The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
THE TRADE THEORIST’S SACRED DIAGRAM:
ITS ORIGIN AND EARLY DEVELOPMENT
ThomasM. HunqQirey
Introduction
Figure 1
In his celebrated 1945 essay on international trade
under variable returns in a simple model’ the noted
Dutch economist Jan Tinbergen presented his version of what Robert Baldwin calls “the sacred diagram
of the international trade economist” [ 1, p. 142).
Tinbergen used the diagram, which consists of a
transformation or production possibility curve, taste
indifference curves, and relative price or terms-oftrade lines, to show how a country gains from the
opportunity to trade at a world price ratio different
from the closed-economy one (see Figure 1). Given
that opportunity, the country does two things. First,
it produces the output mix that maximizes its national
product valued at world prices. That is, it produces
at the point of tangency of the production possibility curve and world price line. Then it trades along
that line, exporting products in which it has a comparative cost advantage in exchange for imports of
products in which it has a comparative disadvantage,
until it reaches its point of maximum satisfaction on
its highest attainable indifference curve. There it
enjoys a bundle of goods that it could not produce
or consume in isolation. Here is the economist’s case
for free trade captured in a single diagram.
That a simple geometrical diagram would become
an icon is hardly surprising. Other economic diagrams
have enjoyed that same distinction-the
Keynesian
cross, Marshallian
sissors,
Hicksian
IS-LM,
Edgeworth-Bowley box, Phillips curve, and Knightian circular flow are cases in point. What is surprising is how little has been written on the trade
diagram’s history. Few systematic surveys of that
history exist; textbooks say little about it. Tinbergen
himself said nothing about earlier versions of the
diagram even though it was 38 years old at the time
he presented it. Who invented the diagram? How
was it initially received? Who exerted the greatest
influence in getting it accepted into trade theory?
’ Tinbergen’s essay, originally entitled “Professor Graham’s Case
for Protection,” was reprinted in 1965 in a slightly abbreviated
version as “International Trade Under Variable Returns in a Very
Simple Model.” See [ 161.
FEDERAL
RESERVE
TINBERGEN’S
DIAGRAM
cu
COMMODITY
1
Before trade the economy produces and consumes
at A, the common point of tangency of transformation
curve and indifference curve. Given the opportunity
to trade at the world price ratio shown by the slope
of line PC, it produces commodity bundle P which it
then trades for bundle C to reach its point of maximum
satisfaction C on its highest attainable indifference
curve.
Source: Tinbergen [16, p. 1291.
Today these issues still remain unresolved and one
finds such writers as Samuelson, Baldwin, Maneschi
and Thweatt disagreeing over whether Viier, Lerner,
Haberler,
or Barone contributed
most to the
diagram’s development. 2 In an effort to rectify this
situation and to provide some needed historical
perspective, this article traces the evolution of the
trade diagram from its 1907 origins to its presentation by Tinbergen in 1945 by which time it had
already become the standard geometrical tool of the
trade theorist. A word of explanation is in order,
however. Today analysts put the diagram to many
2 See Maneschi and Thweatt
the controversy.
BANK
OF RICHMOND
[ 12, pp. 375-781 for a review of
3
uses-to
depict the effects of protection, of noneconomic objectives of tariffs, of domestic market
distortions, and of growth on trade, to name just a
few. Historically, however, economists chiefly employed it to illustrate trade equilibrium and the gains
from trade in a fully competitive economy in which
the balance of payments for simplicity consists of the
balance of trade. Given this article’s historical focus,
it too concentrates on those traditional concerns.
Figure2
FISHER’S DIAGRAM
Historical Evolution
Historically the diagram evolved through at least
eight stages. Each stage saw a different innovator contribute to the diagram’s development. Irving Fisher
(1907) invented the diagram to illustrate a problem
in capital theory, Enrico Barone (1908) extended it
to international trade, and Allyn Young (1928) applied it to a hypothetical closed economy operating
under constant, decreasing, and increasing returns.
Gottfried Haberler (1930) introduced the strictly concave production frontier version into foreign trade
theory. Jacob Viner (193 1) added community indifference curves to Haberler’s diagram and criticized
the entire apparatus. Abba Lerner (1932) extended
the diagram to the level of the aggregate world
economy, Wassily Leontief (1933) applied it to two
countries simultaneously, and Jan Tinbergen (1945)
elegantly consolidated their results. Except for Young,
each analyst used the diagram to emphasize the gains
from trade. Of these analysts, it was Haberler and
Leontief who had the greatest influence. It was they
who convinced trade theorists to add the diagram
to their analytical tool kit. What follows describes
in chronological order the specific contributions of
each of these pioneers.
Irving Fisher
Francis Y. Edgeworth invented indifference curves
in his Matktikal Py&s
188 Similarly,
Pareto
the
of
curves
his
di
poh%-a
1906.
Irving
in
1907
Th
of
was
first
combine
and
mation
together
market
lines
a
diagram
to
it illustrate
gains
exchange
Figure
True,
applied
diagram
a
in
theory
than
the
of
trade.
is,
used to
an
optimum
decision
than
country’s
trade
But
difference
only
ficial.
trade
after
Fisher
the
4
ECONOMIC
REVIEW,
Y’
PRESENT
C
A
CONSUMPTION
.co
Given the interest rate implicit in the slope of line AB,
an investor produces the two-period consumption
bundle P having the highest present value. Then he
trades that bundle for bundle Q by lending PD units
of present consumption for DQ units of future consumption to reach his point of maximum satisfaction Q.
Source: Fisher 14, p. 409).
diagram to demonstrate the gains from trade (albeit
intertemporal rather than international). And like
trade theorists, he showed the individual moving
along the production possibility frontier to the highest
attainable price line and then trading along that line
to reach the point of maximum satisfaction. In terms
of abstract economic
logic, his demonstration
matches that of the trade theorists. To Fisher, then,
must go the credit for inventing the trade diagram.
His diagram appears on page 409 of T/reRate of
Intemt.3 The transformation or production possibility or (as Fisher called it) opportunity curve ZPW
shows an individual’s opportunity
to transform
present consumption (measured on the horizontal
axis) into future consumption
(measured on the
3 Fisher also used the diagram in his Th T~OIYof Zn~eresf
(1930).
On Fisher’s diagram see Hirshleifer 19, pp. 330-34 and
Samuelson 115, pp. 29-333.
JANUARY/FEBRUARY
1988
vertical axis) by investing in real capital projects. The
concave shape of the curve represents diminishing
returns to investment as the sacrifice of more and
more units of consumption today yields smaller and
smaller increments to consumption tomorrow.
The set of convex iso-desirability curves (as Fisher
called them) labeled 10, 20, 30, etc. constitute the
individual’s indifference map. Each curve shows alteinative combinations of present and future consumption that yield equal satisfaction. Higher curves represent higher levels of satisfaction. Finally, the interest
line AB shows the opportunity to convert P dollars
of present consumption into Q dollars of future consumption by lending at the market rate of interest
shown by the slope of the line. In other words, one
can lend as well as invest.
Fisher explains that the individual, if deprived of
the opportunity to lend on the money market, would
choose the two-period consumption combination
shown by the common point of tangency of indifference curve and production possibility curve (point
S).4 This is analogous to the trade diagram’s closedeconomy equilibrium production and consumption
point.
Given the opportunity to lend at the going rate of
interest, however, the individual equates that rate
with the marginal rate of return on real investment
by moving along the production frontier to point P
on the highest attainable interest line AB. That is,
he chooses the two-period consumption bundle
having the highest present value calculated at the
market interest rate shown by the slope of AB. Then
he trades along that line, lending PD (= x’) dollars
of current consumption in exchange for DQ ( = x “)
dollars of future consumption, to reach a point of
maximum satisfaction Q. In short, given the opportunity to trade at a market price, the individual produces the bundle of goods having the highest market
value and then trades it for a preferred bundle lying
beyond the production frontier. But this is exactly
what a fully competitive open national economy does
when given the opportunity to trade at world prices.
