Price Effects on Compound Commodities

• Author: Junichi Minagawa,Thorsten Upmann
• Date: 01 April 2019
• Published date: 01 April 2019
• DOI: http://doi.org/10.1111/sjoe.12297

Scand. J. of Economics 121(2), 630–646, 2019

DOI: 10.1111/sjoe.12297

Price Effects on Compound Commodities*

Junichi Minagawa

Chuo University, Hachioji, Tokyo192–0393, Japan

minagawa@tamacc.chuo-u.ac.jp

Thorsten Upmann†

Helmholtz-Institute for Functional Marine Biodiversity at the Oldenburg University, DE-23129

Oldenburg, Germany

thorsten.upmann@hifmb.de

Abstract

We examinethe effect of simultaneous price changes on the total demand for a group of goods,

which we call a compound commodity. Specifically, we consider unit and proportional cost

components (e.g., taxes,transpor tation costs) imposed on compound commodities. If the unit cost

is positive,then the propor tional cost raises the relativeprice of the more expensive good, and thus

induces substitution towards the less expensive good within this group. Then, the substitution

effect of the proportional cost for a compound commodity is non-negative if and only if the

compound commodity and the other goods are, on average, not strongly substitutable.

Keywords: Commodity taxation; demand for a group of goods; Giffen goods; Slutsky equation;

unit and proportional costs

JEL classification:D01; D11; H20

I. Introduction

In the classic demand theory, it is accepted as fundamentally true that the

substitution effect of an increase in the price of a good always decreases

the demand for that good. However, in practice, price changes frequently

occur for a group of goods rather than for a single good. Therefore, it

might be useful to analyze the substitution effects caused by simultaneous

price changes for a group of goods. In particular, by considering two types

of simultaneous, parallel price changes, we find that the above property for

the demand of a single good does not generally hold for the demand for

a group of goods in economically meaningful situations. Thus, we face a

serious aggregation problem.

Clearly, aggregation is a significant and long discussed issue in

economics, and it can be traced back to Hicks (1939), at least. When

the total expenditure on a group of goods can be treated as a single

*We are grateful for the helpful comments and suggestions of twoanonymous referees.

†Also affiliated with Bielefeld University and CESifo (Munich), Germany.

C

The editors of The Scandinavian Journal of Economics 2018.

J. Minagawa and T. Upmann 631

good, this group is referred to as a composite commodity – a result

well-known as the Hicks composite commodity theorem. The fundamental

condition for this theorem to hold is that the prices of these goods change

proportionally in such a way that the relative prices within this group are

kept constant.1Yet, non-proportional price changes are, as we shall argue,

a common phenomenon, even if such changes result from common cost

components included in all of these prices. Furthermore, little is known

about how the total demand (rather than the expenditure) for a group of

goods is affected by simultaneous price changes, especially by those that

alter relative prices. Here, the total demand for a group of goods represents

the sum of all demands for goods that are similar and are measured by

the same unit. We can think of this group of goods as different varieties

of a particular good (e.g., brands of cigarettes), which can be naturally

aggregated over these varieties. This type of aggregation over similar goods

or varieties of some general good is omnipresent in science (e.g., in the

work of economists and statisticians, as well as in real life): cheese, meat,

fish, transport, accommodation, jewelry, etc., are all typically referred to as

single goods but actually represent aggregates. In this paper, we refer to

such a commodity that is composed of similar goods or varieties of some

general good as a compound commodity. Here, in order to acknowledge the

omnipresence of compound commodities and the fact that their components

are typically subject to simultaneous price changes, we explore the effects

of parallel, non-proportional price changes on the total demand for a group

of goods, or on the demand for a compound commodity.

The basic idea of our arguments is as follows. A per unit cost added to

the prices of two goods decreases the relative price of the more expensive

good and hence leads to a relative increase in the compensated demand

for that good. This observation was first made by Alchian and Allen (1964,

pp. 74–75). Then, holding the unit cost unchanged, a proportional cost

added to both net prices increases the relative price of the more expensive

good and hence leads to a relative decrease in the compensated demand

for that good.2This implication was suggested and tested by Hummels

and Skiba (2004). In the literature on the Alchian–Allen theorem, both

cost components are variously specified: the common unit cost component

is interpreted as a per unit tax, a transportation fee, a wage (opportunity

1There are many studies that have formalized,generalized, and tested the composite commodity

theorem (e.g., Samuelson, 1947; Katzner, 1970; Green, 1976; Deaton and Muellbauer, 1980;

Carter, 1995; Lewbel, 1996; Moro, 2001; Davis, 2003).

2Wefocus on the case where the proportional cost is applied to the net price, b utwe can equally

think of a proportional cost applied to the gross price (i.e., to the net price plus the unit cost).

In some cases (e.g., commodity taxation), the latter specification seems to be applicable, and for

this reason we briefly discuss the latter specification in Section V.

C

The editors of The Scandinavian Journal of Economics 2018.