Micro-Economics-II (ECB-201) B.

A (IIIrd Semester)

Unit-III
GENERAL EQUILIBRIUM AND WELFARE ECONOMICS

Structure
3.0 Introduction
3.1 Unit Objectives
3.2 Edgeworth Box Analysis of an Exchange Economy
3.3 Equilibrium and Efficiency under Pure Exchange
3.4 Production Problems of Measuring Welfare
3.5 Marshallian Approaches
3.6 Pareto’s Welfare Criteria
3.7 Concept of Social Welfare Function
3.8 Summary
3.9 Answer to Check Your Progress
3.10 Questions and Exercises

3.0 Introduction
The modern conception of general equilibrium is provided by a model developed
jointly by Kenneth Arrow, Gérard Debreu, and Lionel W. McKenzie in the 1950s.
General equilibrium analysis is the branch of economics concerned with the
simultaneous determination of prices and quantities in multiple inter-connected markets.
General equilibrium theory tries to ascertain whether independent action by each decision-
maker leads to a position in which equilibrium is attained by all. A general equilibrium is
defined as a state in which all markets and all decision-making units are simultaneously in
equilibrium.
On the other hand the welfare definition of economics is an attempt by Alfred
Marshall, a pioneer of neoclassical economics, to redefine his field of study. This definition
expands the field of economic science to a larger study of humanity. Welfare economics
seeks to evaluate the costs and benefits of changes to the economy and guide public policy
toward increasing the total good of society, using tools such as cost-benefit analysis and
social welfare functions.

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3.1 Unit Objectives

General equilibrium analyzes the economy as a whole, rather than analyzing single
markets like with partial equilibrium analysis. General equilibrium shows how supply and
demand interact and tend toward a balance in an economy of multiple markets working at
once whereas Welfare economics seeks to evaluate the costs and benefits of changes to the
economy and guide public policy toward increasing the total good of society, using tools such
as cost-benefit analysis and social welfare functions.
Thus this unit helps the knowledge seekers to ascertain as to how a student of
economics can maintain equilibrium together with welfare of society.
3.2 Edgeworth Box Analysis of an Exchange Economy
The General Equilibrium of Production and Exchange!
There are several points on the transformation curve; each point will indicate a
different price ratio of the two goods and a different production equilibrium indicating a
different output-mix of the two goods. The general equilibrium of production can occur at
any of the points on the given transfor-mation curve depending upon the prevailing price ratio
of the two goods.
Now, an important question is which of these price ratios of commodities or MRTXY
will be the equilibrium ratio. The general equilibrium level of price ratio (P X/PY) or MRTXY
will be one which on the one hand maximises profits of the firms and on the other maximises
satisfaction of consumers. To analyse the equilibrium price ratio determining output-mix, we
have to introduce in our analysis the consumer’s preference pattern or demand for goods.
It can be easily shown that if MRSXY of the consumers is not equal to the MRTXY in
the production, consumer satisfaction will not be maximised with the result that further
changes in the price ratio of the two goods and output-mix will tend to occur.
Since the marginal rate of transformation (MRTXY) shows the rate at which one good
is ‘transformed’ into another in the production process and marginal rate of substitution
measures the rate at which consumers are willing to exchange one good for the other,
equilibrium cannot be reached unless the two rates are equal.
Thus, only when MRTXY equals MRSXY planned pattern of production will be
consistent with the preferences of consumers and ensure general equilibrium of production
and exchange. This can be made clear with a simple numerical example. For instance,
suppose at a given output-mix of two goods X and Y MRTXY of the producers of the
economy is 3Y/lX and MRSXY of consumers equals 2Y/lX.

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Thus, in this case MRSXY of consumers is less than MRTXY of producers. That is, the
economy can produce 3 units of Y by foregoing one unit of good X, while the consumers are
willing to exchange or buy 2 units of Y for one unit of X. MRS XY of consumers being less
than MRTXY of producers implies that relatively greater quantity of commodity X and the
smaller quantity of commodity Y is being produced than desired by the consumers.
Obviously, if the economy reduces the production of X by one unit and product 3
units more of Y and give them to the consumers, their satisfaction or welfare will increase as
they are willing to get 2 units of Y for the sacrifice of one unit of X. Thus consumers’
satisfaction can be raised by expanding the production of Y and reducing the production of X
until the two rates, namely, MRSXY of consumers and MRTXY of producers become equal.
General equilibrium will thus be reached if with adjustment in output-mix of the two
commodities, MRSXY equals MRTXY. In a free market economy, forces of competition would
ensure such adjustment which will bring about product-mix that will equate MRSXY of
consumers with MRTXY of producers and thus ensuring maximum consumers’ satisfaction.
The general equilibrium of production together with the general equilibrium of exchange (or
consumption) requires that the marginal rate of transformation (MRTXY) be equal not only to
marginal rate of substitution (MRSXY) of the consumers but also MRSXY of the two
consumers be equal to each other.
Thus, for the achievement of general equilibrium of production and exchange
simultaneously we arrive at the following condition:
MRTXY = MRSAXY = MRSBXY
The overall general equilibrium of production and exchange is illustrated in Figure
3.1 and 3.2. Consider Figure 3.1 where a transformation curve TT’ has been drawn. Let us
consider the point L on the production transformation curve TT’. At point L on it OM of
good X and ON of good Y are being produced.
With the given preference pattern and resource endowments of the two consumers,
their indifference curves are tangent to each other at point S and their MRSXY is indicated by
the slope of the tangent line kk’. It will be seen from Figure 3.1 that MRSXY of consumers is
less than MRTXY of producers indicating that production pattern is inconsistent with
consumer’s preferences.

