The consumer's index

• Author: Thijs ten Raa
• Date: 01 March 2020
• DOI: http://doi.org/10.1111/ijet.12243
• Published date: 01 March 2020

Int J Econ Theory. 2020;16:119–122. wileyonlinelibrary.com/journal/ijet © 2019 IAET

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119

Received: 28 February 2019

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Accepted: 10 May 2019

DOI: 10.1111/ijet.12243

ORIGINAL ARTICLE

The consumer’s index

Thijs ten Raa

School of Economics, Utrecht University,

The Netherlands

Correspondence

Thijs ten Raa, Herengracht 31, NL‐1015

BB Amsterdam, The Netherlands.

Email: tenraa@uvt.nl

Abstract

Consumer’s surplus measures the area under the

demand curve between two prices, but is path depen-

dent. There exists a path such that consumer’s surplus

tracks utility and an explicit formula is known for CES

utilities. This paper shows that the CES‐based formula

holds for any homothetic utility, and I call it the

consumer’s index. The index modifies consumer’s

surplus in two ways: the change in income is measured

by its growth factor and the area under the demand

curve is normalized by income.

KEYWORDS

consumer’s surplus, price–income indices, purchasing power

JEL CLASSIFICATION

C43; D60

1

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INTRODUCTION

The measurement of purchasing power is a key issue. Purchasing power is an index of price p,

an n‐dimensional non‐negative row vector, and income m, a positive scalar. An index is

economic if it is ba sed on the utility l evel of consumers . A consumer is supp osed to solve the

problem

Ux px mmax ( ) : ,≤(1)

where xis the consumption vector and Uthe utility function. The solution to the

consumer’s problem (1) is demand x=D(p,m), with value V(p,m)=U(D(p,m)). Vis

called the indirect utility function. An index, I(p,m), tracks utility if it preserves the order

of V(p,m): I(p¹, m¹) ≥I(p

0

,m

0

)ifandonlyifV(p¹, m¹) ≥V(p

0

,m

0

). An index cannot be

(indirect) utility itself, because that is not observed. Indices are based on demand, which is

observable.