Peter Kriesler

English

Research Papers in Economics

 
 
 
 
 
 
 
School of Economics 
UNSW, Sydney 2052 
Australia 
 
http://www.economics.unsw.edu.au 
 
ISSN 1323-8949 
ISBN 978 0 7334 2482 3 
 
 
 
 
 
Partial Equilibrium and Marshall 
 
Peter Kriesler 
 
School of Economics Discussion Paper: 2007/18 
 
 
 
 
 
 
 
 
The views expressed in this paper are those of the authors and do not necessarily reflect those of the 
School of Economic at UNSW. Partial Equilibrium and Marshall 
Peter Kriesler 
School of Economics 
University of New South Wales 
 
With the publication of the first edition of his Principles of Economics in 1890,  Alfred Marshall 
developed partial equilibrium analysis as a method for turning economic theory into a form that 
could be used to formulate policy and aid in the analysis of actual problems. He wanted economics 
to be “an engine for the discovery of concrete truth” (quoted in Hausman 1992, p. 152). In partial 
equilibrium each market or section of the economy is considered as a separate entity, and so its 
interdependence with other markets is not considered. This often is described as ceteris paribus; that 
is, other things being equal. To bring some order and understanding to an extremely complex world 
in which everything affects everything else, partial equilibrium concentrates on key relations, 
holding the rest constant (Hausman 1992). It is not that these factors are believed to be unchanging 
but that they are held in the ceteris paribus “pound.” As Marshall stated in 1922: 
The forces to be dealt with are however so numerous, that it is best to take a few at a 
time: and to work out a number of partial solutions.... Thus we begin by isolating the 
primary relations of supply, demand and price in regards to a particular commodity. We 
reduce to inaction all other forces by the phrase “other things being equal”: we do not 
suppose that they are inert, but for the time being we ignore their activity.... In the 
second stage more forces are released from the hypothetical slumber that had been 
imposed on them. (Marshall 1922, pp. xiv–xv) 
Marshall suggested that, in each stage of the analysis, more factors could be allowed to vary 
The element of time is a chief cause of those difficulties in economic investigations 
which make it necessary for a man with  limited powers to go step by step; 
1
 breaking up a complex question, studying one bit at a time, and at last combining his 
partial solutions into a more or less complete solution of the whole riddle. In breaking it 
up, he segregates those disturbing causes, whose wanderings happen to be inconvenient, 
for the time in a pound called Cæteris Paribus. The study of some groups of tendencies 
is isolated by the assumption other things being equal.... With each step more things can 
be let out of the pound. (Marshall 1922, p. 366, emphasis in original) 
 