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Figure 3.1: General Disequilibrium

Thus, the system is in disequilibrium indicating that relatively greater quantity of X

and smaller quantity Y is being produced than desired by the consumers. In response to this
disequilibrium situation and to maximise their profits producers would tend to produce more
of Y and less of X and this process of adjustment in output mix will continue until the
MRTXY in production is brought into equality with MRSXY of consumers.
Figure 3.2: General Equilibrium

With this equality, general equilibrium of production and exchange (consump-tion)

would be attained. This general equilibrium is shown in Figure 37.6 where at position Q ‘on
the transformation curve TT’, OX2 level of output of X and OY2 level of output of Yare being
produced and MRTXY at point equals MRSXY at E (slopes of JJ’ and PP’ are equal).

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Note that there is general equilibrium of production at point Q’ because all points of
transformation curve corresponds to the points of the production contract curve. There is
general equilibrium of exchange or consumption as MRS of, the two individuals are the same
(their indifference curves being tangent to each other at point E).
There is joint equilibrium of production and exchange as the MRT in production is
equal to MRSXY of the two individuals at the consumption equilibrium point E. Thus, with
point Q on the transformation curve TT’ and point E on the consumption contract curve
drawn in the Edgeworth Box made from point Q’, the following condition of general
equilibrium of production and consump-tion holds good:-
MRTXY = MRSAXY = MRSBXY
General equilibrium of production determines total output X2 of commodity X and
total output K2 of commodity. It is with OX2 and OY2 as the dimensions, Edgeworth Box has
been drawn and indiffer-ence curves of two individuals depicting their scale of preferences
are drawn with CC’ as the contract curve. Consumption equilibrium point E reveals that out
of total output X2 of good X the amount XA is being consumed by individual A and the
remaining amount of X goes to individual B for consumption. Out of total output Y2 of
commodity Y, the amount YA is consumed by A and the remaining amount by the individual
B.
Conclusion:
It follows from above that in our two goods, two persons (2x2x2) model of general
equilibrium, we arrive at the conclusion that the position of general equilibrium can exist.
However, this general equilibrium position is not unique. There can be several points of
general equilibrium on the production possibility curve IT’ in Figure 37.6 and consumption
contract curve in it depending upon the T’, distribution of income which (among other things)
is determined by ownership of resources
A general equilibrium position at point Q’, on the production possibility curve IT’ in
Fig. 3.2 indicates that factor markers of labour and capital and product markets of
goods X and Y are simultaneously in equilibrium and determine the following things:

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Figure 3.3: General Equilibrium of Production

1. Relative prices of factors (w & r) as indicated by the exchange rate of ST’ of labour for
SQ of Y in Figure 3.3
2. Allocation of factors between products AT and Y as indicated by point Q in Figure 3.3.
3. Relative prices of products X and Y as measured by the slope of tangent PP’ in Figure
3.1.
4. The product-mix, that is, the levels of output of goods X and Y as given by point Q’ in
Figure 3.2.
5. The distribution of goods X and Y between the two individuals as indicated by point E in
Figure 3.2.
3.3 Equilibrium and Efficiency under Pure Exchange
The General Equilibrium of Exchange and Consumption: Distribution of Goods
between Individual!
We shall explain general equilibrium in a pure exchange economy. In this pure
exchange system, we assume that there is no production. That is, we consider the case when
two goods are provided to the individuals in the economy from outside the system.
To keep our analysis simple we assume that there are:
1) Two goods, specific bundles of which have been made available to the individuals for
consumption; and
2) There are two individuals between whom exchange of goods has to take place and
equilibrium reached with regard to the distribution of the specific amounts of these two
goods.

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Edgeworth Box and General Equilibrium of Exchange:

In these two goods, two individuals (2×2) model of pure exchange, the famous Edge-
worth Box diagram has been employed to explain the general equilibrium of distribution of
two goods between two individuals. In what follows we first explain the concept of
Edgeworth Box and then analyse the general equilibrium in this pure exchange system.
Consider Figure 3.4 where a box with a certain fixed dimensions has been drawn.
Figure 3.4: Edgeworth Box

Along the X-axis we measure the commodity X and along the X-axis, the commodity
Y. The total available amount of commodity X is OX0 and of commodity Y is OY0. The
available amounts of the two commodities, OX0 and OY0 determine the dimension of the
box. The quantity of A available with the individual A is measured from left to right along
the X-axis with bottom left-hand corner OA as the origin.
And, quantity of commodity Y available with the individual A is measured along the
Y- axis from bottom upwards with the origin 0A. For individual B, the top right hand corner
OB has been taken as the origin and with the given quantities of X and Y, the quantity of X
available for consumption for individual B is measured, right to left, with the origin OB and
the quantity of Y available for B is measured, from top to bottom, from the origin OB.
It follows from above that Edgeworth Box has fixed dimensions representing the
maximum available quantities of X and Y to be distributed between the two individuals. We
further assume that the two individuals between them will entirely consume all the available
quantities of the two goods.
It may be noted that a point in the Edgeworth Box represents a particular distribution
pattern of two goods between the two consumers. This implies that if the two indi-viduals
trade goods with each other and accordingly move from one point in the Edgeworth Box to

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another, the quantities purchased and sold of each good would be equal. Thus, with trade or
exchange of goods, it is the distribution or consumption of two goods of the two individuals
that will change, the total quantities of the two goods remaining constant.
In the Edgeworth Consumption Box we also draw the indifference curves of the two
individuals A and B depicting their scale of preferences between the two goods. As we move
upward from bottom-left to top right, the satisfaction of individual A increases and that of B
decreases, that is, A- moves to successively higher indifference curves and individual B to
successively lower indifference curves.
We can now show that the general exchange equilibrium would lie somewhere on the
contract curve, that is, the curve QT in Fig. 3.5 which passes through the tangency points of
indifference curves of two individuals. At these tangency points of indifference curves,
MRSXY of individual A equals that of individual B.
Thus, the general equilibrium of exchange will occur when the following condition holds
good:-
MRSAXY =MRSBXY
Since a point on the contract curve lies within the Edgeworth box with the fixed
quantities of the two goods, the equilibrium reached after exchange or trading between the
two individuals implies that the distribution for consumption of the two goods between the
two individuals would just exhaust the available quantities of the two goods.
From the above it cannot be known at which specific point or location of the contract
curve, the general equilibrium of exchange will be reached. This is because the equality of
MRSXY of the two individuals exists at all points of the contract curve.
However, if we know the initial distribution of two goods between the two individuals
we can pinpoint the boundaries within which the general equilibrium of exchange would lie.
Consider Figure 3.5. If the initial distribution of two goods between the two individuals is
represented by point C where individual A has XA1 amount of good X and YA1 amount of
good Y. The remaining quantity of good X, that is, X0 – XA1 = XB1 would be allocated to
individual B and the remaining YB1 amount of good Y would go to individual B. At this
initial distribution of goods A and Y between the two individuals A and B the indifference
curves of two individuals are intersecting.
Now, this initial distribution at point C cannot be the position of equilibrium for the
two individuals, since the two individuals can gain in welfare or, in other words, can become
better off if they exchange some amounts of the goods possessed by them and move to the
contract curve.

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If the individuals think that they can benefit from trading or exchange, they will trade with
each others. As long as they think there are possibilities of becoming better off, they will
exchange goods and end up at the contract curve.
Figure 3.5: General Equilibrium of Exchange

With the initial distribution of two goods as implied by point C, if the two individuals
through exchange of goods between them move to the point R on the contract curve,
individual B reaches on his higher indifference curve B4 and therefore becomes better off and
A is no worse off as he remains on the same indifference curve A2 as on the initial
distribution point C.
On the other hand, if through exchange they move to point S on the contract curve,
individual A becomes better off and individual B no worse off as compared to the initial
position C. And if through exchange of goods they move to any point between R and S on the
contract curve both the individuals will gain from exchange of goods as they will be reaching
their respective higher indifference curves.
With initial distribution at point C and through exchange of goods nearer they move
to point R on the contract curve, individual B will benefit more and nearer they move to point
S on the contract curve, the individual A will gain more as compared to the initial distribution
position C.
Where exactly on the contract curve, their equilibrium position of exchange will lie
depends upon the bargaining power of each individual. With their almost equal bargaining
power, their equilibrium position of exchange on the contract curve may lie at point £ where
the two individuals gain almost equally as a result of exchange.

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Thus, if the initial distribution of two individuals is not on the contract curve, there
will be tendency on the part of individuals to trade or exchange goods between themselves
and to move to a point on the contract curve because in doing so they will be increasing their
satisfaction.
It is evident from the foregoing analysis that the position of exchange equilibrium can
be some-where between R and S on the contract curve. On all points between R and S, the
exchange equilibrium can exist. Although equilibrium will exist at a point on the contract
curve, there is no unique position of exchange equilibrium; all points between R and S on the
contract curve are possible equilibrium positions.
If point E on the contract curve is the position of exchange equilibrium actually
reached, then individual A has exchanged the amount of commodity X equal to CK for the
amount of commodity K equal to KE Since point E lies on the contract curve which is the
locus of the tangency points of indifference curves of the two individuals, marginal rate of
substitution between the two goods (MRSXY) of individual A equals marginal rate of
substitution between the two com-modities (MRSXY) of individual B. Thus exchange of CK
of commodity X for KE of commodity Y has been settled between them at the equilibrium
position E.
The general equilibrium of exchange attained at point E on the contract curve has the
following important features:
1. Individuals maximise their satisfaction by equating their MRSXY subject to their initial
endowments of goods.
2. Since the equilibrium point E lies within the Edgeworth Box, drawn with the given
amounts of two goods, the exchange of goods between the two individuals when they
move to the equilibrium point E on the contract curve would imply that quantity sold of
each good equals the quantity purchased of the good.
That is, markets for the two goods would clear. This implies that on moving to the
equilibrium position E, individual A relative to his initial endowment of goods is selling
good X and buying good Y. The opposite is true of individual B who buys good X and
sells good Y. The quantity sold and purchased of each good must equal each other. If this
does not happen the two markets will not clear and shortages or surplus would emerge.
3. The general exchange equilibrium determines not only the final distribution of two goods
between the individuals but also a certain exchange rate (i.e. relative prices of the two
goods). Thus at the equilibrium position E, the exchange rate CK of X for KE of Y has

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been settled between them. It is at this price ratio that exchange of goods takes place
between the individuals.
4. The general equilibrium of exchange does not lead to the determination of absolute prices
of goods but only relative prices of goods.
5. The general equilibrium of exchange must lie on the contract curve, and given the initial
distribution implied by point C, it must lie between the point R and S on the contract
curve. The general exchange equilibrium cannot be at a point in the Edgeworth Box
which is not on the contract curve. This is because at a point which is not on the contract
curve, indif-ference curves of two individuals will intersect each other and therefore their
MRSXY not be equal to each other.
6. The equilibrium can lie anywhere between R and S on the contract curve, that is, general
equilibrium of exchange in this bargaining is not unique.
3.4 Production Problems of Measuring Welfare
The General Equilibrium of Production and Exchange!
There are several points on the transformation curve; each point will indicate a
different price ratio of the two goods and a different production equilibrium indicating a
different output-mix of the two goods. The general equilibrium of production can occur at
any of the points on the given transfor-mation curve depending upon the prevailing price ratio
of the two goods.
Now, an important question is which of these price ratios of commodities or MRTXY
will be the equilibrium ratio. The general equilibrium level of price ratio (P X/PY) or MRTXY
will be one which on the one hand maximises profits of the firms and on the other maximises
satisfaction of consumers. To analyse the equilibrium price ratio determining output-mix, we
have to introduce in our analysis the consumer’s preference pattern or demand for goods.
It can be easily shown that if MRSXY of the consumers is not equal to the MRTXY in
the production, consumer satisfaction will not be maximised with the result that further
changes in the price ratio of the two goods and output-mix will tend to occur.
Since the marginal rate of transformation (MRTXY) shows the rate at which one good
is ‘trans­formed’ into another in the production process and marginal rate of substitution
measures the rate at which consumers are willing to exchange one good for the other,
equilibrium cannot be reached unless the two rates are equal.
Thus, only when MRTXY equals MRSXY planned pattern of production will be
consistent with the preferences of consumers and ensure general equilibrium of production

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and exchange. This can be made clear with a simple numerical example. For instance,
suppose at a given output-mix of two goods X and Y MRTXY of the producers of the
economy is 3Y/lX and MRSXY of consumers equals 2Y/lX.
Thus, in this case MRSXY of consumers is less than MRTXY of producers. That is, the
economy can produce 3 units of Y by foregoing one unit of good X, while the consumers are
willing to exchange or buy 2 units of Y for one unit of X. MRS XY of consumers being less
than MRTXY of producers implies that relatively greater quantity of commodity X and the
smaller quantity of commodity Y is being produced than desired by the consumers.
Obviously, if the economy reduces the production of X by one unit and product 3
units more of Y and give them to the consumers, their satisfaction or welfare will increase as
they are willing to get 2 units of Y for the sacrifice of one unit of X. Thus consumers’
satisfaction can be raised by expanding the production of Y and reducing the production of X
until the two rates, namely, MRSXY of consumers and MRTXY of producers become equal.
General equilibrium will thus be reached if with adjustment in output-mix of the two
commodities, MRSXY equals MRTXY. In a free market economy, forces of competition would
ensure such adjustment which will bring about product-mix that will equate MRSXY of
consumers with MRTXY of producers and thus ensuring maximum consumers’ satisfaction.
The general equilibrium of production together with the general equilibrium of exchange (or
consumption) requires that the marginal rate of transformation (MRTXY) be equal not only to
marginal rate of substitution (MRSXY) of the consumers but also MRSXY of the two
consumers be equal to each other.
Thus, for the achievement of general equilibrium of production and exchange
simultaneously we arrive at the following condition:
MRTXY = MRSAXY = MRSBXY
The overall general equilibrium of production and exchange is illustrated in Figure
3.6 and 3.7. Consider Figure 3.6 where a transformation curve TT’ has been drawn. Let us
consider the point L on the production transformation curve TT’. At point L on it OM of
good X and ON of good Y are being produced.
With the given preference pattern and resource endowments of the two consumers,
their indifference curves are tangent to each other at point S and their MRSXY is indicated by
the slope of the tangent line kk’. It will be seen from Figure 3.6 that MRSXY of consumers is
less than MRTXY of producers indicating that production pattern is inconsistent with
consumer’s preferences.

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Figure 3.6: General Disequilibrium

Thus, the system is in disequilibrium indicating that relatively greater quantity of X

and smaller quantity Y is being produced than desired by the consumers. In response to this
disequilibrium situation and to maximise their profits producers would tend to produce more
of Y and less of X and this process of adjustment in output mix will continue until the
MRTXY in production is brought into equality with MRSXY of consumers.
Figure 3.7: General Equilibrium

With this equality, general equilibrium of production and exchange (consumption)

would be attained. This general equilibrium is shown in Figure 3.7 where at position Q ‘on
the transformation curve TT’, OX2 level of output of X and OY2 level of output of Yare being
produced and MRTxy at point equals MRSXY at E (slopes of JJ’ and PP’ are equal).
Note that there is general equilibrium of production at point Q’ because all points of
transformation curve corresponds to the points of the production contract curve. There is

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general equilibrium of exchange or consumption as M RS of, the two individuals are the
same (their indifference curves being tangent to each other at point E).
There is joint equilibrium of production and exchange as the MRT in production is
equal to MRSXY of the two individuals at the consumption equilibrium point E. Thus, with
point Q on the transformation curve TT’ and point E on the consumption contract curve
drawn in the Edgeworth Box made from point Q’, the following condition of general
equilibrium of production and consump-tion holds good:
MRTXY = MRSAXY = MRSBXY
General equilibrium of production determines total output X2 of commodity X and
total output K2 of commodity. It is with OX2 and OY2 as the dimensions, Edgeworth Box has
been drawn and indifference curves of two individuals depicting their scale of preferences are
drawn with CC’ as the contract curve. Consumption equilibrium point E reveals that out of
total output X2 of good X the amount XA is being consumed by individual A and the
remaining amount of X goes to individual B for consumption. Out of total output Y2 of
commodity Y, the amount YA is consumed by A and the remaining amount by the individual
B.
Conclusion:
It follows from above that in our two goods, two persons (2x2x2) model of general
equilibrium, we arrive at the conclusion that the position of general equilibrium can exist.
However, this general equilibrium position is not unique. There can be several points of
general equilibrium on the production possibility curve IT’ in Figure 3.7 and consumption
contract curve in it depending upon the T’, distribution of income which (among other things)
is determined by ownership of re-sources.
A general equilibrium position at point Q’, on the production possibility curve IT’ in Fig. 3.7
indicates that factor markers of labour and capital and product markets of goods X and Y are
simultaneously in equilibrium and determine the following things:
Figure 3.8: General Equilibrium of Production

