Price Theory in Economics
Thomas A. Weber∗
Forthcoming in: Özer, Ö., Phillips, R. (Eds.) Oxford Handbook of Pricing Management, Oxford University Press.
Contents
1 Origin of Value and Prices 1
2 Price-Taking Behavior and Choice 3
2.1 Rational Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Utility Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Effects of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Price Discovery in Markets 10
3.1 Pure Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Competitive Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Complete Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Incomplete Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Disequilibrium and Price Adjustments 18
4.1 Walrasian Tâtonnement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Information Transmission in Markets . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Externalities and Nonmarket Goods 22
5.1 Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 Nonmarket Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Strategic Pricing with Complete Information 28
6.1 Monopoly Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.2 Oligopoly Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.3 Entry Deterrence and Limit Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7 Strategic Pricing with Incomplete Information 34
7.1 Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.2 Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.3 Mechanism Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.4 Oligopoly Pricing with Asymmetric Information . . . . . . . . . . . . . . . . . . . 42
8 Dynamic Pricing 44
9 Behavioral Anomalies 45
10 Open Issues 47
∗
Department of Management Science and Engineering, 344 Huang Engineering Center, Stanford University,
Stanford, CA 94305-4121, U.S.A. E-mail: webert@stanford.edu.
,2
,And there is all the difference in the world
between paying and being paid.
The act of paying is perhaps
the most uncomfortable infliction (...)
But being paid, —what will compare with it?
The urbane activity with which man receives money
is really marvellous.
Herman Melville, Moby Dick
1 Origin of Value and Prices
Price theory is concerned with explaining economic activity in terms of the creation and transfer
of value, which includes the trade of goods and services between different economic agents. A
puzzling question addressed by price theory is, for example: why is water so cheap and diamonds
are so expensive, even though water is critical for survival and diamonds are not? In a discussion
of this well-known ‘Diamond-Water Paradox,’ Adam Smith (1776) observes that
[t]he word value, it is to be observed, has two different meanings, and sometimes
expresses the utility of some particular object, and sometimes the power of purchasing
other goods which the possession of that object conveys. The one may be called “value
in use;” the other, “value in exchange.” (p. 31)
For him, diamonds and other precious stones derive their value from their relative scarcity and
the intensity of labor required to extract them. Labor therefore forms the basic unit of the
exchange value of goods (or ‘items’), which determines therefore their ‘real prices.’ The ‘nominal
price’ of an item in Smith’s view is connected to the value of the currency used to trade it and
might therefore fluctuate. In this labor theory of value the Diamond-Water Paradox is resolved
by noting that it is much more difficult, in terms of labor, to acquire one kilogram of diamonds
than one kilogram of water.
About a century later, the work of Carl Menger, William Stanley Jevons, and Léon Walras
brought a different resolution of the Diamond-Water Paradox, based on marginal utility rather
than labor. Menger (1871) points out that the value of an item is intrinsically linked to its utility
‘at the margin.’ While the first units of water are critical for the survival of an individual, the
utility for additional units quickly decreases, which explains the difference in the value of water
and diamonds. Commenting on the high price of pearls, Jevons (1881) asks “[d]o men dive for
pearls because pearls fetch a high price, or do pearls fetch a high price because men must dive in
order to get them?” (p. 102), and he concludes that “[t]he labour which is required to get more
of a commodity governs the supply of it; the supply determines whether people do or do not
want more of it eagerly; and this eagerness of want or demand governs value” (p. 103). Walras
(1874/77) links the idea of price to the value of an object in an exchange economy by noting that
the market price of a good tends to increase as long as there is a positive excess demand, while
, 2 1 Origin of Value and Prices
it tends to decrease when there is a positive excess supply. The associated adjustment process is
generally referred to as Walrasian tâtonnement (“groping”). Due to the mathematical precision
of his early presentation of the subject, Walras is generally recognized as the father of general
equilibrium theory.1
To understand the notion of price it is useful to abstract from the concept of money.2 In a
barter where one person trades a quantity x1 of good 1 for the quantity x2 of good 2, the
ratio x1 /x2 corresponds to his price paid for good 2. If apples correspond to good 1 and bananas
to good 2, then the ratio of the number of apples paid to the number of bananas obtained in
return corresponds to the (average) price of one banana, measured in apples. The currency in
this barter economy is denominated in apples, so that the latter is called the numéraire good,
the price of which is normalized to one.
The rest of this survey, which aims at providing a compact summary of the (sometimes techni-
cal) concepts in price theory, is organized as follows. In Section 2, we introduce the concepts of
“rational preference” and “utility function” which are standard building blocks of models that
attempt to explain choice behavior. We then turn to the frictionless interaction of agents in mar-
kets. Section 3 introduces the notion of a Walrasian equilibrium, where supply equals demand
and market prices are determined (up to a common multiplicative constant) by the self-interested
behavior of market participants. This equilibrium has remarkable efficiency properties, which
are summarized by the first and the second fundamental welfare theorems. In markets with
uncertainty, as long as any desired future payoff profile can be constructed using portfolios of
traded securities, the Arrow-Debreu equilibrium directly extends the notion of a Walrasian equi-
librium and inherits all of its efficiency properties. Otherwise, when markets are “incomplete,”
as long as agents have “rational expectations” in the sense that they correctly anticipate the
formation of prices, the Radner equilibrium may guarantee at least constrained economic effi-
ciency. In Section 4 we consider the possibility of disequilibrium and Walrasian tâtonnement as a
price-adjustment process in an otherwise stationary economy. Section 5 deals with the problem
of “externalities,” where agents’ actions are payoff-relevant to other agents. The presence of
externalities in markets tends to destroy the efficiency properties of the Walrasian equilibrium
and even threaten its very existence. While in Sections 3 and 4 all agents (including consumers
and firms) are assumed to be “price takers,” we consider strategic interactions between agents
in Sections 6 and 7, in the presence of complete and incomplete information, respectively. The
discussion proceeds from optimal monopoly pricing (which involves the problems of screening,
signaling, and, more generally, mechanism design when information is incomplete) to price com-
petition between several firms, either in a level relationship when there are several oligopolists
in a market, or as an entry problem, when one incumbent can deter (or encourage) the entrance
of other firms into the market. Section 8 deals with dynamic pricing issues, and in Section 9
we mention some of the persistent behavioral irregularities that are not well captured by classi-
cal price theory. Finally, Section 10 concludes and provides a number of directions from which
further research contributions may be expected.
1
The modern understanding of classical general equilibrium theory is well summarized by Debreu’s (1959)
concise axiomatic presentation and by Arrow and Hahn’s (1971) more complete treatise. Mas-Colell (1985)
provides an overview from a differentiable viewpoint, and McKenzie (2002) a more recent account of the theory.
Friedman (1962/2007), Stigler (1966), and Hirshleifer et al. (2005) present ‘price theory’ at the intermediate level.
2
Keynes’ (1936) theory of liquidity gives some reasons for the (perhaps somewhat puzzling) availability of
money, which, after all, cannot be directly consumed, but provides a fungible means of compensation in exchange.
