Working Paper 2012:2
Department of Economics
School of Economics and Management
When More Poor Means Less
Poverty: On Income Inequality and
Purchasing Power
Andreas Bergh
Therese Nilsson
January 2012
0
When more poor means less poverty: On
income inequality and purchasing power
Andreas Bergh
a,*
Therese Nilsson
b
Department of Economics, Box 7082, S-220 07 Lund, Sweden.
Research Institute of Industrial Economics, Box 55665, SE-102 15 Stockholm,
Sweden
Abstract
We show theoretically that the poor can benefit from price changes induced by
higher income inequality. As the number of poor in a society increases, or
when the income difference between rich and poor increases, the market for
products aimed towards the poor grows and such products become more
profitable. As a result, there are circumstances where an increase in poverty
associates with higher purchasing power of the poor. Using cross-country data
at two points in time on the price of rice and Big Mac hamburgers, we confirm
the relationship between inequality and purchasing power of the poor, and
show that it is robust to several control variables and also to a first-difference
specification.
JEL classification: D63; I3
Keywords: Inequality; Poverty; Prices; Purchasing power
a
Research Institute of Industrial Economics and Department of Economics, Lund
University, Sweden.
b
Department of Economics, Lund University, and Research Institute of Industrial
Economics (IFN), Sweden
E-mail addresses: Andreas.Bergh@nek.lu.se (A. Bergh)
Therese.Nilsson@nek.lu.se (T. Nilsson)
* Corresponding author. Tel. +46 46 222 46 43. Fax +46 46 222 41 18.
1
1. Introduction
In Africa, the retail chain Pick ‘N Pay is investing in the poorer parts of the
continent through low-price format stores, rather than expanding its existing
high and middle-end supermarkets. According to Weatherspoon and Reardon
(2003), this illustrates a trend: Supermarkets geared towards the poor.
1
In China, rural farmers commonly used washing machines not only to wash
clothes, but also to wash vegetables. Haier, China’s biggest home appliance
manufacturer, responded by developing a washing machine with larger pipes
and providing instructions on how to clean vegetables in it. Anderson and
Billou (2007) use this particular example to illustrate that products are often
developed specially for the poor, rather than modeled on what has worked for
middle and high-income groups. Similarly, the Philippine telecom corporation
Smart Communications launched very small pricing packages on telecom that
matched the many poor consumer’s incomes and needs.
The examples above illustrate that, provided that the market is sufficiently big,
it is part of a profit maximizing strategy for firms to sell low priced products
and services to poor consumers. This paper notes that as a result, the price
structure will depend on the income distribution. As a somewhat counter-
intuitive result, higher income inequality will under some circumstances
associate with higher purchasing power and possibly improved welfare of the
poor.
As noted by Pendakur (2002), the price structure is usually ignored when
measuring economic inequality. The income of rich and poor in a country is
deflated using the same price vector.
2
But if prices depend on the income
distribution, changes in the income distribution will not necessarily imply
similar changes in the distribution of purchasing power. The distributional
importance of the price structure is noted by Broda and Romalis (2009), who
show that much of the increase in income inequality in the US has been offset
by a relative decline in the prices of products that poorer consumers buy – the
so called Walmart-effect. We argue that this is no coincidence: Higher income
inequality will often imply higher demand for products targeted towards the
poor, and the increasing supply of these goods will mitigate adverse effects of
higher income inequality by its impact on the distribution of purchasing power.
1
Incidentally, the African supermarket chain Massmart was bought by Walmart in 2010,
a chain that in the US has been highly successful providing low-price products to cash-
constrained Americans.
2
Using Canadian data on regional price information and expenditure-dependent price
deflators Pendakur (2002) shows that relative prices affect both the level of and year-to-
year changes in family inequality.
2
This paper develops a simple model to analyze the effects of income inequality
on the distribution of purchasing power (section 2). The claim that higher
income inequality has purchasing power effects that are beneficial for the poor
is then tested empirically using data from middle- and high-income countries
on income inequality and the price of two inferior goods: rice and Big Mac
hamburgers (section 3). Section 4 concludes with some remarks on directions
for future research.
2. A simple model and some theoretical
considerations
Assume that society consists of two groups, rich and poor, with incomes λ>0
and
),,0(
respectively. The poverty rate in the population is r.
Normalizing the population to 1, total income will be
.1
rrY
The
share of total income held by poor will be
./Yr
From the properties of the
commonly used Gini-coefficient
(see, for example, Lambert 1993), it follows
that coefficient will increase as the poverty rate increases from 0 to 0.5, and
then decrease as the poverty rate approaches 1. Assuming that r < 0.5, and
using G to denote the Gini-coefficient for income, our model has the
properties that a higher poverty rate increases the Gini-coefficient, and a higher
income of the poor decreases it: G
γ
< 0 and G
r
> 0. Figure 1 illustrates the
model graphically.
3
Figure 1. The Gini coefficient in a model with two income groups
Assume further that there are N goods with prices p
1
,…,p
N
. Let α
1
,…,α
N
be
the consumption weights of the poor, let β
1
,…,β
N
be the consumption weights
of the rich (in both cases, weights sum to 1), and let p
R
and p
P
be the price
indices associated with the consumption patterns of rich and poor, so that
p
R
= β
1
p
1
+…+β
N
p
N
, and
p
P
= α
1
p
1
+…+α
N
p
N
.
The purchasing power of the poor will be
,
P
p
and the purchasing power of
the rich will be
.
R
p
Assuming α = β for all goods corresponds to using what
Pendakur (2002) calls a naïve price vector where p
R
= p
P
, describing the special
case of homothetic preferences where consumption weights are independent
of income. If poor spend bigger shares of their income on relatively cheaper
goods, we have p
R
> p
P
, and inequality of purchasing power will be smaller than
inequality of income. This gives us a formal definition of the Walmart-effect:
Definition The Walmart effect: p
R
> p
P
implies that
.
In the model, there are three different ways in which the distribution of income
may change: By a change in the income of the poor γ, by a change in the
income of the rich λ, and by a change in the poverty rate r. If prices are
constant, these income changes translate directly to changes in purchasing
Yr /
r
0
1
1
Cumulative share of income
Cumulative share of population
