Chapter 2: Income Standards, Inequality, and Poverty
are positive but not larger than one. When ϱ = 1, then the cost of a child is equal to the cost of an adult. The lower the value of ϱ, the lower the cost of each child compared to an adult. Similarly, when ϑ = 1, no economy of scale is assumed. The lower the value of ϑ, the larger the economy of scale is assumed to be. For example, suppose there are five members in a household: three adults and two children. If a child is assumed to be half as costly as an adult, then ϱ = 0.5 and ϑ = 0.5. Then AELSMS = (3 + 0.5 × 2)0.5 = 2. Therefore, if the actual total income of the household is Rs 20,000, then the real per capita income of the household is equivalent to Rs 10,000. However, if no economy of scale is assumed and each child is considered as equally expensive as an adult, then the household’s per capita income is only Rs 4,000. In the subsequent analysis in this chapter, we assume that we are using a dataset having all the information required for constructing a welfare indicator either at the individual level or at the household level. The dataset may cover the entire population or may just be a collection of samples from the population. There are other important issues one should take into account regarding a dataset (such as its survey design, sample coverage, sample variability, and so on), which are not covered in this chapter.2 To keep explanations and mathematical formulas simple, we make two fundamental assumptions. First, we use income as the welfare indicator and assume that information on income is available for every person in our dataset. Second, we assume that every household contains only one adult member. As a result of the second assumption, we do not need to make any adjustment for the economy of scale and equivalent scale because each member is an adult and lives in a single-member household. However, the tools and techniques introduced in this chapter can be easily extended to situations when the welfare indicator is consumption expenditure and more than one person lives in a household.
Basic Concepts Suppose our reference society X consists of N people, where the income of person n is denoted by xn for all n = 1,2,…,N. Thus, the income distribution data for society X has N incomes. For the sake of simplicity, we assume these incomes are ordered so that x1 ≤ x2 ≤ … ≤ xN.
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