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1. Relative prices of factors (w & r) as indicated by the exchange rate of ST’ of labour for
SQ of Y in Figure 3.8
2. Allocation of factors between products AT and Y as indicated by point Q in Figure 3.8.
3. Relative prices of products X and Y as measured by the slope of tangent PP’ in Figure
3.7.
4. The product-mix, that is, the levels of output of goods X and Y as given by point Q’ in
Figure 3.7.
5. The distribution of goods X and Y between the two individuals as indicated by point E in
Figure 3.7.
3.5 Marshallian Approaches
The Marshallian theory of economic welfare is based on his tool of consumer s
surplus. Marshall begins with the individual consumer’s surplus or welfare and then makes
the transition to the aggregate consumer’s surplus. To explain the aggregate welfare of the
community, he uses his tax-bounty analysis. First, we explain the individual consumer’s
surplus or welfare and then the aggregate economic welfare.
Marshall’s Individual Consumer’s Welfare:
Marshall explains the individual consumer’s welfare with his tool of consumer’s
surplus. Marshall defines consumer’s surplus as “the excess of the price which he would be
willing to pay rather than go without the thing, over that which he actually does pay, is the
economic measure of this surplus satisfaction.”
The price which a consumer pays for a commodity like salt, match box, postcard, etc.
is always less than what he is willing to pay for it so that the satisfaction which he gets from
its purchase is more than the price paid for it and thus he derives a surplus satisfaction which
increases his welfare. He explains the consumer’s surplus from a given change in price as the
area between the demand curve and the price axis within a range of the price variation.
Consumer’s surplus is represented diagrammatically in Fig. 3.9 where DD1 is the demand
curve for the commodity. If OP is the price, OQ units of the commodity are purchased and
the price paid is OP × OQ = area OQRP.

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Figure 3.9: Consumer's Surplus

But the total amount of money, he is prepared to pay for OQ units is OQRD. 8
Therefore, consumer’s surplus =OQRD-OQRP = DRP. If the price of the commodity falls to
OP1, the consumer’s surplus increases to DR1P1 and conversely a rise in price would diminish
it.
According to Prof. Hicks, this “Marshall’s measure” of the consumer’s surplus
“involves nothing more introspective or subjective than the demand curve itself.” The area
under the demand curve after deducting consumer’s expenditure on the commodity represents
consumer’s surplus. This is based on the assumption of constant marginal utility of money for
the consumer.
It is thus free from interpersonal comparisons of utility. So far we have studied the
individual consumer’s surplus which is the sum total of the surplus from a number of
commodities he buys, with a given money income.
By adding up consumer’s surplus from anyone commodity enjoyed by a number of
individuals, the market consumers’ surplus for that commodity can be known. The demand
schedule so formed will be the market demand curve. But it presupposes the nonexistence of
interpersonal differences in customs, habits and incomes of the consumers.
Marshall’s Tax-Bounty Analysis of Aggregate Welfare:
The above analysis relates to the individual consumer’s surplus (welfare). In order to
arrive at the aggregate consumers’ surplus, Marshall adds the individual consumer’s
surpluses in a market. This he does by assuming that most markets are homogeneous with
respect to the income class of the buyers and regards the individual buyer as a model
representative of the group.
To get rid of the problem of interpersonal utility comparisons and value judgements,
Marshall says that for practical purposes the area between the demand curve and the price is
taken to be a good approximation of the sum of the individual consumers’ surpluses.

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Marshall uses his tax-boundary analysis to explain the aggregate economic welfare.
According to Marshall, aggregate economic welfare can be increased by taxing diminishing
returns industries and using the tax receipts to subsidies increasing returns industries. To
arrive at this conclusion, he explains the following three possible cases.
Figure 3.10: Quantity and Price

Constant Returns:
Marshall shows that a tax imposed on a commodity obeying the law of constant costs
or constant returns results in a loss of consumer’s surplus greater than the amount of tax
receipts, and conversely, a subsidy in this case exceeds the gain in consumers’ surplus. This
is illustrated in Fig. 3.10, where SS is the supply curve of the commodity before the tax.
Since constant cost conditions prevail, the supply price is the same for all units of the
commodity. Thus, the supply curve is perfectly elastic. DD1 is the demand curve for the
commodity. E is the initial equilibrium point where the consumers’ surplus is SDE.
Suppose, a uniform tax ТЕ per unit of the commodity bought is levied. The supply
curve shifts up by the amount of the tax to S1-S1, parallel to the old supply curve SS. As a
result, the loss of consumers’ surplus is the area SS1AE (= SDE – S1DA). The tax receipts to
the government are equal to the area SS1AB. Thus the loss of consumer’s surplus is greater
than the gain to the government because SS1AE > SS’AB.
The net loss of consumers’ surplus is the shaded area ABE. In the same way, if a
subsidy shifts the long-run supply curve down from S1S1 to SS (whereby supply increases)
the triangle ATE above the demand curve means the excess of subsidies paid out over
consumers’ surplus gained.

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Diminishing Returns:
When the industry is operating under diminishing returns to scale or (increasing
costs), the effects of a tax is not so certain. Whether the tax receipts will exceed the loss in
consumers’ surplus will depend upon the steepness of the long-run supply curve.
Figure 3.11: Quantity and Price

This case is illustrated in Fig. 3.11 where the initial supply curve is SS. After the
imposition of tax, it shifts to S1S1. The demand curve DD1 intersects the supply curve SS at
point E and the new supply curve at point A. ТА per unit of tax is levied on OX1 quantity of
the product purchased and the total tax receipts are equal to the area С RAT and the loss in
consumers’ surplus is RAEP. The receipts from tax shown as the shaded rectangle CPBT are
greater than the net loss in consumers’ surplus, shown as the shaded triangle AEB.
Increasing Returns:
When the industry is operating under increasing returns to scale or diminishing costs,
the long-run supply curve slopes downward as SS in Fig. 3.12. With the DD1 demand curve,
OX commodity is produced at the equilibrium point E. If a tax is levied, the cost of
production will increase, the price of the commodity will rise and there will be loss in
consumers’ surplus. However, the effect of a subsidy on a decreasing cost industry depends
on the slope of the supply curve.
Figure 3.12: Quantity and Price

