It is difficult to show mathematically if the US actually lies above this straight line because all the figures available are in the form

In document International measurements of economic and socio-economic aggregates using non-monetary indicators (Page 51-69)

III. Present Study

2 It is difficult to show mathematically if the US actually lies above this straight line because all the figures available are in the form

of Paasche or Laspeyres indices; such data do not take into account the substitution effect that takes place in the US, whereas more

necessities will be consumed as the relative price of the necessities is lower.

Graph 2.1

Case II Case

Case I

D and R are two similar and developed countries


Case III

Case II

Case I

E n g e l ’

P is an underdeveloped country and R is a developed country

cf. S a m u e l s o n ’s Graph in (1974), (Fig.2, p.607).

this is corroborated by the fact that the Laspeyres quantity index is

higher than the Paasche quantity index. In conclusion, there is a strong

possibility that the Belgium-US comparison and the Netherlands-US com­

parison correspond to Case III of Table 2.1, when the Paasche and the

Laspeyres quantity indices do not provide respectively lower and upper

bounds to the exact quantity indices.

(b) The ECLA Study

The ECLA Study, The Measurement of Latin America Real Income

in US Dollars offers a very unusual result: the various Latin American

countries fare better when their per capita GNP is weighted with their

own prices (Paasche) than when it is weighted with US prices (Laspeyres).

The authors notice such an anomaly and propose the following explanation:

'the strong inverse correlation between prices charged

and quantities consumed ... leads to a great amount of

substitution of dearer for cheaper goods'.

Such a statement is not quite sufficient because it does not

stress which goods are dearer and which goods are cheaper. Indeed,

according to Samuelson's theory, a situation where the Paasche quantity

index is greater than the Laspeyres quantity index can only correspond to

Case II of Table 2.1, i.e. the relative price of the necessities is

higher in the poorer countries, but the so-called income effect is greater

than the price effect and the equilibrium point of the richer country is

situated inside the angle formed by the cross-country Engel's path and

the straight line joining the origin to the poorer country's equilibrium.

Such a situation is more likely to appear in the comparison between the

US and the Latin-American countries than between the US and Western

European countries. Indeed, the US and the Latin-American countries

represent very different levels of development and the slope of the cross­

country Engel's path is much smaller, thus creating a much wider angle

We must now examine the data to find if any indication about

the relative price of the necessities can be unveiled. Unfortunately,

in the study mentioned above, the breakdown of the main expenditure is

not fine enough to distinguish between necessities and luxuries. However,

this study is partly based on A Measurement of Price Levels and the

Purchasing Power of Currencies in Latin America 1960-1962, (E/CN.12/653);

excerpts from this last study are also published in the Economic Bulletin

for Latin America, (Vol. VIII, No.l, March 1963). In this study the

comparison is carried on between seven Latin-American cities, Buenos Aires,

Rio De Janeiro, Santiago de Chile, Mexico City, Lima, Montevideo, Caracas,

and an average of two American cities, Los Angeles and Houston. Further­

more, the results are restricted to purchasing power parity comparisons

of an average Latin-American basket of goods thus yielding solely Paasche-

type price indices.

A further problem arises because the data are always presented

in the form of indices relative to a base city. However, it seems that

it is possible to construct relative price levels for the two relevant

categories, necessities and luxuries, P /P-, , and these price levels would n 1

still be indexed to a relative price level of 1 in the base city. Hence

to compare the relative price level, P^/P^, eac^ city we w i H choose

the data of Table 23, Part b of the excerpts entitled 'Inter City

Differences in Price Level at Free Market Exchange Rate', where all the

prices are indexed to an average price of 100 for each item in Los Angeles-

Houston. Total expenditures are broken down into consumption expenditures

and fixed investments (government is not included); consumption is rep­

resented by eight broad categories: food, beverages, tobacco, clothing

and textile, housing transport and communications, personal care and

recreation, while fixed investment is represented by three broad categor­

We will assume that food, clothing and housing represent the

inelastic categories. The average price index of these three categories

can be roughly constructed as a weighted average (according to their

local importance) of the three respective prices indices. Then we will

compare this price level to the average price level of total expenditures.

As it is in all cases higher, this can be interpreted as an indication

that the average price level of the necessities is higher in each Latin-

American city than in the US where P^/P^ = 1. If clothing is excluded

from the category of inelastic goods, these results stand only for four

countries, but we are aware that these conclusions may not be extremely

accurate in the light of all the difficulties already stressed. Indeed,

we can infer only that since the Paasche quantity index is greater than

the Laspeyres quantity index for all the Latin-American countries and

since there is some indication that the relative price of the necessities

in seven Latin-American cities might be higher than in two US cities,

the US-Latin-American comparison could correspond to Case II of Table 2.1,

where the exact indices provide the upper and the lower bounds to the

Paasche and the Laspeyres quantity indices.

(c) Usher's study

Finally we inspected Usher's data which yielded a Laspeyres

quantity index greater than the Paasche in the comparison between Thailand

and the UK. In some way, these were the most comprehensive data for our

experiments as the price data in both countries were reported.

