Table Of ContentGENERAL EQUILIBRIUM
MODELS OF MONETARY
ECONOMIES
Studies in the Static Foundations of
Monetary Theory
Edited by
Ross M. Starr
Department of Economics
University of California, San Diego
La Jolla California
}
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Library of Congress Cataloging-in-Publication Data
General equilibrium models of monetary economies
edited by Ross M. Starr.
(Economic theory, econometrics, and mathematical economics)
Bibliography: p.
Includes index.
1. Equilibrium (Economics) 2. Money. 3. Value.
I. Starr, Ross M. II. Series.
HB145.G44 1988 332.4 88-6182
ISBN 0-12-663970-1
89 90 91 92 9 8 7 6 5 4 3 2 1
Printed in the United States of America
To
C. S. and D. E. S.
1
MONEY IN FORMAL GENERAL
EQUILIBRIUM ANALYSIS
This volume presents work developed primarily over the last two decades
using mathematical general equilibrium theory to treat a classic problem of
economic theory, the integration of the theory of money and the theory of
value. Questions addressed include the functions money performs in the
economy, how it promotes efficient allocation, and how the value of an
intrinsically worthless fiat money is sustained in a market equilibrium. The
analytic approach is the Arrow-Debreu model of Walrasian general equilib-
rium theory. Use of this detailed general equilibrium model is intended to
provide a framework to represent money as a device for facilitating trade
among economic agents. To provide a function for money, there must be
sufficient variety in agents and goods to make trade desirable, and to generate
impediments to trade so that money can ease the difficulty. Hence an inquiry
into the foundations of the role of money necessarily requires modelling the
interaction of multiple traders and goods. A smaller model—of partial equi-
librium, of Robinson Crusoe, or of the Edgeworth box—is insufficient. A less
detailed approach may adequately characterize interactions in a monetary
economy when the properties of money and finance are assumed, but it
cannot provide a foundation for a theory of money.
The Arrow-Debreu general equilibrium model is a formal analytic counter-
part of a common classroom exercise, considering an economy without
money. The model presents a smoothly functioning economy with no money
or financial institutions. The conventional functioning of money is otiose in
the Arrow-Debreu model because the functions of money and finance are
General Equilibrium 3 Copyright © 1989 by Academic Press, Inc.
Models of All rights of reproduction in any form reserved.
Monetary Economies ISBN 0-12-663970-1
performed by the markets themselves. Futures markets execute the intertem-
poral allocation functions which would otherwise be performed using a store
of value. Trade is not bilateral, but omni-lateral; all trade takes place in a
single marketing instant and place where traders meet all other traders at
once. Each household and firm executes only a single lifetime transaction.
Hence no role for a medium of exchange can arise as a token of value carried
between trades. The Arrow-Debreu theory positively denies a role for money
as a store of value or as a medium of exchange. A class of models that so fully
repudiates money seems a curious jumping-off place for a monetary theory. It
was Hicks' suggestion (selection 2) that starting from this point, we should
consider money as a device for overcoming "frictions" in the smooth
functioning that the model assumed. In order to do this we must make the
frictions explicit. Hicks urged the profession to "look the frictions in the
face," suggesting that their analysis will not actually prove intractable. That is
the research plan undertaken by this body of work. The Arrow-Debreu
model assumes away all impediments to trade. Introduction of explicit
difficulties of trade is a lever for deducing the peculiar functions of money.
The frictionless non-monetary Arrow-Debreu world is a precise and exacting
jumping-off point for looking directly at the frictions in trade that generate
the role of money and finance.
A common alternative formulation to represent the demand for money is to
put money as an argument in the household utility function. The studies of
this volume reject that formulation as unhelpful at best. The object of these
papers is to explain the function of money in an economy. Entering money as
an argument of the utility function would transparently and uselessly assume
the conclusion of the inquiry.
"Imbedding money in preferences or technologies does nothing to explain its role as a
store of value. Moreover, such reduced forms are at best poor proxies for their
structural counterparts. Worst of all, to the extent that this maneuver is successful, it is
also likely to be misleading." Cass and Shell (1980)
Principal classic functions of money are as a medium of exchange and as a
store of value. We first consider how the Arrow-Debreu Walrasian model
deals with these functions without the use of money. Compared to the
bilateral trading process in actual economies the mechanism of trade in an
Arrow-Debreu model is simplified in a way that implies that there is no role
for a medium of exchange, money, in the trading process. The mechanism of
trade is simply absent. There is no role for shops, retailers, wholesalers, credit
or means of payment. All trade takes place between the individual and an
abstract market. There is an abstract price formation mechanism, sometimes
personified as the Walrasian auctioneer. Once general equilibrium prices
have been announced, agents deliver their excess supplies to the market and
withdraw their excess demands, consistent with budget constraint. Inasmuch
4 MONETARY THEORY AND MICROECONOMIC THEORY
as prices are market clearing, there is no unsatisfied excess demand. The
agent's trade is a single transaction, the delivery of goods and withdrawal of
demands. Some record keeping is required to ensure that budget constraints
are fulfilled, but there is no explicit account in the model of the process by
which such records are kept. Since each agent and firm's transaction takes
place in a single exchange, there is no role for a token or carrier of value to be
held between transactions, hence no role for a medium of exchange. The
perfection and simplicity of trade in the model preclude a role for money as a
facilitator of transactions. You can't improve on perfection.
The task of formalizing a demand for a medium of exchange consists of
modelling the process of trade in a fashion that adds some difficulty, struc-
ture, and complexity. This analysis is presented in Part II of the collection.
Trade is formalized as a succession of bilateral trades. Hence a role for a
medium of exchange as a carrier of value between trades arises endogenously.
A distinctive element of the Arrow-Debreu model is the availability of a
full set of futures markets for intertemporal allocation. A commodity is
defined by its description and by its delivery date. A typical household
endowment then consists of goods—including labor—dated for availability
in the present (spot) and in the future. The intertemporal allocation process
works in the following way. There is a single date of active trade. Trade takes
place in dated commodities: current goods spot and futures contracts (goods
contracted for delivery in the future). A typical household endowment con-
sists of both current and future goods. Thus, a household whose principal
endowment is labor would sell current labor and contracts to deliver labor in
the future. In exchange for these sales the household would receive abstract
purchasing power to be credited toward its purchases on the market. It would
then purchase spot goods for current consumption and contracts for delivery
of future consumption. The household goes to the market with a portfolio of
securities representing its endowment and when all trades have been com-
pleted it leaves the market with a portfolio of securities representing its
lifetime consumption plan. Prices are present discounted values of dated
goods. The household budget constraint is that the value of all of its purchases
must equal the value of its sales. The household budget constraint is hence a
lifetime budget constraint expressed in terms of present discounted values of
sales and purchases.
Two quite distinct functions are performed by the futures markets in this
model. One is price determination. As an outcome of the equilibrium, all
agents know the trade-off between present and future consumption and
between goods at a variety of dates. The other function performed is a capital
market function. The futures markets allow the timing of household con-
sumption to be allocated independent of the timing of sales by the household
or of firms it owns. This is the function that capital markets and debt
instruments play in a monetary economy. When the equilibrium allocation is
achieved, every household has arranged its desired consumption plan for the
MONEY IN FORMAL GENERAL EQUILIBRIUM ANALYSIS 5
present through the future, subject to its lifetime budget constraint. Firms
maximize the present discounted values of their profit streams. The allocation
is Pareto efficient in terms of household lifetime utility functions. All trade
takes place at a single initial date. The rest of economic activity consists of
fulfillment of the contracted plans of households and firms.
There is no reopening of markets at subsequent dates. If the markets were
reopened, they would be inactive—there would be no desired net trades. All
intertemporal allocation takes place at a single date through the use of futures
markets. An intertemporal store of value can perform no function here, since
markets do not reopen over time. We conclude that a theory of money as a
store of value requires a sufficient reason for the reopening of markets or,
equivalently, a sufficient impediment to the use of futures markets. This
impediment is formalized as a transaction cost structure that favors the use of
spot markets. In a non-monetary economy, a breakdown in the efficiency of
the equilibrium allocation follows. The resulting theory of intertemporal
financial structure and money as a store of value is presented in Part III of the
collection.
There is one essential step in moving from the Arrow-Debreu model to the
models of bilateral trade (Part II) and intertemporal allocation (Part III) that
allows distinct functions of money to emerge. The single lifetime budget
constraint must be replaced by a succession of budget balance requirements.
In each trade (Part II) and at each date (Part III) the value of sales is required
to equal the value of purchases. This requirement so distorts the pattern of
trade interpersonally and intertemporally as to result in possible misalloca-
tion. A solution to the difficulty is the provision of a financial asset (money),
so that trade in the financial asset can sustain budget balance in each transac-
tion without a corresponding change in resource allocation. The financial
asset is identified as money, and restoration of efficient resource allocation in
equilibrium is shown to result.
Virtually all of the studies presented in the collection portray pure ex-
change rather than production economies. This necessarily implies an attenu-
ated treatment of capital markets. Nevertheless the essential issues of the
inquiry, the role of money in facilitating reallocation over time and between
agents, can be amply portrayed. The plan of the field is to retain the clarity,
generality, and rigor of mathematical general equilibrium theory, while intro-
ducing sufficient difficulty of trade to create a demand for money and financial
institutions. The studies of Parts II, III, and IV of this volume are chosen as
representative of the success we have had in fulfilling this research agenda.
6 MONETARY THEORY AND MICROECONOMIC THEORY
2
A SUGGESTION FOR SIMPLIFYING THE
THEORY OF MONEY
by John R. Hicks
In this essay Professor Hicks argues for the use of the microeconomic theory
of optimizing behavior as the basis of monetary theory. He calls for the same
sort of marginalist revolution that formed the modern theory of value.
