly quasi-concave utility function. Therefore the

indifference curves for individuals are convex to their origin.

7
In the Edgeworth box diagram, the allocation A0 is not Pareto efficient. It is possible to

exchange commodities between two individuals so as to make them both better off. The

allocation A’ is Pareto superior than A0. Such new allocation puts both individuals on

indifference curves. It is further from their respective origins. The A2 allocation in the diagram

is inversely of the A0 allocation. It is lens shaped area and it is defined by the indifference

curves through A0.

The allocation A2 is superior to A0. In the above diagram, allocation cannot cross the

indifference curves. This is because all allocations are Pareto efficient. There are different

allocations in the box diagram. The indifference curves are tangent at A1, A3 or A4. All tangent

point in the box diagram is efficient. The indifference curves and its slope are negative. It is

because of the marginal rate of substitution.

8
In the box diagram, the locus cc of points of tangency between the indifference curves. Such

point is a tangency between two curves. Such points are set of all Pareto efficient allocations

of given total output. It is measured both sides of the diagram. In the exchange economy that

is barter system where goods are exchanged for goods, the consumers have fixed endowments

of consumption goods. The efficient consumption conditions are required for the Pareto

efficiency.

In the box diagram, each allocation and point generates the utility combinations. Such utility

combinations are written as (u1, u2). The Pareto efficient allocations on the curve cc would

generate utility combinations. Such utility combinations of the individuals are considered as

utility frontiers. The inefficient allocations would generate combinations inside the utility

frontier.

Kaldor-Hicks Efficiency THEORY

Pareto efficiency occurs where at least one party benefits and nobody is made worse off. Kaldor

Hicks states that a decision can be more efficient – as long as there is a net gain to society –

enabling any potential losers to be compensated from the net gain.

Example of Kaldor Hicks

9
The total benefit is £220m. But, two groups lose out – local residents and the environment.

To build the airport would not be Pareto efficient because although there is a net gain of £170m

– two groups lose out and are worse off.

However, according to the Haldor-Hicks criteria, it would be efficient to go ahead because of

the net-gain and the fact that, in theory, the groups losing out could be compensated.

Under Kaldor Hicks, the key principle is the idea that, in theory, people could be compensated.

This compensation doesn’t actually have to occur. Whereas under Pareto efficiency, this

compensation would have to occur through voluntary agreements between two parties.

Kaldor-Hicks criteria may be used to judge the effectiveness of a Cost-Benefit

Analysis scheme.

Problems of Kaldor Hicks

 Just because, in theory, compensation may be given to those who lose out, in practice

it may not. Local residents would feel unfairly treated if the airport went ahead.

10
 Kaldor-Hicks criteria can lead to an increase in inequality and be perceived as unfair.

For example, those under flight path may feel it is unfair they have been singled out to

have to put up with an airport nearby.

 It places economic welfare and total economic utility above other moral considerations.

Utilitarianism vs notions of fairness.

SELF TEST QUESTIONS.

QUESTION1

Consider a society of two individuals (Jones and Kay) with two goods (X and Y). Let Xi and

Yi(i=J,K) denote individual i's consumption of X and Y. The preferences of J and K are known

to be represented by UJ =XJYJ and UK = Xk 2Yk YJ . Initial endowments are: Jones has 8 X and

8 Y; Kay has 10 X and 16 Y.

a. Determine the competitive equilibrium and the resulting utility levels.

b. As you can see from Kay's utility function, he suffers from a "keep up with the Joneses"

complex regarding the consumption of Y. Does this particular externality result in a

competitive equilibrium which is not Pareto optimal? Analytically verify your answer by

demonstrating Pareto optimality (or nonoptimality) or by providing a counterexample.

QUESTION2

Individuals A and B both derive utility from the consumption of Food and all other Goods. A

is more wealthy, but she is also altruistic because she derives utility from B's consumption of

food. Utility functions are Agricultural Economics 636 EOL © by Dr. Ron Griffin 6 UA = FA 2GA

2 FB 1/2 and UB = FB 2GB 2. The initial endowment is FA,GA,FB, G (B) = (10,10,2,2). Show

whether or not self-interested market behaviour will lead to economic efficiency in this

situation.

11
FURTHER READING SUGESTIONS

Read and make notes on:

The remaining theories of welfare economics.

12