However, whether the relative price level of the necessities

(food, clothing and housing) was weighted with a basket of goods repres­

enting Thai or British consumption, it was lower in Thailand than in the

UK which is quite consistent with the results L >P and thus this

q q

corresponds straightforwardly to Case I of Table 2,1, where the Paasche

and Laspeyres quantity indices provide respectively lower and upper bounds

to the exact quantity indices. T

C4) Conclusions on the PPP approach

The results of the very rough examinations of former studies

show that it is important to know something about the directions of

change of the relative prices of the necessities, and about the variations

in the pattern of consumption before one can draw straightforward

conclusions about the role of the Paasche and the Laspeyres indices as

lower or upper bounds to some exact indices. In summary, it becomes

clear that, from a theoretical point of view, the index number problem

causes the international comparison of monetary aggregates to be rather


The last chapter was concerned with problems of measurement

and problems of comparability of aggregate monetary quantities. Among

all these difficulties, the index number problem appeared to be the

worst one. In this chapter, we will ignore these problems and focus on

aggregate expenditure and its relation to welfare. A number of questions

will be raised and these will be classified into two main sections. In

the first section, the concept of a measure of aggregate welfare will be

studied; in the second section, the problem of what should be included

in a measure of aggregate welfare will be discussed.



In the case of one individual consumer, preference theory

provides a framework to appraise whether his economic welfare has improved

or deteriorated in response to a given change. Unfortunately, if we want

to measure the overall welfare of more than one individual, or if we want

to be able to observe an unambiguous increase or decrease in this overall

measure of welfare, we will be faced with very complex difficulties.

These questions have been examined at great length in welfare economics

and we will present the main theoretical findings. Some attempts to

integrate these welfare concerns in the empirical literature will then

be discussed.

I . Discussion of the New Economic Welfare Issues

We will now investigate if a change in overall welfare can be

measured at all by some aggregate indicator. More specifically, if we

assume that the aggregate indicator is national income measured as EPQ,

does an increase in this measure imply an increase in social welfare?

An increase in national income usually results in improvement

for some and deterioration for others as the structure of prices and the

structure of the distribution of income will be affected. How will total

welfare be affected? How can we weight the gains of some against the

losses of others?

Roughly speaking, social welfare should contain an evaluation

of the welfare of all the individuals in the society. It is only under

very specific and narrow conditions that the welfare of every individual

can be summed up in order to form a social welfare function. Unfortunate

ly, in the real world, the task of weighting the welfare of the various

individuals to perform any comparisons or summation is doomed as individ­

ual welfare is a highly subjective concept. As a result, if we assume a

given amount of social welfare, there is only one seemingly unambiguous

case in which we can say there has been an increase : the welfare of at

least one individual has increased while the welfare of the others have

remained stationary (nobody has incurred a decrease in welfare). This is

of course the traditional Pareto criterion for an improvement in social


The Compensation Principle

Kaldor (1939) and Hicks (1939) have separately suggested further criteria of comparisons, known as the compensation principle. It must first be noted that they hold only under the assumption of con­ stant tastes. As stressed by Hicks,'it is only under this assumption

[of constant wants] that quantitative comparisons are possible.' These criteria are based on the assumption of unlimited and costless lump-sum compensations. If two situations are to be compared, an initial situation 1 with income EP^Q^, and a new situation 2 with income ^2^2* according to Hicks, we can state that situation 2 is no worse than situation 1 if the gainers cannot be bribed by the losers to give up the change, Hicks actually compares situation 2 to situation 1 using the prices of situation 2 : i.e. if ^ 2 ^ 2 > ^2^1* s^tuat^-on 2 represents a welfare improvement over situation 1. The Kaldor criterion is symmetrical to Hicks' and states that if the gainers can bribe the losers into making the change from 1 to 2, we will experience an overall welfare improvement when E P . ^ > It: must be noted that these

criteria are measures of potential welfare.

However, it was soon shown by Scitovsky (1941) that either of these two compensation principles taken separately could lead to some contradiction; that is, both situations could be preferred to each other

(the criteria are not asymmetric). Hence, Scitovsky recommended combining the two criteria. Unfortunately, this does not solve the problem for as shown by Samuelson (1950), the Scitovsky double criterion may result in intransitivity.

In order to illustrate these problems, Samuelson introduced the concept of utility possibility frontier defined as the locus of Pareto optima, given a fixed aggregate EPQ, for every possible distribution; this curve or n-dimensional plane measures the ordinal level of utility for each of the n individuals corresponding to various distribution of

income. Hence there will be a utility possibility frontier corresponding

to 1 and another one corresponding to 2. So Hicks was comparing a given

point on the utility possibility frontier of 2 and the whole utility

possibility frontier of 1, while Kaldor was comparing a given point on

the utility possibility frontier of 1 and the whole utility possibility

frontier of 2; Scitovsky was performing these two comparisons success­

ively. However, a basic difficulty remains because there is no reason

at all why the two utility possibility frontiers should not cross hence

introducing the possibility of non-asymmetry to the hypothetical compari­

sons .

In conclusion, the welfare economists had to adopt a much more

stringent criterion, the Samuelson criterion, stating that there is an

unobjectionable increase in welfare only when the entire utility possib­

ility frontier shifts outwards, i.e. there is no intersection of the old

and the new utility possibility frontier.

(2) The Assumptions Supporting a Concept of Real Expenditure as a

Measure of Actual Social Welfare

This new criterion, although theoretically very sound, was, due

to its cumbersome nature, rather impractical.1 Furthermore, it did not

solve the problem whether the compensation should actually be paid. If

so, there would be special costs incurred due to the redistribution itself

and to the creation of new inefficiencies. To deal with this, Samuelson

developed the concept of a utility feasibility frontier lying inside the

utility possibility frontier and tangent to the utility possibility

frontier at the present point of laissez-faire.

In contrast to these problems, the Hicks criterion (comparing

EP2Q2 and E?2Q^) has a definite advantage in making actual welfare

comparisons. As far as the measurement of welfare is concerned, it seems

1 It can be characterised in terms of set inclusions but this approach

to offer an improvement over the usual concept of deflated GNP. It

differs from it in three respects:

(i) it relates to private consumables;1

(ii) it uses consumer prices and not producer prices or

factor costs;

(iii) it calls for present prices, not base period prices, i.e.

it is a backward or Paasche index.

Although Samuelson pointed out that its welfare implication is

strictly limited to only the immediate neighbourhood of the actual

position, the possibility of salvaging this concept and of giving it a

wider scope has been considered by others in the literature.

Indeed, Chipman and Moore in two basic articles (1973a, 1973b)

and Ohyama (1972) have presented a more rigorous treatment of the prob­

lems involved in the compensation principle in the context of a competi­

tive general equilibrium, and they were thus able to draw more definite

conclusions to the problem of valuation of real income.

In the context of a competitive equilibrium model, Chipman and

Moore show that, unless preference were identical and homothetic, policy

decisions based on the Hicks criterion could prove unsupportable. These

are indeed very strong and limiting assumptions. However, it turns out

that Hicks’ compensation principle could be lent some support from a

completely different angle. The assumption then needed are much weaker:

free disposability, non-satiation, no external economies of diseconomies

(and no transport costs). Given these assumptions, Chipman and Moore,

and Ohyama in the context of a competitive equilibrium, prove that, if

the redistribution of income is controlled by lump-sum redistributive

measures so that welfare is maximised according to a given social welfare

function, the Hicks criterion can be interpreted as a measure of actual


social welfare.1

Ohyama gives a final, but conditional, support to the Hicks

criterion by stating that 'a policy change is beneficial if it brings

about an increase in the aggregate real income in the so-called Paasche

backward index for all relevant distributions.’ Of course, the problems

raised in this last sentence can be solved only if we assume the exist­

ence of a social indifference map with surfaces strongly convex towards

the origin


if we assume homogeneous utility functions of the first


In conclusion, overall welfare comparisons can be carried out

under two completely different sets of assumptions. First, if everybody

has similar and homothetic tastes, a social utility function can be

defined regardless of the state of distribution; in this case there is

a direct link between income and welfare comparisons. However, this is

very unrealistic and welfare economists have found it more palatable to

assume the existence of a well-behaved social welfare function strongly

convex and possessing the property of cardinality (to counteract the

conclusions of Arrow’s impossibility theorem (1951)) and, as Chipman and

Moore pointed out, the compensation principle thus becomes more suitable

in the case of a collectivist economy rather than in the case of a laissez

faire one.

The previous discussion presented the notion of hypothetical

and costless lump-sum compensations to assess any improvement in social

welfare. However, we stressed that if these compensations were actually

paid, some costs would be incurred and would have to be taken into account

Similarly, it is frequently taken for granted that a more

equal distribution of income increases social welfare.2 But carrying out

1 These ideas were also developed by Samuelson (1956).

2 The welfare economic foundation for this is questionable; it

an actual redistribution would be costly as we would be moving along the

utility feasibility frontier and not along the utopian utility possibility

frontier. We also know that it is likely that the gap between the two

curves will increase as we travel further from the original equilibrium

point where the two curves are tangent. So if there was some way to

value in terms of income the increase in welfare that could be gained by

a redistribution towards greater equality, the net result of any such

policy could be estimated beforehand.

II. The Measurement of Inequality

Atkinson (1970) undertook to measure the gross increase in

welfare (excluding the cost of an actual redistribution) that a country

would sustain if its income was perfectly equally distributed across

its population. This can conversely be regarded as the loss in welfare

due to inequality. Atkinson approached this problem in a rigorous manner:

he developed an index of inequality based on sounder theory than the

traditional indices (Gini etc.); he also showed that the traditional

indices of inequality were often based on questionable assumptions.

The level of inequality of the income distribution can be

illustrated by a Lorenz curve which shows the proportion of total income

received by the bottom x per cent of the population. First, Atkinson

points out that any measure of inequality assumes implicitly a specific

form for the social welfare function. If the assumptions about the

social welfare function are limited to the case of increasing and strictly

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