Interdependence in Prices and Markets 
Marshall was fully aware of the interdependence between most markets and prices in the economy, 
as is apparent from notes xiv and xxi of the mathematical appendix to his Principles, where he 
outlined the basis of a general equilibrium system. However, he realized that attempting to analyze 
that interdependence would render the economic problem so complex that the main causal factors 
could not be isolated. Hence, he regarded partial equilibrium analysis and the use of ceteris paribus 
as important approximations that allow casual inferences to be made and real-world problems to be 
studied. 
In particular, Marshall concentrated on the role of price in individual markets as the main 
determinant of the quantities supplied and demanded. To illustrate this, one can examine the 
demand for oranges (D0), which will depend on their price (P0), all other prices in the economy  (P1 
.... Pn ), the income of all individuals in the economy (Y1 ....... Ym), the weather, people’s tastes, 
international factors, and so forth: 
D0 = f(P0, P1 .... Pn, Y1 ....... Ym, weather, tastes, etc.) 
Some of these factors, such as weather and tastes, are not economic variables, and so they 
normally are considered exogenous. This does not mean that it is assumed that they do not change 
but that their changes cannot be  explained  within economics, and so they are unlikely to 
2
 be influenced significantly by economic variables. What is left is the general equilibrium demand 
function for oranges in terms of all prices and incomes in the economy. Clearly, this is extremely 
complex because in general equilibrium everything affects everything else. Therefore, it is difficult 
to use the theory to make meaningful statements about causality or policy. 
In partial equilibrium analysis each market is considered in isolation. When each market is 
concentrated on individually and when part of the economy is broken off and relations within that 
part are considered, causal inferences can be made. In addition, it is assumed that demand and 
supply are separable and can be represented as independent curves, with price determined as the 
balance of those forces. To calculate the partial equilibrium demand function for oranges, the price 
of oranges is considered as the main determinant, other things being equal. In other words, all 
variables that are not determined within that market, particularly all other prices and incomes, are 
assumed for the analysis to be given and constant. This leaves the partial equilibrium demand curve 
for oranges: 
D0 = f (P0) 
Marshall’s Four Time Periods 
According to Marshall, the question of which factors are left in the ceteris paribus pound depends 
on the time allowed for those factors to respond to changes in the market. In particular, the length of 
time that is allowed for supply to respond to changed conditions will exert an important influence 
on the operation of the market. Accordingly, Marshall distinguished four time periods that are 
appropriate for economic analysis, determined on the basis of which factors are held constant in 
each situation. The first is the very short run, or the market period in which it is assumed that goods 
are already at market and must be sold, so that supply cannot vary and price is determined mainly 
by demand. In the short period, quantity supplied is allowed to vary as a result of variations in 
production through changes in the variable factors, but the quantity and structure of fixed capital 
goods cannot be varied. As plants are fixed,  firms can neither enter or exit the market, and 
3
 so a supernormal profit can be made even in competitive industries. In the long period, plants can 
be varied and firms can enter or exit from the market, and so all factors are variable. In this case no 
supernormal profit can be sustained in a competitive market. Finally, in what Marshall referred to as 
the “secular long period” knowledge, population, technology, and tastes all can vary. 
Applications and Problems 
Clearly, in evaluating partial equilibrium it is not relevant to consider the question of whether the 
underlying assumptions are realistic. As approximations, they are intended to focus on key 
relations, intentionally abstracting from secondary ones, which are held constant in the ceteris 
paribus pound. Demand and supply are determined by more than just the price of a commodity. 
However, in evaluating assumptions it is necessary to look at whether they capture the key aspects 
of any relationship, whether what is assumed away is as important as what is included, whether the 
variables that are assumed to be constant vary systematically with the variables included in the 
analysis, and whether the variables that are assumed to be independent, in this case supply and 
demand, are in fact interdependent. 
As a result of these considerations, partial equilibrium can be applicable only to 
commodities that are relatively unimportant in terms of household budgets and that have neither 
close substitutes nor complements. If a commodity has close complements or substitutes, changes in 
its price will lead to changes in demand conditions in other markets, which will lead to changes in 
prices in those markets. This means that the variables that are being held constant will change as a 
result of changes in the endogenous variables. This contradicts the ceteris paribus clause because 
ceteris are not paribus. Any change in price will lead, through its effect on other markets, to a shift 
in the demand curves in the market that is being considered. The things that are being held constant 
vary systematically with the ones being looked at, and this undermines the basis of partial 
equilibrium. In addition, if the commodity was an important part of the household budget, changes 
in its price would lead to changes in the  household’s real income, thus changing 
4
 another of the variables that have been held constant. In other words, for partial equilibrium it must 
be assumed that the income effect of a price change is very small. This means that the partial 
equilibrium framework is relevant only for goods on which only a relatively small proportion of the 
household budget is spent and for which there are no close substitutes or compliments. 
Further problems arise when the partial equilibrium framework is utilized to determine 
prices and outputs in competitive industries. A competitive industry will produce at that price for 
which aggregate demand for its output is equal to aggregate supply. In a partial equilibrium 
framework supply and demand must be independent of each other. The individual firm is assumed 
to face a U-shaped cost curve, and in perfect competition it faces an infinitely elastic demand curve. 
In long run equilibrium price will cover costs exactly so that there are no economic profits. 
In 1926 Piero Sraffa published an article that showed that there are severe logical problems 
in the use of the partial equilibrium framework for the analysis of perfectly competitive industries. 
He demonstrated that some elements of the analysis are inconsistent with partial equilibrium 
analysis and other elements are inconsistent with perfect competition. 
Also, there are the standard problems associated with partial equilibrium analysis, 
specifically, the fact that demand and supply are often interdependent rather than independent and 
that the analysis is relevant only for unimportant markets. In other words, it is rare that one can 
break away part of the economy and assume that the interdependencies between it and the rest of 
the economy are negligible. Nevertheless, partial equilibrium analysis remains important in 
macroeconomics, particularly the distinctions between the short period, the long period, and the 
secular long period. 
Bibliography 
Hausman, Daniel M. 1992. Supply and Demand Explanations and Their Ceteris Paribus Clauses. In 
Essays on Philosophy and Economic Methodology. Cambridge, U.K., and New York: 
Cambridge University Press. 
5
 Marshall, Alfred. 1922. Principles of Economics: An Introductory Analysis, 8th ed. London: 
Macmillan. 
Persky, Joseph. 1990. Retrospectives: Ceteris Paribus. Journal of Economic Perspectives 4 (3): 
187–194. 
Sraffa, Piero. 1926. The Laws of Returns under Competitive Conditions. Economic Journal 36: 
535–550 
6
 

Partial Equilibrium and Marshall

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics