Market Segmentation and Income Distribution

Abstract

The eighth chapter discusses household income inequality in a number of countries. It examines its implications in terms of the purchasing power of different income groups. Concepts and measures of inequality and income elasticity and preference are introduced. This chapter then uses these concepts and measures in the classification of basic and progressive commodities and consumer preferences as income rises. Analyses of changing preferences for different commodities as income changes in selected countries with different cultures, population and income levels illustrate the basic nature of some commodities and preference for other commodities as affluence rises. The analyses include both arc-elasticity concepts and measures and income preference ratios for different types of commodities and household behaviour as income rises. The selected countries cover a wide geographical scope, a range of income levels and cultures. The chapter examines common trends and differences regarding preferences for given commodity groups as income rises. Some generic propositions are made based on the analyses undertaken for the selected countries.

Appendices

Appendix 1: Gini Coefficient Estimation – Example

The following example uses data from a household income and expenditure survey conducted by the Australian Bureau of Statistics (ABS, 2000).

Following the equation and notation in Box 8.1

$${\textbf{\textit{G = Gini}}}\;{\textbf{\textit{Coefficient}}} = {\textbf{\text{1}}} - \Sigma {{\textbf{\textit{(y}}}_{{\textbf{\textit{i} + 1}}} + {\textbf{\textit{y}}}_{\textbf{\textit{i}}}}\textbf{\textit{)}} \;{\textbf{\textit{(x}}}_{{\textbf{\textit{i} + 1}}} - {\textbf{\textit{x}}}_{\textbf{\textit{i}}} \textbf{\textit{)}}$$

	Proportion
Household income quintile	Number of households	Household income
	x i	y i
Q1	0.2	0.0366
Q2	0.2	0.0933
Q3	0.2	0.1621
Q4	0.2	0.2537
Q5	0.2	0.4543

	Cumulative		(a)	(b)	(a)*(b)
Quintile	x i ∧	y i ∧	$x_{i + 1} ^{\wedge}- x_{i}^{\wedge}$	$y_{i + 1} ^{\wedge}+ y_{i}^{\wedge}$
Q1	0.2	0.0366	0.2	0.0366	0.0073
Q2	0.4	0.1299	0.2	0.1665	0.0333
Q3	0.6	0.2921	0.2	0.4220	0.0844
Q4	0.8	0.5458	0.2	0.8379	0.1676
Q5	1.0	1.0000	0.2	1.5458	0.3092
				$\sum {a\,^{*}\,b = }$	0.6017

$${\textbf{\textit{G}}} = 1 - 0.6017 = \;\;\;{\textbf{0}}{\textbf{.3983}}\;{\textbf{or}}\;{\textbf{39}}{\textbf{.8\% }}$$

An alternative method for estimating the Gini Coefficient is using Simpson’s Rule

Cumulative
Quintile	x i ∧	y i ∧	$\left(y_{i + 1} ^{\wedge} + y_i ^{\wedge}\right)/2$
Q1	0.2	0.0366	0.0183
Q2	0.4	0.1299	0.0833
Q3	0.6	0.2921	0.2110
Q4	0.8	0.5458	0.4189
Q5	1.0	1.0000	0.7729

$$\begin{array}{l} \sum {\left[\left({\textrm{\textit{y}}}_{{\textrm{\textit{i}}} + 1} ^{\wedge} + {\textrm{\textit{y}}}_{\textrm{\textit{i}}} ^{\wedge}\right)/2\right]} = 1.5044 \\ \sum {\left\{ \left[\left({\textrm{\textit{y}}}_{{\textrm{\textit{i}}} + 1} ^{\wedge} + {\textrm{\textit{y}}}_{\textrm{\textit{i}}} ^{\wedge}\right)/2\right]/5\right\} = 0.30088} \\ \end{array}$$

$${\textbf{\textit{G}}} = 1 - \left(2\,^{*}\,0.30088\right) = 1 - 0.6017 = {\textbf{0}}{\textbf{.3983 or 39}}{\textbf{.8\% }}$$

Appendix 2: Arc Elasticity Estimation – Example

The following example uses data from India’s household expenditure survey for 2004–05 (NSSO, 2007) using total expenditures as surrogate for income.

Following the equation and notation in Box 8.2

$${\textbf{\textit{e}}} = {\textbf{\textit{arc}}}\;{\textbf{\textit{elasticity}}} = \textbf{\textit{[}}{\textbf{\textit{(y}}}_{\textbf{\textrm{1}}} {\textbf{ \textit{-- y}}}_{\textbf{\textrm{2}}}\textbf{\textit{)}}/{\textbf{\textit{(y}}}_{\textbf{\textrm{1}}} {\textbf{ + \textit{y}}}_{\textbf{\textrm{2}}}\textbf{\textit{)}}\textbf{\textit{]}}/\textbf{\textit{[(}}{\textbf{\textit{x}}}_{\textbf{\textrm{1}}} {\textbf{\textit{ -- x}}}_{\textbf{\textrm{2}}}\textbf{\textit{)}}/{\textbf{\textit{(x}}}_{\textbf{\textrm{1}}} {\textbf{ + \textit{x}}}_{\textbf{\textrm{2}}}\textbf{\textit{)]}}$$

Average 30-days household expenditure per capita (Rupees)
Expenditure Item	Lowest 20 percent	Highest 20 percent
Food	235.91	763.40
Transport	7.90	207.28
All items	421.97	2,391.28

The arc elasticity for food between the lowest and the highest 20 percent of households is estimated as follows

• $\begin{array}{ll}{\textbf{\textit{e}}}_{\textbf{f}} = \left\{ \left(235.91 - 763.40\right)/\left(235.91 + 763.40\right)\right\}/\\ \qquad \left\{ \left(421.97 - 2,391.28\right)/\left(421.97 + 2,391.28\right)\right\}\end{array}$

• $\begin{array}{ll}{\textbf{\textit{e}}}_{\textbf{f}} = \left( - 527.49/999.31\right)/\left( - 1,969.31/2,813.25\right)\\ = - 0.52785/ - 0.70001 = {\textbf{0}}{\textbf{.754}}\end{array}$

Note: The arc elasticity equation is slightly different from that in Box 8.2. The division by 2 of the numerator and denominator is not required.

The arc elasticity for transport between the lowest and the highest 20 percent of households is

• $\begin{array}{ll}{\textbf{\textit{e}}}_{\textbf{t}} = \left\{ \left(7.90 - 207.28\right)/\left(7.90 + 207.28\right)\right\}/\\ \left\{ \left(421.97 - 2,391.28\right)/\left(421.97 + 2,391.28\right)\right\}\end{array}$

• $\begin{array}{ll}{\textbf{\textit{e}}}_{\textbf{t}} = \left( - 199.38/215.18\right)/\left( - 1,969.31/2,813.25\right)\\ = - 0.92657/ - 0.70001 = {\textbf{1}}{\textbf{.324}}\end{array}$

Thus, food with an arc elasticity of less than 1.00 is considered to be inelastic or a basic commodity, as household expenditures on food tend to rise less than proportional as total expenditures increase from the lowest to the highest 20 percent of households. Transport with an arc elasticity of more than 1.00 is designated as elastic or a progressive (affluence) commodity as household expenditures on transport grow more than proportionately as household total expenditures increase from the lowest to the highest 20 percent of households.

Appendix 3: Income Preference Ratio Estimation – Example

The following example uses data from the 1999 household expenditure survey of Japan (SBJ, 2000).

	Household monthly average expenditure (Yen)
Households from lowest to highest 20 percent	Current housing	Clothing and footwear	Personal care	All items
Q1	20,694	8,990	5,883	215,150
Q2	22,882	12,365	7,101	272,198
Q3	22,329	13,738	7,552	292,838
Q4	19,570	19,547	9,755	369,895
Q5	22,278	28,856	13,286	492,255
All households	21,408	17,024	8,809	335,115

Following the equation and notation in Box 8.3

$${\textbf{\textit{r}}}_{{\textbf{\textit{i}1}}} ^{\textbf{\textit{n}}} {\textbf{ = \textit{Income}}}\;{\textbf{\textit{Preference}}}\;{\textbf{\textit{Ratio}}} = \textbf{\textit{(g}}_{{\textbf{\textit{in}}}} {\textbf{/\textit{g}}}_{\textbf{\textit{i}1}}\textbf{\textit{)}}{\textbf{\textit{(G}}}_{{\textbf{\textit{in}}}} {\textbf{/\textit{G}}}_{{\textbf{\textit{i}1}}}\textbf{\textit{)}}$$

The IPRs for the current housing are

• IPR_Q1 = (20,694/21,408)/(215,150/335,115) = 0.9666/0.6420 = 1.506

• IPR_Q2 = (22,882/21,408)/(272,198/335,115) = 1.0689/0.8123 = 1.316

• IPR_Q3 = (22,329/21,408)/(292,838/335,115) = 1.0430/0.8738 = 1.194

• IPR_Q4 = (19,570/21,408)/(369,895/335,115) = 0.9141/1.1038 = 0.828

• IPR_Q5 = (22,278/21,408)/(492,255/335,115) = 1.0406/1.4689 = 0.708

The IPRs indicate that household expenditures on current housing fell more than proportionately as household income increased from the lowest to the highest 20 percent. This indicates that housing is a (B) basic commodity.

The IPRs for clothing and footwear are

• IPR_Q1 = (8,990/ 17,024)/(215,150/335,115) = 0.5281/0.6420 = 0.823

• IPR_Q2 = (12,365/ 17,024)/(272,198/335,115) = 0.7263/0.8123 = 0.894

• IPR_Q3 = (13,738/ 17,024)/(292,838/335,115) = 0.8070/0.8738 = 0.924

• IPR_Q4 = (19,547/ 17,024)/(369,895/335,115) = 1.1482/1.1038 = 1.040

• IPR_Q5 = (28,856/ 17,024)/(492,255/335,115) = 1.6950/1.4689 = 1.154

The IPRs show that household expenditures on clothing and footwear rose more than proportionately as household income increased from the lowest to the highest 20 percent. This would make clothing and footwear an (A) affluence/progressive commodity.

The IPRs for personal care are

• IPR_Q1 = (5,883/8,809)/(215,150/335,115) = 0.6678/0.6420 = 1.040

• IPR_Q2 = (7,101/8,809)/(272,198/335,115) = 0.8061/0.8123 = 0.992

• IPR_Q3 = (7,552/8,809)/(292,838/335,115) = 0.8573/0.8738 = 0.981

• IPR_Q4 = (9,755/8,809)/(369,895/335,115) = 1.1074/1.1038 =1.003

• IPR_Q5= (13,286/8,809)/(492,255/335,115) = 1.5082/1.4689 = 1.027

The IPRs for personal care indicate that expenditures on this item vary little as income rises from the lowest to the highest 20 percent. It has no consistent pattern. This would indicate that this commodity has no progression characteristics either upwards or downwards as household income rises and could be considered a (C) commodity.