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If the supply curve is less elastic, as shown in Fig. 3.12 the grant of AT amount of
subsidy per unit of output to this industry will increase its output to OX1 .The total amount of
subsidy is RTAK and the gain in consumer’s surplus is RPET. As the area RPET > RTAK
the gain in consumers’ surplus is greater than the amount of subsidy payment by the
government. If the long-run supply curve is more elastic, as in the case of constant cost
industry, subsidy payment will exceed consumers’ surplus even in diminishing cost industry.
Conclusion:
Marshall concludes that aggregate welfare can be increased if the government
imposes a tax on diminishing returns or increasing cost industries (where tax receipts are
greater than the loss in consumers’ surplus) and spends the proceeds to subsidies increasing
returns or diminishing cost industries where the gain in consumers’ surplus is more than
subsidy payments.
3.6 Pareto’s Welfare Criteria
The welfare of a society depends, in the broadest sense, upon the satisfaction levels of
all its consumers. But almost every change in the economic state of the society will have
favourable effects on some members and unfavorable effects on others.
Evaluation of such a social change is impossible unless the economist is ready to go
into interpersonal comparison of utility under some value judgement, which he may not be
willing to do. Rather, he will be willing to evaluate such changes where at least one person
has been better off and no one worse off.
This criterion refers to economic efficiency which can be objectively measured. It is
called Pareto criterion after the famous Italian economist Vilfredo Pareto (1848-1923).
According to this criterion any change that makes at least one individual better-off and no
one worse-off is an improvement in social welfare. Conversely, a change that makes no one
better-off and at least one worse-off is a decrease in social welfare. The criterion can be stated
in a somewhat different way: a situation in which it is impossible to make anyone better-off
without making someone worse-off is said to be Pareto-optimal or Pareto-efficient.
For the attainment of a Pareto-efficient situation in an economy three marginal
conditions must be satisfied:
a) Efficiency of distribution of commodities among consumers (efficiency in exchange)
b) Efficiency of the allocation of factors among firms (efficiency of production)
c) Efficiency in the allocation of factors among commodities (efficiency in the product-mix,
or composition of output).

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Before examining these marginal conditions we discuss briefly the main weaknesses of
the Pareto criterion. The Pareto criterion cannot evaluate a change that makes some
individuals better- off and others worse-off. Since most government policies involve changes
that benefit some and harm others it is obvious that the strict Pareto criterion is of limited
applicability in real-world situations.
Furthermore, a Pareto-optimal situation does not guarantee the maximisation of the social
welfare. For example, we know that any point on the produc-tion possibility curve represents
a Pareto-efficient situation. To decide which of these points yields maximum social welfare
we need an interpersonal comparison of the individual consumer’s utility. We will show that
the Pareto- optimal state is a necessary but not sufficient condition for maximum social
welfare.
Let us examine now the three marginal conditions that must be satisfied in order to attain
a Pareto-efficient situation in the economy.
(a) Efficiency of distribution of commodities among consumers:
Applying the Pareto optimality criterion to the case of distribution of commodities Y
and X, we can say that a distribution of the given commodities X and Y between the two
consumers is efficient if it is impossible by a redistribution of these goods to increase the
utility of one individual without reducing the utility of the other. In figure 3.13 we show the
Edge-worth box for the given commodities X and Y.
Figure 3.13: Edgeworth Box of Exchange

We know that only points on the Edge-worth contract curve satisfy the Pareto-
optimality condition. Any other distribution off the contract curve is inefficient. For example,
point z is inefficient, since a redistribution of the commodi-ties such as to reach any point
between a and b increases the utility of both con-sumers. A movement to a increases the
utility of B without reducing the utility of A.

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Similarly, the distribution implied by b increases the utility of A without reducing the
utility of B. Thus all the points from a to b represent improvements in social welfare
compared with the distribution at z. By reversing the argument it can be seen that a
movement from a point on the contract curve to a point off it results in a decrease in social
welfare.
Thus the contract curve shows the locus of Pareto-optimal or efficient distribution of
goods between consumers. This curve is formed from the points of tangency of the two
consumers’ indifference curves, that is, points where the slopes of the indifference curves are
equal. In other words, at each point of the contract curve the following condition is satisfied
MRSAx,y = MRSBx,y
Therefore we may state the marginal condition for a Pareto-efficient distribution of
given commodities as follows:
The marginal condition for a Pareto-optimal or efficient distribution of commodities
among consumers requires that the MRS between two goods be equal for all consumers.
(b) Efficiency of Allocation of Factors among Firm-Producers:
To derive the marginal condition for a Pareto-optimal allocation of factors among
producers we use an argument closely analogous to the one used for the derivation of the
marginal condition for optimal distribution of commodities among consumers. In the case of
allocation of given resources K and L we use the Edge-worth box of production which is
shown in figure 3.14.
Figure 3.14: Edgeworth box of production

Only points on the contract curve of production are Pareto-efficient. Point H is

inefficient, since a reallocation of the given K and L between the producers of X and Y such
as to reach any point from c to d inclusive results in the increase of at least one commodity
without a reduction in the other. The contract curve is the locus of points of tangency of the
isoquants of the two firms which produce X and Y, that is, points where the slopes of the
isoquants are equal. Thus at each point of the contract curve the following condition holds
MRSXL,K = MRSYL,K

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Therefore we may state the marginal condition for a Pareto-optimal allocation of

factors among firms as follows:
The marginal condition for a Pareto-optimal allocation of factors (inputs) requires that
the MRTS between labour and capital be equal for all commodities produced by different
firms.
(c) Efficiency in the Composition of Output (Product-Mix):
The third possible way of increasing social welfare is a change in the product-mix. To
define the third marginal condition of a Pareto-optimal state in an economy we will use the
production possibility curve. Recall that the slope of the PPC is called the ‘marginal rate of
(product) transformation’ (MRPTx,y), and it shows the amount of Y that must be sacrificed
in order to obtain an additional unit of X. In other words the MRPT is the rate at which a
good can be transformed into another. The marginal condition for a Pareto-optimal or -
efficient composition of output re-quires that the MRPT between any two commodities be
equal to the MRS between the same two goods:
MRPTxy = MRSAx,y = MRSBx,y
Since the MRPT shows the rate at which a good can be transformed into another (on
the production side), and the MRS shows the rate at which consumers are willing to exchange
a good for another, the rates must be equal for a Pareto-optimal situation to be attained.
Suppose that these rates are unequal. For example assume

The above inequality shows that the economy can produce two units of Y by
sacrificing one unit of X, while the consumers are willing to exchange one unit of Y for one
unit of X. Clearly the economy produces too much of X and too little of Y relatively to the
tastes of consumers. Welfare therefore can be increased by increasing the production of Y
and decreasing the production of X.
In summary a Pareto-optimal state in the economy can be attained if the follow-ing
three marginal conditions are fulfilled:
1. The MRSX,Y between any two goods be equal for all consumers.
2. The MRTSL,K between any two inputs be equal in the production of all commodities.
3. The MRPTX,Y be equal to the MRSXY for any two goods.

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A situation may be Pareto-optimal without maximising social welfare. However,

welfare maximisation is attained only at a situation that is Pareto-optimal. In other words,
Pareto optimality is a necessary but not sufficient condition for welfare maxi-misation. All
points on the PPC are Pareto-optimal. The choice among these alternative Pareto-optimal
states requires some measure or criterion of social welfare.
3.7 Concept of Social Welfare Function
The concept of ‘Social Welfare Function’ was propounded by A. Bergson in his
article ‘A Re­formulation of Certain Aspects of Welfare Economics’ in 1938. Prior to its
various concepts of social welfare had been given by different welfare theorists but they
failed to provide a satisfactory solution to the problem of maximisation of social welfare and
measurement. Bentham talked of welfare in terms of ‘the greatest happiness of the greatest
number.’
Neo-Classical welfare theorists discussed the problem of social welfare on the basis of
cardinal measurability of utility and interpersonal comparison of utility. Analysis of Pareto
optimality maximises social welfare by satisfying various marginal conditions of production,
distribution and allocation of resources among products. But unfortunately they are not
fulfilled due to the existence of various externalities and imperfections in the market.
Moreover, Pareto optimality analysis fails to measure the changes in welfare resulting from
any change which benefits one section of society and harms the other.
Compensation principle as given by Kaldor-Hicks-Scitovsky attempts to measure the
changes in social welfare resulting from such economic changes which harm some and
benefit others through hypothetical compensating payments.
Compensation theorists claimed to give a value-free objective criterion based on
ordinal concept of utility but, this is based upon implicit value judgements and does not
evaluate changes in social welfare satisfactorily.
By providing the concept of social welfare function Bergson and Samuelson have attempted
to provide a new approach to welfare economics and have succeeded in rehabilitating welfare
econom-ics. They have put forward the concept of social welfare function that considers only
the ordinal preferences of individuals.
They agree to Robbins’ view that interpersonal comparison of utility involves value
judgements but they assert that without making some value judgements, economists cannot
evaluate the impact of changes in economic policy on social welfare.

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Thus, according to them, welfare economics cannot be separated from value

judgements. According to them, welfare economics is essentially a normative study. But the
approach to study it must be scientific despite the fact that the use of value judgements in it is
unavoidable.
Bergson-Samuelson Social Welfare Function:
Social welfare function is an ordinal index of society’s welfare and is a function of the
utility levies of all individuals constituting the society.
Bergson-Samuelson social welfare function can be written in the following manner:
W= W(U1, U2,U3…………. , Un)
Where W If represents the social welfare U1, U2, U3, . .. ., Un represent the ordinal
utility indices of different individuals of the society. The ordinal utility index of an individual
depends upon the goods and services he consumes and the magnitude and kind of the work he
does. The important thing to note about social welfare function is that in its construction
explicit value judgements are introduced.
Value judgements determine a form of the social welfare function; with a different set
of value judgements, the form of social welfare function would be different. Value
judgements are essentially ethical notions which are introduced from outside economics. The
value judgements re-quired to construct a social welfare function may be obtained through
democratic process with voting by individuals or it may have to be imposed on the society in
a dictation manner.
Whatever the case may be, the form of social welfare function depends upon the value
judgements of those who decide about them since it expresses their views regarding the effect
which the utility level of each individual has on the social welfare. In the worlds of Prof.
Scitovsky. “The social welfare function can be thought of as a function of each individual’s
welfare which in turn depends both in his personal well being and on his appraisal of the
distribution of welfare among all members of the community”.
Since the value judgements required for the formation of social welfare function are
not of the economist himself and instead they are introduced from outside economics they are
not obtained through any scientific method.
It has been claimed that social welfare function has solved the basic problem of
welfare economics, since it thinks unnecessary for the economists themselves to make value
judgements concerning what is a desirable distribution of welfare as between in individuals
constituting the society. In other words, economist need not himself decide about what is the

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most desirable distribution of welfare. He can take value judgements regarding distribution as
given from outside economics.
Bergson’s social welfare function is supposed to be dependent on changes in
economic events that have a direct effect on individual welfares. The ordinal utility level of
an individual is a function of his own consumption of goods and services and not of others.
Moreover, the utility level of an individual depends on his own value judgments
regarding the composition of different goods and services consumed which depends upon his
tastes. An individual may derive more utility from the consumption of liquor whereas another
individual may derive very nominal utility or no utility at all from it.
Social Welfare Function and Value Judgements:
So far we have been mainly concerned with the value judgements of individuals
regarding their utility levels. From the view point of social welfare function, the value
judgements regarding the welfare of the society as a whole are relevant.
The formulation of a welfare function for the society as a whole is a very difficult task
because utility being a mental phenomenon cannot be measured or estimated accurately by
any person or institution entrusted to furnish value judgements regarding the changes in
social welfare, Moreover, addition and subtraction of utilities of different individuals by an
authorised person or institution too is a very difficult task.
The social welfare function and its form depend upon the value judgements of the
person or institution that the society has authorised to decide. The authorised person or
institution may be anybody but for true value judgements regarding the social welfare he
must be unbiased because changes in social welfare will depend upon his value judgements.
“These judgements as to what constitute justice and virtue in distribution may be
those of the economist himself or those set up by the legislature, by some other governmental
authority or by some other unspecified person or group.” A social welfare function can be
attained by common consensus or it may be forced upon the society by a dictator.
Since the forms of social welfare functions are known by value judgements about
social welfare, therefore there arises the problem of finding an authority who could give
purely unbiased value judgements. Bergson and Samuelson have assumed a “Superman” who
provides value judgements about changes in social welfare.
Superman alone can take decisions about the solution of various problems of the
economy. What goods and services should be produced and supplied in the society? How
much of various goods should be produced? What should be the quality and kind of goods?

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What should be capital intensity of producing a particular type of good? What should
be the pattern of distribution of national income among different sections of the society?
Which wants should be satisfied at present and which at a future date and so on. All these
questions can be answered by the superman alone in accordance with his views about the
determinants of social welfare.
The society would have to accept the solutions of all these questions provided by him
assumption that he will give any value judgements which aim to achieve maximum social
welfare rather than maximum self-interest. Thus we are free from the addition, subtraction,
measurement and interpersonal comparisons of utilities by assumption the existence of a
superman.
In modern age of democratic govern-ments people elect their representatives who
constitute the Government. The political party in majority forms the Government and rules
the country. The representatives’ Government formed by the majority rule formulates various
policies on the basis of value judgements and it is expected that all the policy decisions by the
Government will aim at maximising social welfare rather than maximising the welfare of an
individual or a particular section of the society.
Bergson and Samuelson expressed the view that all value judgements used to
construct the social welfare function must be consistent which implies that if in a given
situation A is preferred to B and B is preferred to C then A must be preferred to C. This is
nothing new to the students of economics as this is the well know assumption of transitivity
in social choice among various alternatives.
We can explain the social welfare function with the help of social indifference curves
or welfare frontiers. Let us assume a society of two persons. In such a case social welfare
function can be represented with the help of social indifference curves.
In Fig. 3.15 the utilities of individuals A and B have been represented on the
horizontal and vertical axes respectively. W1, W2 and W3 are the social indifference curves
representing succes-sively higher levels of social welfare. A social indifference curve is a
locus of various combinations of utilities of A and B which result in an equal level of social
welfare.
The properties of social indifference curves are just like that of individual consumer’s
indifference curves. Given a family of social indifference curves, the effect of a proposed
change in policy on social welfare can be evalu-ated. In terms of Fig. 3.15 any policy change
that moves the economy from Q to T is an improve-ment.

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Figure 3.15: Social Indifference Curves Depicting Social Welfare Function

Similarly, a movement from Q to S or from R to S also represents an improvement in

social welfare, and a movement from T to Q or T to S represents a decrease in social welfare.
A movement along the same social indifference curve represents no change in the level of
social welfare.
Analysis of Pareto optimality failed to provide a ‘unique optimum solution’ which
represents maximum social welfare. There are a large number of solutions which are
optimum on the basis of Pareto criterion. In terms of Edgeworth-box diagram every point on
the contract curve represents the optimum position. In terms of Grand Utility Possibility
Frontier, all points on it are Pareto optimal or economically efficient. But Pareto criterion
does not tell us the best of them.
Thus, Paretian analysis leaves us with a lot of indeterminacy in the choice of
maximum social welfare point. Now, the significance of social welfare function is that it
enables us to obtain a unique optimum position regarding social welfare.
This unique optimum position is best of all the Pareto optima and therefore ensures
the maximum social welfare. By including the concept of grand utility possibility frontier
along with Bergson-Samuleson social welfare function we are able to obtain a unique
optimum position or maximum social welfare position which is explained below.
3.8 Summary
General equilibrium – treating all markets and their interactions simultaneously – is
thought here to be the appropriate model to decide whether there are well-defined solutions to
the economic decision-making mechanism and whether they have efficiency properties
making them desirable.

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Welfare economics and ethics are inseparable and interpersonal comparisons or value
judgments are inseparable from welfare economics. All democratic countries have the ideal
of a welfare state and the various legislative measures like free education, heavy excise duty
on wine, compulsory national insurance, etc. are all value judgments.
Welfare economics seeks to achieve a state that will maximise the overall satisfaction
for a society, maximising the producer and consumer surplus for the various markets
comprised in the society.
3.9 Answer to Check Your Progress
Marshallian Theory of Economic Welfare: It is based on his tool of consumer s surplus.
Marshall begins with the individual consumer’s surplus or welfare and then makes the
transition to the aggregate consumer’s surplus.
Pareto-efficient situation in an economy three marginal conditions must be satisfied:
a) Efficiency of distribution of commodities among consumers (efficiency in exchange)
b) Efficiency of the allocation of factors among firms (efficiency of production)
c) Efficiency in the allocation of factors among commodities (efficiency in the product-
mix, or composition of output).
Social Welfare Function: The concept of ‘Social Welfare Function’ was propounded by A.
Bergson in his article ‘A Re­formulation of Certain Aspects of Welfare Economics’ in 1938.
Prior to its various concepts of social welfare had been given by different welfare theorists
but they failed to provide a satisfactory solution to the problem of maximisation of social
welfare and measurement.
3.10 Questions and Exercises
1. Discuss the Edgeworth box analysis of an exchange economy
………………………………………………………………………………………………
2. Critically examine the Marshallian theory of economic welfare
………………………………………………………………………………………………
3. Discuss the Pareto-efficient situation how a Pareto-efficient situation can be attainment in
an economy
………………………………………………………………………………………………
4. Explain the concept of Bergson-Samuelson Social Welfare Function
………………………………………………………………………………………………

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