Hicks notes that monetary and financial behavior and institutions represent
accomodation to imperfections, "frictions," in other markets, particularly
asset markets. His research program then is "to look the frictions in the face,
and see if they are really so refractory after all." This is certainly the essential
methodological view of the technical papers in this volume. The subsequent
papers add the recognition that money is a tool for economic interaction
among agents and goods to Hicks' requirement that difficulties of trade be
made explicit. Hence it necessarily requires a multiple agent-multiple good
(general equilibrium) model. This is very much the framework in which Hicks
viewed goods markets in Value and Capital.
The following is printed with permission from Economica, New Series, vol. 11, 1935.
General Equilibrium 7 Copyright © 1989 by Academic Press, Inc.
Models of All rights of reproduction in any form reserved.
Monetary Economies ISBN 0-12-663970-1
A Suggestion for Simplifying the
Theory of Money1
By J. R. HICKS
After the thunderstorms of recent years, it is with peculiar diffidence and even
apprehension that one ventures to open one's mouth on the subject of money.
In my own case these feelings are particularly intense, because I feel myself to
be very much of a novice at the subject. My education has been mostly in the
non-monetary parts of economics, and I have only come to be interested in
money because I found that I could not keep it out of my non-monetary
problems. Yet I am encouraged on reflection to hope that this may not prove
a bad approach to the subject: that some things at least which are not very
evident on direct inspection may become clearer from a cross-light of this
sort.
It is of course very largely by such cross-fertilisation that economics prog-
resses, and at least one department of non-monetary economics has hardly
emerged from a very intimate affair with monetary theory. I do not, however,
propose to resume this particular liaison. One understands that most econo-
mists have now read Böhm-Bawerk; yet whatever that union has bred, it has
not been concord. I should prefer to seek illumination from another point of
view—from a branch of economics which is more elementary, but, I think in
consequence better developed—the theory of value.
To anyone who comes over from the theory of value to the theory of
money, there are a number of things which are rather startling. Chief of these
is the preoccupation of monetary theorists with a certain equation, which
states that the price of goods multiplied by the quantity of goods equals the
amount of money which is spent on them. This equation crops up again and
again, and it has all sorts of ingenious little arithmetical tricks performed on
it. Sometimes it comes out as MV = PT; and once, in its most stupendous
Ε Γ - S
transfiguration, it blossomed into Ρ = — Η ——. Now we, of the theory
of value, are not unfamiliar with this equation, and there was a time when we
'A paper read at the Economic Club, November 1934. The reader is asked to bear in mind the
fact that the paper was written to be read aloud, and to excuse certain pieces of mischief.
8
SUGGESTION FOR SIMPLIFYING THE THEORY OF MONEY
used to attach as much importance to it as monetary theorists seem to do still.
This was in the middle of the last century, when we used to talk about value
being "a ratio between demand and supply." Even now, we accept the
equation, and work it, more or less implicitly, into our systems. But we are
rather inclined to take it for granted, since it is rather tautologous, and since
we have found that another equation, not alternative to the quantity equa-
tion, but complementary with it, is much more significant. This is the equa-
tion which states that the relative value of two commodities depends upon
their relative marginal utility.
Now, to an ingénu, who comes over to monetary theory, it is extremely
trying to be deprived of this sheet-anchor. It was marginal utility that really
made sense of the theory of value; and to come to a branch of economics
which does without marginal utility altogether! No wonder there are such
difficulties and such differences! What is wanted is a "marginal revolution"!
That is my suggestion. But I know that it will meet with apparently crushing
objections. I shall be told that the suggestion has been tried out before. It was
tried by Wicksell, and though it led to interesting results, it did not lead to a
marginal utility theory of money. It was tried by Mises, and led to the
conclusion that money is a ghost of gold—because, so it appeared, money as
such has no marginal utility. 1 The suggestion has a history, and its history is
not encouraging.
This would be enough to frighten one off, were it not for two things. Both
in the theory of value and in the theory of money there have been develop-
ments in the twenty or thirty years since Wicksell and Mises wrote. And these
developments have considerably reduced the barriers that blocked their way.
In the theory of value, the work of Pareto, Wicksteed, and their successors,
has broadened and deepened our whole conception of marginal utility. We
now realise that the marginal utility analysis is nothing else than a general
theory of choice, which is applicable whenever the choice is between alterna-
tives that are capable of quantitative expression. Now money is obviously
capable of quantitative expression, and therefore the objection that money
1A more subtle form of the same difficulty appears in the work of Marshall and his followers.
They were aware that money ought to be subjected to marginal utility analysis; but they were so
dominated by the classical conception of money as a "veil" (which is valid enough at a certain
level of approximation) that they persisted in regarding the demand for money as a demand for
the things which money can buy—"real balances." As a result of this, their invocation of
marginal utility remained little more than a pious hope. For they were unable to distinguish, on
marginal utility lines, between the desire to save and the desire to hoard; and they necessarily
overlooked that indeterminateness in the "real balance" (so important in some applications of
monetary theory), which occurs when the prices of consumption goods are expected to change.
On the other hand, I must admit that some versions of the Marshallian theory come very close to
what I am driving at. Cf. Lavington, English Capital Market, ch. vi.
A SUGGESTION FOR SIMPLIFYING THE THEORY OF MONEY 9