Modern users of the trade diagram note that international equilibrium requires the world price ratio
be such as to balance trade across nations. In other
words, the desired exports of one nation must at the
equilibrium price ratio equal the desired imports of
another and vice versa. Fisher argued the same about
the equilibrium rate of interest. That rate, he said,
equates the desired lending of one individual with
the desired borrowing of another-that
is, it ensures
4 Fisher omits the relevant indifference
ing the diagram.
that the legs of the trade triangle PDQ are equal in
length but opposite in sign across lenders and
borrowers. Thus Fisher did more than specify trade
equilibrium conditions for a single individual facing
a given market rate. He also specified the market
equilibrium conditions that determine that rate. True,
he did not show such conditions in his diagram. That
is, he did not extend it to the two-person case. But
he stated how it could be done. His work presaged
later uses of the diagram to depict world trade
equilibrium in the two-country case.
Enrico Barone
If Fisher was the first to use the diagram to show
the gains from itzzemmpora~trade, then Enrico
Barone, the Italian mathematical economist and
author of the famous article on “The Ministry of
Production in the Collectivist State,” was the first
to use it to depict the gains from intemahnaf
trade.5 In a long footnote in the 1908 edition of
his Pn*m$i di economkzpobica, he presented a diagram
showing pre- and post-trade equilibrium positions for
a single national economy that produces and consumes two goods A and B (see Figure 3). His
diagram, like Fisher’s, consists of three types of
curves.
His “production indifference” or transformation
curve AB shows the maximum alternative combinations of the two goods the economy can produce from
available resources. Its nonlinear curved shape indicates that production takes place under conditions
of nonconstant costs. The slope of the curve at any
point M represents what Barone called “comparative
cost,” or the ratio of the marginal costs of production.
The curves bearing the numbers 3 and 8 are two
of a set of community taste indifference curves that
represent demand conditions in the economy. Each
curve shows alternative commodity bundles yielding
equal satisfaction, Higher curves represent higher
levels of satisfaction as indicated by the higher
numbers they bear. Finally, the curve PC is the world
price line whose slope indicates the relative cost of
obtaining goods A and B on the world market.
Before trade, the country produces and consumes
at the autarky equilibrium point M characterized by
the common tangency of production possibility and
taste indifference curves. The slope of that tangent
represents the domestic pre-trade price ratio and
indicates that the country has a comparative cost
advantage over the rest of the world in the production of good B.
curve to avoid clutter5 What follows draws heavily on Maneschi and Thweatt
FEDERAL
RESERVE
BANK
OF RICHMOND
[ 121.
5
Figure 3
BARONE’S
DIAGRAM
N
D
COMMODITY
R
B
B
Here are
the elements
in modern
sions of
diagram- the
apparatus, the
between autarky
economy) and
prices that
trade feasible,
movement to
specialization point
maximum-value output,
post-trade separation
production and
tion points,
the trade
that reconciles
points. All
was a
performance that
have made
the leading
in the
development. Such,
was not
case. For
its brilliance,
contribution went
unnoticed and
had no
ble influence
the work
his contemporaries
immediate successors.
himself may
been
partly
for this
of affairs.
burying
diagram in footnote of
1908 Prim@ he
effectively
its importance.
he may
intended to
so is
by his
to include
diagram in
other writings.
any
rate is not
be found
later editions
the PrinWhen it
finally restored
the 1936
tion it
seemed original.
then, other
had independently
the diagram
had
developed
beyond Barone.
in recent
with the
of the
scarce 1908
of the
have scholars
able to
firm the
of Barone’s
Allyn
Given
opportunity to
along the
price
line
the country
production from
point
M
specialization point
Then it
commodity
bundle
for bundle
by exporting
of B
QC
of
to reach
point of
satisfaction C.
Maneschi and
[12. p.
When trade opens
at the
price ratio
by the
of line
the country
its comadvantage by
to production
P where
ratio of
marginal costs
the world
ratio and
valued at
prices
is
In short,
country produces
the
point
tangency of
transformation curve
the (highest
world price
Then it
along that
exporting PQ
good B exchange
imports of
of good
until it
the point
maximum satisfaction
By taking
vantage of
it separates
production and
sumption points
consumes beyond
transformation
6
ECONOMIC
Young
After
and Barone,
on the
languished. During
next 20
(1909-1929)
only
new version
in print
it was
to the
ones. In
ignorance of
contributions of
and Barone,
A.
Young
the appendix
his famous
Economic
humaL
on “Increasing
and Economic
presented a
version of
diagram that
to him
straight from
(see Figure
Young did
use his
to illustrate
parative advantage
the gains
trade. Still
merits recognition
at least
reasons. He
Gottfried Haberler
two years
defining
slope of
production frontier
“curve
of
costs”) as
opportunity cost
producing unit increase
either good
terms of
amount of
other good
Also he
plained better
his predecessors
a concave
reflects increasing
cost, a
curve constant
and a
curve decreasing
Finally, he
how increasing
in
one
might introduce
convex segment
a otherwise
curve. In
connection
JANUARY/FEBRUARY
1988
Gottfried Haberler
Figure 4
YOUNG’S DIAGRAM
We have seen how Fisher in 1907 invented the
diagram, how Barone in 1908 extended it to international trade, and how Young in 1928 applied it to
the closed economy. In 1930, however, Gottfried
Haberler in his seminal paper on comparative cost,
did what none of his predecessors had done.6 He
introduced into international trade theory a strictly
concave production
possibility
curve showing
diminishing returns and increasing costs in the production of both goods (see Figure 5). Fisher and
Young, of course, had worked with such concave
transformation curves, but not within the context of
international trade theory. Barone, on the other hand,
had used transformation curves to analyze foreign
trade; But the curves he used were not strictly
concave.
,.
u
COMMODITY
X
Curves dd and cc are the production
ing increasing costs and constant
tively. Curves dPi and cPi represent
decreasing costs prevail over part of
frontier. Tangency .with indifference
yields equilibrium at P in the first set
the second.
frontiers showcosts, respeccases in which
the production
curves II, etc.,
of cases, P, in
6 See Haberler [6] for an English translation of his 1930 paper
from the original German. Haberler’s diagram and its underlying analysis also appears in Chapter 10 of his The Thory of
Intemationat Trade, with Its Applicationsto Commmiial PO&Y
(1936).
Figure 5
HABERLER’S
STRICTLY CONCAVE
PRODUCTION FRONTIER
A
Source: Young 118, p. 540).
a
he discussed stability of closed-economy equilibrium
under increasing, constant, and decreasing costs. He
correctly noted that stability is ensured in all cases
provided collective indifference
curves possess
greater convexity than the production frontier.
As for collective indifference curves, he noted that
their location on the diagram assumes a f=ed distribution of income when in fact that distribution and thus
the indifference map itself changes with movements
along the production frontier. In other words, a
reallocation of production from good X to good Y
redistributes income from X producers to Y producers
and thus shifts the indifference map. For this reason
he thought such curves should be treated as an expository device and not as a rigorous conception. His
discussion anticipated Lerner and Tinbergen, both
of whom analyzed decreasing costs, and Viner, who
criticized the concept of community indifference
maps.
FEDERAL
RESERVE
0
b&l b
COMMODITY
B
B
The concavity of curve ab shows that successive unit
increases in one good require progressively larger
decreases in the other. The opportunity cost of each
good increases as more is produced.
Source: Haberler [6, p. lo]
BANK
OF RICHMOND
Nor had Haberler’s predecessors adequately explained the reasons for the curve’s concave shape.
Such concavity they attributed to diminishing returns
and increasing costs without specifing the forces
causing these phenomena. Haberler, however, explained the causes of the curve’s concavity by invoking the notion of specific and nonspecific factors
of production. Specific factors he defined as those
tied to a particular industry and suitable to the production of no other good. Nonspecific factors on the
other hand are those freely transferable between industries and equally suited to the production of both
goods.
Using a two-good, three-factor model, he assumed that each good requires for its production one
specific factor which it uses exclusively and a
nonspecific factor shared in common with the other
industry. Combining increasing amounts of the
nonspecific factor with fixed amounts of a specific
one to produce more of either good yields decreasing increments of output, i.e., diminishing returns.
Thus the amount of one good sacrificed to free
enough nonspecific resources to produce a unit increase in the other good must rise as output of the
latter good increases. The same thing would happen,
Haberler noted, if all resources, though mobile,
were not equally well-suited for different employments. For example, suppose that of the nation’s
fixed stock of resources all initially employed in producing A, part is better suited to producing B. One
might think of mountainous land better suited to
skiing or mining than to wheat production. Transferring such resources to B at first results in a large
rise in the output of that good at the cost of little
sacrifice of A. Beyond some point, however, continued expansion of B necessitates the transfer of
resources less and less suited to B production and
more and more suited to A production. At that point
the opportunity costs of B in terms of A sacrificed
rises. Either case, Haberler said, yields a smooth concave curve with the marginal opportunity cost of
transforming one good into the other rising continuously over the whole range of the curve.
Finally,
Haberler
better
than any of his
predecessors explained the place of the transformation curve in the theory of comparative advantage.
According to him, the curve together with demand
conditions
(indifference
curves) determines
an
economy’s production point and thus relative commodity costs in the absence of trade. On the assumption that prices equal costs, those curves also determine relative commodity prices. Differences in these
autarky relative costs and prices across nations reflect
comparative advantages that make trade mutually
8
ECONOMIC
REVIEW,
advantageous. When trade takes place at the equilibrium world price ratio each nation tends to
specialize in the production of the commodity of its
comparative advantage. As it does so, however, it
incurs increasing opportunity costs. Specialization
continues up to the point at which marginal opportunity costs equal world prices, i.e., up to the point
at which the transformation curve just touches the
world price line. Each nation then trades along that
line, exporting its comparative advantage commodity
in exchange for the other commodity, until it reaches
its point of maximum satisfaction.
Haberler’s analysis had a galvanizing effect on his
contemporaries.
In quick succession Jacob Viner,
Abba Lerner, and Wassily Leontief combined his
concave transformation curve with collective indifference curves to obtain the basic diagram of the trade
theorist. Each of these writers, however, put the
diagram to somewhat different uses described below.
Jacob Viner
Viner’s version of the diagram, presented in a
lecture at the London School of Economics in January
1931 but not published until the 1937 appearance
of his StudiRFin th Thq of InternationalTrzade,shows
before- and after-trade equilibria for a single country
(see Figure 6). Before trade, the country produces
and consumes at point K on the highest attainable
indifference curve tangent to the production frontier.
When presented with the opportunity to trade at a
world price ratio different from the autarky onethis difference indicated by the different slopes of
the price lines FFr and mm ‘-the country shifts production to point G and then trades along the world
price line, exporting Gs units of wheat in exchange
for imports of sH units of copper. In so doing, it ends
up consuming commodity bundle H lying on a higher
indifference curve than the autarky bundle K consumed before trade.
Except for the concavity of the production possibility curve, Viner’s diagram is virtually the same as
Barone’s. But Viner did one thing that neither Barone
nor anyone else had done up to that time. He pointed
to certain logical flaws in the diagram’s construction
and questioned its usefulness in showing the gains
from trade.
In particular, he focused on the shortcomings of
community
indifference
maps and production
possibility curves. Community indifference maps
were suspect because they embodied the assumption of a fixed distribution of income when in fact
trade would change that distribution and thus the
indifference map itself. Likewise the production
JANUARY/FEBRUARY
1988
Figure6
straightforward. Job preferences and the resulting
compensating pay differentials drive a wedge between
commodity
prices
the ratio
factor
marginal
reflected in
slope of
transformation schedule.
other words,
would
not
opportunity costs
Haberler supposed.
trenchant criticisms
less than
For the
possibility curve
simply too
a tool
abandon. Despite
restrictive assumptions,
captured the
of
a
commodity supply
For that
trade theorists
the diagram
its
underlying
cost interpretation
Viner’s real
interpretation.
VINER’S DIAGRAM
Abba Lemer
AMOUNT
OF WHEAT
Given the opportunity to trade at world prices shown
by the slope of line FF,, the economy shifts production from autarky bundle K to bundle G, which it then
trades for preferred bundle H by exporting Gs wheat
for sH copper.
Source: Viner 117, p. 5211.
possibility curve was flawed because it assumed
perfectly inelastic (fixed) factor supplies when in fact
those supplies vary with changes in their prices.
Trade, by changing factor prices, would change the
quantities of factors supplied and thus the production possibility curve itself. Nor was this the only
problem. The curve, Viner noted, also embodied
the assumption of factor indifference between alternative uses when in reality factors may prefer one
employment to another. Assuming factors employed
in the industry of their preference are paid the value
of their marginal product there, they must receive
a premium over that to induce them to work in the
other industry. In that case, factor costs to one industry will not equal sacrificed factor product in the
other, and the cost of securing a unit increase in either
good is not accurately measured by the quantity of
the other good given up.’ Viner’s conclusion was
7 An example will suffice. Industry A pays each unit of labor
a real wage wA equal to its marginal product there. But that same
labor unit costs industry B the amount We +d, where d is the
wage differential or pay premium that compensates for the
nonpecuniary
disadvantages
(subjective disutility) of workFEDERAL
RESERVE
Unlike Viner, Lerner accepted the trade diagram
uncritically. He used it to depict trade equilibrium
for the aggregate world economy in a two-country
model.* His demonstration,
as presented in his
celebrated 1932 Economicaarticle on “The Diagrammatical Representation of Cost Conditions in International Trade,” required three steps.
First, he derived the world transformation curve
by optimally adding national production possibilities
at equal marginal cost ratios. He did so by sliding
one country’s production possibility block along the
other’s with the slopes or marginal opportunity cost
ratios always kept equal (see Figure 7). In this way
he traced out an efficient world production possibility
frontier, something nobody had done before.
Second, he confronted this world production frontier with a global community indifference curve which
he implicitly derived by aggregating over the underlying country curves (not shown by him). The
resulting common point of tangency of the two curves
determines the world production and consumption
points as well as the equilibrium terms of trade.
Finally, he located each country’s post-trade production point by moving the world terms-of-trade lime
parallel to itself until it just touched the individual
production possibility curves. He did not identify the
consumption point or the exports and imports of each
ing in B. Thus labor’s cost to B exceeds its foregone product
in A by the factor d. Similarly, labor’s marginal product in B equals
its wage rate there, wA +d. But that same unit of labor costs A
only We. Thus labor’s cost to .A understates
its sacrificed alternative product by the factor d. True costs deviate
from opportunity cost.
8 On Lerner see Mundell [ 13, pp. 147-483 and Samuelson [ 15,
p. 6453.
BANK
OF RICHMOND
9
pattern of international
specialization is efficient. No
matter which of the two countries specializies completely, the same commodity totals will be produced.
Another trait of such a point is if a change in world
tastes is moving the world production combination past
one, the optimal pattern of specialization
may shift
markedly 13, pp. 162-631.
Figure7
LERNER’S DERIVATION
OF THE WORLD
TRANSFORMATION
CURVE
Wassily Leontief
Y
0
I
m
I.
B
Mb
COMMODITY
B
Moving one country’s production block along the
other’s traces out the world transformation curve AB.
The diagram shows three successive positions of the
second country’s block o’a’b’ as it slides along the
first country’s production frontier ab. Tangency of
transformation curve and indifference curve yields
world equilibrium at P with country post-trade production points being p’ and p, respectively.
Source:
Lerner[I 1, p. 901.
nation. But he did remark that both nations would
benefit from trade even if they possessed identical
concave transformation curves provided their indifference maps differed. His remark anticipated Wassily
Leontief s geometrical demonstration of this case.
He also showed what the world production
possibility curve looks like when at least one of the
countries produces under conditions of increasing
returns such that its production frontier is convex.
Richard E. Caves neatly summarizes his analysis.
He proved that increasing returns necessitate complete
specialization by at least one country. This can occur not
only when both countries’ transformation
curves are
convex to the origin, but also if one (national) transformation curve is convex while the other shows a constant rate of transformation,
or even concavity to the
origin, so long as the convexity of the one exceeds the
concavity of the other. There will normally be points on
the world transformation
curve where more than one
10
ECONOMIC
REVIEW,
In the year after Lerner’s article appeared,
Leontief in his paper on “The Use of Indifference
Curves in the Analysis of Foreign Trade” completed
Lerner’s demonstration of world trade equilibrium.
He did so by depicting for both countries the posttrade consumption points and trade triangles that connect those points with their corresponding production points, something Lerner had failed to do. Unlike
Lerner, however, he did not work with world production possibility and taste indifference curves.
Instead, he focused on the curves of each country,
combining them together in a single chart. In this
way he was able to use the diagram to show how trade
affects both countries simultaneously.
He showed how gains from trade arise when (1)
production conditions alone and (2) demand conditions alone differ across countries. In the first case,
countries have different production possibility curves
but identical indifference maps (see Figure 8A). In
the second case (anticipated by Lerner), production
possibility curves are the same and only indifference
maps differ across countries (see Figure 8B).
Figure 8A depicts the first case. Here the country
possessing the vertically elongated transformation
curve produces at q where its output valued at world
prices is maximized. Then it trades along the relative
price line qP2, exporting qf of good A against imports of fPz of good B, and consumes at P2, a point
it could not reach before trade when it was constrained to consume on its production possibility
curve. Likewise the other country gains by producing its highest valued output at K, trading along the
price line KPi, and consuming at Pi beyond its
production possibility frontier.
As for equilibrium conditions, Leontief specified
that the price lines connecting the production and
consumption points must be of the same slope and
length for both countries. The first condition ensures
that both countries face the same price ratio or terms
of trade. The second ensures that exports of one
country equal imports of the other. In other words,
it ensures that the trade triangles PlRK and qfPz are
the same, as required for international equilibrium.
JANUARY/FEBRUARY
1988
LEONTIEF’S
DIAGRAMS
Figure8a
Figure8b
Different Transformation Curves,
Identical Indifference Maps
Identical Transformation Curves,
Different Indifference Maps
m
C
g
b
c*
6
One country produces at q and exports qf of A for
fP, of B. The other produces at K and exports KR of
B for RP, of A. The equilibrium world price ratio shown
by the common slope of lines qP, and P,K must be
such as to make the trade triangles identical.
pp.25,
C,b
B
GOOD B
GOOD B
Source: Leontief [lo,
M
Both countries produce at K, one exporting KR, of A
for R,P’, of B, the other exporting KR, of 6 for R,P;
of A. The equilibrium world price ratio must be such
as to make the trade triangles identical.
27)
Trade also enables countries to consume beyond
their production possibility curves when only demand
conditions (indifference maps) differ. Leontiefs
second diagram shows why: different demand conditions result in different pre-trade equilibrium
points on the production possibility curve. At these
different points, comparative costs differ making trade
advantageous.
Thus before trade the country with the steeper indifference curves initially consumes and produces at
PI on its production possibility curve while the other
country does the same at Pa. The different slopes
of the production possibility curve at those two
autarky points show that comparative costs differ
across countries making trade profitable. When trade
takes place at the equilibrium price ratio given by
the slope of line PiPi, each country produces at K
and exports the good in which it has a (pre-trade)
cost advantage. The first country exports KRI of good
A for imports of RrPr’ of good B, reaching consumption point Pi in the process. Similarily, the other
country exports RaK of good B in exchange for imports of RaPi of good A, and consumes at P1 beyond
its production possibility curve. Both countries gain
from trade despite having identical production frontiers. Here in Leontiefs 1933 diagram is everything
and more found in the earlier constructions of his
predecessors.
In short, Leontief brought the diagram to its
highest stage of development up to the mid-1940s
and established it as the standard geometrical tool
of the international trade textbooks. It was his version, showing as it does in one Cartesian plane the
mutual gains from trade and the international
equilibrium
conditions
for both
countries
simultaneously, that entered such influential early
texts as D.B. Marsh’s fir/d Trade and Investment
(195 1) and Charles Kindleberger’s ZnterxatiwzaL
Economics (1953). Even today one finds it in such
leading texts as Caves’ and Jones’ cyofcd Trade and
Payments and W. Ethier’s Modern International
Economics.
FEDERAL RESERVE BANK OF RICHMOND
11
Jan Tinbergen
That Leontiefs diagram had by the 1940s already
become the standard way to depict international
equilbrium under conditions of increasing costs and
competitive markets is evident from a glance at
Tinbergen’s 1945 contribution.
His treatment of
this case differs in no essential way from Leontiefs.
Like Leontief he shows the individual open economy
producing at the point of tangency of the production frontier and world price line and then trading
along that line to reach the consumption point of
maximum satisfaction (see Figure 1). And like Leontief he shows that a similar outcome holds for the
other country whose exports must also equal the imports of the first and vice versa.
Tinbergen extends Leontiefs analysis in two minor
respects. He lets production possibility curves and
indifference maps differ across countries. And he
depicts the two-country equilibrium in a box diagram
showing the second country’s system of coordinates
lying diagonally opposite those of the first (see Figure
9). But these are merely trivial differences in mode
of presentation. The results he obtains are exactly
the same as those shown in Leontiefs diagrams.
Figure 9
TINBERGEN’S
TWO-COUNTRY DIAGRAM OF
WORLD TRADE EQUILIBRIUM
P
COMMODITY
COMMODITY
1
1
1 cv
0’
t
Country A’s coordinates are plotted from 0, country
B’s from 0’. Global equilibrium requires both countries produce and consume at common points of
tangency P and C on the world price line PC.
Source: Tinbergen 116, p. 1371.
12
ECONOMIC
REVIEW,
Only when he drops Leontiefs assumptions of
competitive behavior and increasing costs does he
develop some novel results. He considers three cases,
two of which yield the perverse outcome that trade
may worsen rather than improve a country’s welfare.
He takes first the case of decreasing costs prevailing in both industries such that the transformation
curve becomes convex rather than concave to the
origin. He shows here that with trade the only stable
equilibria in production are the terminal points on
the curve representing complete specialization in one
good or the other. Which good the country chooses
to produce upon the opening of trade depends on
the slope of the world price line and the shape of
the indifference curves. Either choice will yield gains
from trade.
Next he considers the case (anticipated by Young
and Lerner) in which decreasing costs prevail in one
industry and increasing costs in the other such that
the production frontier contains convex and concave
segments. He argues that in this case an open trading
economy may myopically choose production and consumption points that worsen its welfare compared
to the no-trade situation (see Figure 10). That is,
given the world price ratio shown by the slope of line
VC, the economy chooses production point V and
consumption point C which is inferior to autarky
point A. But he then notes that this construction
assumes that producers and consumers lack perfect
knowledge of their opportunities.
Otherwise they
would produce at T and trade along the price line
TW (same slope as VC) to reach consumption point
C’ which is superior to the autarky point.
Last he presents a case in which monopoly
pricing in the industry possessing a comparative cost
advantage distorts relative commodity prices and
causes the country to produce and export the wrong
good, namely the good in which it has a comparative
disadvantage. Depending on the shape of the indifference map, the economy may be better off or worse
off than before trade (see Figure 11).
These results of course differ from Leontiefs. But
Tinbergen reached them with the same geometrical
tools. He changed the shape and location of the
diagram’s curves, to be sure. But he put those curves
to their traditional use to depict international
equilibrium and the gains (or losses) from trade, albeit
for anomalous cases. In this respect, his work continued the tradition stretching from Barone to
Leontief.
JANUARY/FEBRUARY
1988
Figure 10
Figure 11
TRADE EQUILIBRIUM WITH A MIXED
TRANSFORMATION
CURVE
MONOPOLY PRICING
IN THE COMPARATIVE
ADVANTAGE INDUSTRY
COMMODITY
\
0
1
COMMODITY
Imperfect knowledge and a mixed (concave-convex)
transformation curve can make the country worse off
with than without trade. At the world price ratio given
by the slope of line VC, the economy produces at V
and consumes at point C which lies on a lower indifference curve than the autarky point A. Conversely,
with perfect knowledge the economy produces at T
and consumes at C’, reaping a clear gain.
Source: Tinbergen 116, p. 1331.
The Diagram Since Tinbergen
1
Monopoly pricing raises the relative price of good 1
(slope of line AB) above its relative marginal cost (slope
of the production frontier at autarky point A) and
makes it appear that comparative advantage lies in
good 2 when in fact it lies in good 1. Consequently,
when trade opens up at the world price ratio given
by the slope of line PQ, the economy specializes in
the wrong good, producing at P and trading along
line PQ to reach point C, or C, depending on the location of the indifference map. Trade yields losses in the
first case, gains in the second.
Source: Tinbergen [16, p. 1361.
After Tinbergen,
Haberler in 1950 used the
diagram to distinguish between the consumption (exchange) and production (specialization) components
of the total gain from trade. The total gain of course
is the jump from the autarky consumption point to
the preferred point on the (highest attainable) world
price line just touching the production possibility
curve. Of this total, the consumption gain stems from
the opportunity to exchange the pre-trade bundle of
goods at world prices. Haberler shows this gain as
the movement from P to T” along a world price line
passing through the pre-trade consumption point (see
Figure 12). Added to this is the production gain
stemming from the opportunity
to produce the
highest valued bundle of commodities measured at
world prices. Haberler shows this gain as the moveFEDERAL
RESERVE
ment from T” to T’ that results when the economy
produces the output mix whose marginal opportunity cost just equals the world terms of trade.
The point of Haberler’s demonstration is this: of
the two sources of gain, exchange and specialization,
the first is fundamental. For, as the diagram shows,
exchange yields gains even in the absence of
specialization (that is, in the absence of a change of
production). The economy simply trades its given
autarky bundle for a preferred one at world prices.
By contrast, specialization without exchange yields
no gains. For it never pays to produce the output
mix valued highest at world prices when one cannot
trade at those prices: in such cases the autarky mix
BANK
OF RICHMOND
13
Figure
HABERLER ON THE
GAINS FROM TRADE
QUANTITIES
OF B
Consumption
(exchange) gains are shown by the
jump from P to T” as the economy swaps its autarky
bundle for a preferred one at world prices. Production (specialization) gains are shown by the further
jump to T’ that results when the economy produces
and trades the output bundle P’ having the highest
value at world prices. Trade yields gains even in the
absence of specialization.
Source: Haberler [8, P. 381
14
ECONOMIC
REVIEW,
is preferred. On the contrary, specialization without
trade yields losses since a closed economy must be
self-sufficient (diversified) in all goods. In short,
exchange rather than specialization is the necessary
and sufficient condition for trade gains.
Haberler’s demonstration
did not exhaust the
diagram’s potential: new uses were found for it.
Haberler himself employed it again in 1950 to illustrate the infant industry argument for protection. In
1952 James Meade employed it to derive trade indifference curves used in advanced trade geometry.
Harry Johnson in 1964 used it to depict noneconomic
objectives of tariffs. Jagdish Bhagwati in 19.57 used
it to show the effects of technological progress on
the terms of trade and national welfare. Robert
Mundell in 1957 used the diagram to show how
international factor mobility negates the protective
effects of tariffs. Haberler in 1950, Bhagwati and
Ramaswami in 1963, and Johnson in 1965 employed
the diagram to analyze domestic market distortions
(divergences between private and social marginal
costs) arising from external economies or diseconomies and rigid factor prices. The best corrective,
they showed, is not a tariff but rather taxes and subsidies in the sector in which the distortions arise.
In all these uses the diagram proved its strength
and versatility. So much so that trade theorists will
undoubtedly employ it again and again. When they
do, they will owe a large debt of gratitude to the
pioneers who developed this powerful tool. Even today, if one understands the diagram one understands
the logic of comparative advantage and gains from
trade.
JANUARY/FEBRUARY
1988
References
1. Baldwin,
R.E. “Gottfried
Haberler’s
Contribution
to International
Trade Theory and Policy.” QaartAy
humaL of Economics97 (February 1982): 141-48.
2. Barone, E. Prim@ di economiapolitica. Roma: Tipografia
Nazionale di G. Bertero, 1908.
3. Caves, R.E. Traa’e and Economic Smccture. Cambridge,
MA.: Harvard University Press, 1960.
4. Fisher, I. TireRate of Interest.New York: Macmilhan Co.,
1907.
Th Theory of Interest. New York: Macmillian
5.
co.,
1930.’
6. Haberler, G. “The Theory of Comparative Costs and Its
Use in the Defense of Free Trade.” WehwittschajhMes
hhiv 32 (July 1930): 349-70. As reprinted in Selected
&rays of Gbttjkd Haberler, edited by A.Y.C. Koo. Cambridge, MA.: MIT Press, 1985, pp. 1-19.
7. . Tire Thory of International Trade, witfi Its
&plications to Conzmetz%i Policy. London: William Hodge
& Co., 1936.
8.
“Some Problems in the Pure Theory of International Trade.” Economic Journal60 (June 1950): 223-40.
As reprinted in SeLectedhays of Cottjied Haberbr, edited
by A.Y.C. Koo. Cambridge, MA.: MIT Press, 1985, pp.
37-54.
9. Hirshleifer, J. “On the Theory of the Optimal Investment
Decision.” Journal of PoliticalEconomy 66 (August 1958):
329-52.
10. Leontief, W.W. “The Use of Indifference Curves in the
Analysis of Foreign Trade.” Qaarterb Journal of Economics
47 (May 1933): 493-503. As reprinted in InternationalTrade,
selected Readings, edited by J. Bhagwati. Harmondsworth,
England: Penguin Books, 1969, pp. 21-29.
FEDERAL
RESERVE
Representation
of
11. Lerner, A.P. “The Diagrammatical
Cost Conditions in International Trade.” Economica 34
(August 1932): 346-56. As reprinted in his Ersayssin &on&
Analysis.London: Macmillian Co., 1953, pp. 8.5-100.
“Barone’s 1908
A., and W.O. Thweatt.
12. Maneschi,
Representation of an Economy’s Trade Equilibrium and the
Gains from Trade.” .lbtunaZof ZnternotioaZZkmotnics 22
(May 1987): 375-82.
13. Mundell, R.. “Abba Lerner and the Theory of Foreign
Trade.” In Thory for Economic Efiemy:
hays in Honor
ofAbba P. Lerner, edited by H.I. Greenfield, A.M. Levenson, W. Hamovitch, and E. Rotwein. Cambridge, MA.:
MIT Press, 1983.
14. Samuelson, P.A. “A.P. Lerner at Sixty.” Review of Economic Stadies 3 1 (1964): 169-78.
15. -.
“Irving Fisher and the Theory of Capital.”
In Ten Economic &dies in the Tradition of Zmig F&er.
New York: J. Wiley, 1967, pp. 17-37.
16. Tinbergen, J. “Professor Graham’s Case for Protection.” In
Appendix I of his ZntrmatinaL Economic Co-operation.
Amsterdam: Elsevier, 1945. Reprinted as “International
Trade under Variable Returns in a Very Simple Model’
in Appendix II of his InternationaLEconomiGZnteqratkm.
2d ed., rev. Amsterdam: Elsevier, 1965, pp. 126-37.
17. Viier, J. StudLz in the T/leotyof Zntenwtiona/
Traak New York:
Harper & Brothers, 1937.
18. Young, A.A. “Increasing Returns and Economic Progress.”
EconomicJoumaZ 38 (December 1928): 527-42.
BANK
OF RICHMOND
15
THEORETICAL ANALYSIS
OFTHEDEMANDFORMONEY
Bennett T. McCalcum and Marvin S. Goodfiend’
In any discussion of the demand for money it is
important to be clear about the concept of money
that is being utilized; otherwise, misunderstandings
can arise because of the various possible meanings
that readers could have in mind. Here the term will
be taken to refer to an economy’s medim of exchange; that is, to a tangible asset that is generally
accepted in payment for any commodity. Money thus
conceived will also serve as a store of value, of course,
but may be of minor importance to the economy in
that capacity. The monetary asset will usually also
serve as the economy’s medium of account-i.e.,
prices will be quoted in terms of money-since
additional accounting costs would be incurred if the
unit of account were a quantity of some asset other
than money. The medium-of-account
role is, however, not logically tied to the medium of exchange
(Wicksell, 1906; Niehans, 1978).
Throughout
much of Western history, most
economies have adopted as their principal medium
of exchange a commodity that would be valuable even
if it were not used as money. Recently, however,
fiat money-intrinsically
worthless tokens made of
paper or some other cheap material-has
come to
predominate. Under a commodity money arrangement, the exchange value of money will depend upon
the demand for the monetary commodity in its nonmonetary, as well as its monetary, uses. But in a
discussion of money demand, as distinct from a
discussion of the price level, any possible nonmonetary demand for the medium of exchangewhich will be absent anyhow in a fiat money
system-can
legitimately be ignored.
Bennett T. McCallum is H. J. Heinz Professor of Economics,
Carnegie-Mellon
University, and Research Advisor, Federal
Reserve Bank of Richmond. Marvin S. Goodfriend is Economist
and Vice President, Federal Reserve Bank of Richmond.
This article is reprinted with permission from Th Nm Paf’m:
ADictionaryof Economics, edited by John Eatwell, Peter Newman,
and Murray Milgate. 4 volumes. London: The Macmillan Press:
New York: Stockton Press, 1987.
l
16
ECONOMIC
REVIEW.
The quantity of money demanded
in tiny
economy-indeed,
the set of assets that have
monetary status-will be dependent upon prevailing
institutions, regulations, and technology. Technical
progress in the payments industry will, for instance,
tend to alter the quantity of money demanded for
given values of determinants such as income. This
dependence does not, however, imply that the demand for money is a nebulous or unusable concept,
any more than the existence of technical progress
and regulatory change in the transportation industr)
does so for the demand for automobiles. In practice,,
some lack of clarity pertains to the operational
measurement of the money stock, as it does to the
stock of automobiles or other commodities. But in.
an economy with a well-established national currency, the principle is relatively clear: assets are part
of the money stock if and only if they constitute
cfaimsto currency, unrestricted legal claims that can
be promptly and cheaply exercised (at par). This principle rationalizes the common practice of including
demand deposits in the money stock of the United
States, while excluding time deposits and various
other assets.
The rapid development
during the 1960s and
1970s of computer and telecommunications
technologies has led some writers (e.g., Fama, 1980) to
contemplate
economies-anticipated
by Wicksell
(1906)-in which virtually all purchases are effected
not by the transfer of a tangible medium of exchange,
but by means of signals to an accounting networksignals that result in appropriate debits and credits
to the wealth accounts of buyers and sellers. If there
were literally no medium of exchange, the wealth
accounts being claims to some specified bundle of
commodities, the economy in question would be
properly regarded and analyzed as a nonmonetary
economy-albeit
one that avoids the inefficiencies
of crude barter. If, by contrast, the accounting network’s credits were claims to quantities of a fiat or
commodity medium of exchange, then individuals’
credit balances would appropriately be included as
part of the money stock (McCallum, 1985).
JANUARY/FEBRUARY
1988
Basic Principles
An overview of the basic principles of money demand theory can be obtained by considering a
hypothetical
household that seeks at time t to
maximize
(1)
uh,llt)
+
+
Pu(ct+
1A+
1)
+
P2U(Ct+2Jt
+2)
. . .
where ct and It are the household’s consumption and
leisure during t and where fl = I/( 1+6), with 6 > 0
the rate of time preference.
The within-period
utility function u(*;) is taken to be well-behaved so
that unique positive values will be chosen for ct and
Ct. The household has access to a productive
technology described by a production function that
is homogeneous of degree one in capital and labor
inputs. But for simplicity we assume that labor is
supplied inelastically,
so this function can be
written as yt = f(kt - I), where yt is production during t and kt - 1 is the stock of capital held at the end
of period t - 1. The function f(e) is well-behaved, so
a unique positive value of kt will be chosen for the
upcoming period. Capital is unconsumed output, so
its price is the same as that of the consumption good
and its rate of return between t and t +I is f ‘(kt).
Although this setup explicitly recognizes the
existence of only one good, it is intended to serve
as a simplified representation-one
formally justified
by the analysis of Lucas (1980)-of
an economy in
which the household sells its specialized output and
makes purchases (at constant relative prices) of a large
number of distinct consumption goods. Carrying out
these purchases requires shopping time, st, which
subtracts from leisure: Ict = 1 - st, where units are
chosen so that there is one unit of time per period
available for shopping and leisure together. (If labor
were elastically supplied, then labor time would have
to be included in the expression.) In a monetary
economy, however, the amount of shopping time required for a given amount of consumption will depend negatively upon the quantity of real money
balances held by the household (up to some satiation level). For concreteness, we assume that
(2)
St = $h,m)
where rl/(*;) has partial derivatives $1 > 0 and $2
I 0. In (Z), rnt = MJPt, where Mt is the nominal
stock of money held at the end of t and Pt is the
money price of a consumption bundle. (A variant with
Mt denoting the start-of-period money stock will be
mentioned below.) The transaction variable is here
specified as ct rather than ct + Ak, to reflect the idea
FEDERAL
RESERVE
that only a few distinct capital goods will be utilized, so that the transaction-cost to expenditure ratio
will be much lower than for consumption goods.
Besides capital and money, there is a third asset
available to the household. This asset is a nominal
bond, i.e., a one-period security that may be purchased at the price l/( 1 +Rt) in period t and redeemed for one unit of money in t + 1. The symbol
Bt will be used to denote the number (possibly
negative) of these securities purchased by the
household in period t, while bt = Bt/Pt.
In the setting described, the household’s budget
constraint for period t may be written as follows:
(3)
f&t- I) + vt 2 ct + kt - kt-1
+ mt - (1+7rTt)-‘mt-1
+ (l+Rt)-‘bt
- (l+nt)-‘bt-1.
Here vt is the real value of lump-sum transfers
(net of taxes) from the government while 7rt is the
inflation rate, at = (Pt - Pt - l)/Pt - 1. Given the objective of maximizing (l), first-order conditions
necessary for optimality of the household’s choices
include the following, in which 4t and Xt are
Lagrangian multipliers associated with the constraints
(2) and (3), respectively:
(4)
w(ct, 1 -St)
(3
-uz(ct,l
(6)
-d&z(ct,mt)
(7)
-Xt
(8)
-Xt(l+RJ-1
- 4trl/l(ct,md
-St)
+ $t
-
- Xt = 0
= 0
At + Pit + l(1 +7rt + 1) - ’ = 0
+ &+l[f’(kt)
+
11 =
0
+ ,&+1(1+at+1)-’
= 0.
These conditions, together with the constraints (2)
and (3), determine current and planned values of ct,
St, mt, kt, bt, &, and Xt for given time paths of vt,
Rt, and 7rt (which are exogenous to the household)
and the predetermined
values of kt - 1, mt - 1, and
bt _ 1. (There is also a relevant transversality condition, but it can be ignored for the issues at hand.)
Also, it values can be obtained from 4 = 1 -st and,
with Pt _ 1 given, Pt, Mt, and Bt values are implied
by the nt, mt, and bt sequences.
The household’s optimizing choice of rnt can be
described in terms of two distinct concepts of a
money demand function. The first of these is a
proper demand function, that is, a relationship
giving the chosen quantity as a function of variables
that are either predetermined
or exogenous to the
BANK
OF RICHMOND
17
economic unit in question. In the present context,
the money demand function of that type will be of
the form
(9)
m
= tL(kt-l,mt-l,bt-l,vt,vt+l,...,
Rt,Rt + I 9. . . . Tt,Rt+
l,...)
where the variables dated t + 1, t + Z,.. . must be
understood as anticipated values. Now, it will be
obvious that this relationship does not closely resemble those normally described in the literature as
“money demand functions.” There is a second type
of relationship implied by the model, however, that
does have such a resemblance. To obtain this second expression, one can eliminate /3X,+ 1(1 + nt + 1) - ’
between equations (6) and (8), then eliminate Xt and
finally dt from the resultant by using (4) and (5).
These steps yield the following:
(10)
-uz(ct,l
-st)$2(ct,mt)
-uz(ct,l
-st) $lhmt)l
= h(ct,l
-St)
11-(I +Rt)-‘I.
Then $(ct,mJ can be used in place of st and the result
is a relationship that involves m& mt, ct, and Rt. Consequently, (10) can be expressed in the form
(11)
hbm,ct,Rit)
= 0
and if the latter is solvable for mt one can obtain
(12)
MtlPt = L(ct,Rt).
Thus the model at hand yields a porztjidio-balance
relationship
between real money balances demanded, a variable measuring the volume of transactions conducted, and the nominal interest rate
(which reflects the cost of holding money rather than
bonds). It can be shown, moreover, that for reasonable specifications of the utility and shopping-time
functions, L(*;) will be increasing in its first argument and decreasing in the second.
There are, of course, two problems in moving from
a demand function (of either type) for an individual
household to one that pertains to the economy as
a whole. The first of these involves the usual problem of aggregating over households that may have
different tastes and/or levels of wealth. It is well
known that the conditions permitting such aggregation are extremely stringent in the context of any
sort of behavioral relation; but for many theoretical
purposes it is sensible to pretend that they are
satisfied. The second problem concerns the existence
of economic units other than households-“firms”
18
ECONOMIC
REVIEW,
being the most obvious example. To construct a
model analogous to that above for a firm, one would
presumably posit maximization of the present value
of real net receipts rather than (l), and the constraints would be different.
In particular, the
shopping-time function (2) would need to be replaced
with a more general relationship depicting resources
used in conducting transactions as a function of their
volume and the real quantity of money held. The
transaction measure would not be ct for firms or,
therefore, for the economy as a whole. But the
general aspects of the analysis would be similar, so
we shall proceed under the presumption that the
crucial issues are adequately represented in a setting
that recognizes
only economic
units like the
“households” described above.
The distinction between the proper money demand function (9) and the more standard portfoliobalance relation (12) is important in the context of
certain issues. As an example, consider the issue of
whether wealth or income should appear as a “scale
variable” (Meltzer, 1963). From the foregoing, it is
clear that wealth is an important determinant of
money demand in the sense that kt _ I, rnt - 1, and
bt- 1 are arguments of the demand function (9).
Nevertheless, formulation (12) indicates that there
is no separate role for wealth in a portfolio-balance
relation if appropriate transaction and opportunitycost variables are included.
An issue that naturally arises concerns the foregoing discussion’s neglect of randomness. How would
the analysis be affected if it were recognized that
future values of variables cannot possibly be known
with certainty? In answer, let us suppose that the
household knows current values of all relevant
variables including Pt, Rt, and vt when making decisions on rnt and ct, but that its views concerning
variables dated t + 1, t + 2,. . . are held in the form of
nondegenerate probability distributions. Suppose also
that there is uncertainty in production, so that the
marginal product of capital in t + 1, f ‘(kt), is viewed
as random. Then the household’s problem becomes
one of maximizing the expectation of (l), with u(.;)
a Von Neumann-Morgenstern
utility function, given
information available in period t. Consequently, the
first-order conditions (4)-(8) must be replaced with
ones that involve conditional expectations. For example, equation (7) would be replaced with
(71
-Xt + PEt{Xt+l[f’(kt)
+ 11) = 0
where Et(.) denotes the expectation of the indicated
variable conditional upon known values of Pt, Rt, vt,
and so on. With this modification, the nature of the
JANUARY/FEBRUARY
1988
proper demand function becomes much more
complex-indeed,
for most specifications no closed
form solution analogous to (9) will exist. Nevertheless, the portfolio-balance relation (12) will continue to hold exactly as before, for the steps described
in its derivation above remain the same except that
it is E&3Xt+ ,(I+ nt + 1)- ‘1 that is eliminated between
equations corresponding to (6) and (8). From this
result it follows that, according to our model, the relationship of Mt/Pt to the transaction and opportunitycost variables is invariant to changes in the probability
distribution of future variables.
Another specificational variant that should be mentioned reflects the assumption that it is money held
at the start of a period, not its end, that facilitates
transactions conducted during the period. If that
change in specification were made and the foregoing analysis repeated, it would be found that the
household’s concern in period t would be to have the
appropriate level of real money balances at the start
relation
of period t + 1. The portfolio-balance
analogous to (12) that would be obtained in the deterministic case would relate mt + I to ct + 1 and Rt, where
mt+l = Mt + i/Pt+ 1 with Mt + 1 reflecting money
holdings at the end of period t. Consequently,
Mt + l/Pt would be related to Rt, planned ct + 1, and
PtlPt + 1. Thus the theory does not work out as
cleanly as in the case considered above even in the
absence of randomness, and is complicated further
by the recognition of the latter. The fundamental
nature of the relationships are, however, the same
as above.
Another point deserving of mention is that if labor
is supplied elastically, the portfolio-balance relation
analogous to (12) will include the real wage-rate as
an additional argument. This has been noted by Karni
(1973) and Dutton and Gramm (1973). More
generally, the existence of other relevant margins of
substitution can bring in other variables. If stocks of
commodities held by households affect shopping-time
requirements, for example, the inflation rate will appear separately in the counterpart of (lZ)-see Feige
and Parkin (1971).
Finally, it must be recognized that the simplicity
of the portfolio-balance relation (12) would be lost
if the intertemporal utility function (1) were not timeseparable. If, for example, the function u(c&) in (1)
were replaced with u(c&Jt _ 1) or u(ct,ct - r,1;), as has
been suggested in the business cycle literature, then
the dynamic aspect of the household’s choices would
be more complex and a relation like (12)-i.e.,
one
that includes only contemporaneous variables-could
not be derived.
FEDERAL
RESERVE
Historical Development
The approach to money demand analysis outlined above, which features intertemporal optimization choices by individual economic agents whose
transactions are facilitated by their holdings of money,
has evolved gradually over time. In this section we
briefly review that evolution.
While the earlier literature on the quantity theory
of money contained many important insights, its
emphasis was on the comparison of market equilibria
rather than individual choice, i.e., on “market experiments” rather than “individual experiments,” in
the language of Patinkin (1956). Consequently, there
was little explicit consideration of money demand
behavior in pre-1900 writings in the quantity theory
tradition. Indeed, there was little emphasis on money
demandperse even in the classic contributions of Mill
(1848), Wicksell (1906), and Fisher (191 l), despite
the clear recognition by those analysts that some particular quantity of real money holdings would be
desired by the inhabitants of an economy under any
specified set of circumstances. Notable exceptions,
discussed by Patinkin (1956, pp. 386-417), were provided by Walras and Schlesinger.
In the English language literature, the notion of
money demand came forth more strongly in the “cash
balance” approach of Cambridge economists, an
approach that featured analysis organized around the
concepts of money demand and supply. This organizing principle was present in the early (c. 187 1) but
unpublished writings of Marshall (see Whitaker,
1975, pp. 165-68) and was laid out with great
explicitness
by Pigou (1917). The Cambridge
approach presumed that the quantity of money
demanded would depend primarily on the volume
of transactions to be undertaken, but emphasized
volition on the part of moneyholders
and recognized (sporadically) that the ratio of real balances to
transaction volume would be affected by foregone
“investment income”, i.e., interest earnings. In this
regard Cannan (192 l), a non-Cambridge economist
who was influenced by Marshall, noted that the
quantity of money demanded should be negatively
related to anticipated inflation-an
insight previously expressed by Marshall in his testimony of 1886
for the Royal Commission on the Depression of
Trade and Industry (Marshall, 1926). In addition,
Cannan developed very clearly the point that the relevant concept is the demand for a stock of money.
Although the aforementioned theorists developed
several important constituents of a satisfactory money
demand theory, none of them unambiguously cast
his explanation in terms of marginal analysis. Thus
a significant advance was provided by Lavington
BANK
OF RICHMOND
19
(192 1, p. 30), in a chapter entitled “The Demand
for Money,” who attempted a statement of the
marginal conditions that must be satisfied for optimality by an individual who consumes, holds money,
and holds interest-bearing securities. But despite the
merits of his attempt, Lavington confused-as
Patinkin (1956, p. 418) points out-the
subjective
sacrifice of permanently
adding a dollar to cash
balances with that of adding it for only one period.
Thus it was left for Fisher (1930, p. 2 16) to provide
a related but correct statement. The discussions of
both Lavington and Fisher are notable for identifying the interest rate as a key determinant of the
marginal opportunity cost of holding money.
In a justly famous article, Hicks (1935) argued persuasively that progress in the theory of money would
require the treatment of money demand as a problem of individual choice at the margin. Building upon
some insightful but unclear suggestions in Keynes’s
Tranie on Money (1930), Hicks investigated an agent’s
decision concerning the relative amounts of money
and securities to be held at a point in time. He emphasized the need to explain why individuals willingly hold money when its return is exceeded by
those available from other assets and-following
Lavington and Fisher-concluded
that money provides a service yield not offered by other assets. Hicks
also noted that the positive transaction cost of
investing in securities makes it unprofitable to undertake such investments for very short periods. Besides
identifying the key aspects of. marginal analysis of
money demand, Hicks (1935) pointed out that an
individual’s total wealth will influence his demand
for money. All of these points were developed further in Chapters 13 and 19 of Hicks’s y,cIle and
Cap&al (1939). The analysis in the latter is, some
misleading statements about the nature of interest
notwithstanding,
substantively very close to that
outlined in the previous section of this article. Hicks
did not, however, provide formal conditions relating
to money demand in his mathematical appendix.
The period between 1935 and 1939 witnessed,
of course, the publication of Keynes’s Genmaf Thory
(1936). That work emphasized the importance for
macroeconomic analysis of the interest-sensitivity of
money demand-“liquidity
preference,” in Keynes’s
terminology-and
was in that respect, as in many
others, enormously influential. Its treatment of money
demand per se was not highly original, however, in
terms of fundamentals. (This statement ignores some
peculiarities resulting from a presumably inadvertent
attribution of money illusion; on this topic, again see
Patinkin, 1956, pp. 173-74).
20
ECONOMIC
REVIEW,
The importance
of several items mentioned
above-payments
practices, foregone interest, and
transaction costs-was
explicitly depicted in the
formal optimization models developed several years
later by Baumol (1952) and Tobin (1956). These
models, which were suggested by mathematical
inventory theory, assume the presence of two assets
(money and an interest-bearing
security), a fixed
cost of making transfers between money and the
security, and a lack of synchronization
between
(exogenously given) receipt and expenditure streams.
In addition, they assume that all payments are made
with money. Economic units are depicted as choosing the optimal frequency for money-security transfers
so as to maximize interest earnings net of transaction costs.
In Baumol’s treatment, which ignores integer constraints on the number of transactions per period,
the income and interest-rate elasticities of real money
demand are found to be ‘/2 and - %, respectively.
Thus the model implies “economies of scale” in making transactions. Tobin’s (1956) analysis takes account of integer constraints, by contrast, and thus
implies that individuals respond in a discontinuous
fashion to alternative values of the interest rate. In
his model it appears entirely possible for individual
economic units to choose corner solutions in which
none of the interest-bearing
security is held. A
number of extensions of the Baumol-Tobin approach
have been made by various authors; for an insightful
survey the reader is referred to Barro and Fischer
(1976).
Miller and Orr (1966) pioneered the inventory
approach to money demand theory in a stochastic
context. Specifically, in their analysis a firm’s net
cash inflow is generated as a random walk, and the
firm chooses a policy to minimize the sum of transaction and foregone interest costs. The optimal decision rule is of the (S,s) type: when money balances
reach zero or a ceiling, S, the firm makes transactions to return the balance to the level s. In this
setting there are again predicted economies of scale,
while the interest-rate elasticity is - i/3. For extensions the reader is again referred to Barre and Fischer
(1976).
The various inventory models of money demand
possess the desirable feature of providing an explicit
depiction of the source of money’s service yield to an
individual holder. It has been noted, e.g., by
Friedman and Schwartz (1970), that the type of transaction demand described by these models is unable
to account for more than a fraction of the transaction balances held in actual economies. Furthermore,
their treatment of expenditure and receipt streams
JANUARY/FEBRUARY
1988
’
as exogenous is unfortunate and they do not generalize easily to fully dynamic settings. These points
imply, however, only that the inventory models
should not be interpreted too literally. In terms of
fundamentals they are closely related to the basic
model outlined in the previous section.
A quite different approach was put forth by Tobin
(1958), in a paper that views the demand for money
as arising from a portfolio allocation decision made
under conditions of uncertainty. In the more influential of the paper’s models, the individual wealth-holder
must allocate his portfolio between a riskless asset,
identified as money, and an asset with an uncertain
return whose expected value exceeds that of money.
Tobin shows how the optimal portfolio mix depends,
under the assumption of expected utility maximization, on the individual’s degree of risk aversion, his
wealth, and the mean-variance characteristics of the
risky asset’s return distribution. The analysis implies
a negative interest sensitivity of money demand,
thereby satisfying Tobin’s desire to provide an additional rationalization of Keynes’s (1936) liquidity
preference hypothesis. The approach has, however,
two shortcomings. First, in actuality money does not
have a yield that is riskless in real terms, which is
the relevant concept for rational individuals. Second,
and more seriously, in many actual economies there
exist assets “that have precisely the same risk
characteristics as money and yield higher returns”
(Barr0 and Fischer, 1976, p. 139). Under such conditions, the model implies that no money will be held.
Another influential item from this period was provided by Friedman’s well-known “restatement” of the
quantity theory (1956). In that paper, as in Tobin’s,
the principle role of money is as a form of wealth.
Friedman’s analysis emphasized margins of substitution between money and assets other than bondse.g., durable consumption goods and equities. The
main contribution of the paper was to help rekindle
interest in monetary analysis from a macroeconomic
perspective, however, rather than to advance the
formal theory of money demand.
A model that may be viewed as a formalization of
Hicks’s (1935, 1939) approach was outlined by
Sidrauski (1967). The main purpose of Sidrauski’s
paper was to study the interaction of inflation and
capital accumulation in a dynamic context, but his
analysis gives rise to optimality conditions much like
those of equations (4)-(8) of the present article and
thus implies money demand functions like (9) and
(12). The main difference between Sidrauski’s model
and ours is merely due to our use of the “shoppingtime” specification, which was suggested by Saving
(1971). That feature makes real balances an arguFEDERAL
RESERVE
ment of each individual’s utility function only indirectly, rather than directly, and indicates the type
of phenomenon that advocates of the direct approach
presumably have in mind. Thus Sidrauski’s implied
money demand model is the basis for the one
presented above, while a stochastic version of the
latter, being fundamentally similar to inventory or
direct utility-yield specifications, is broadly representative of current mainstream views.
Ongoing Controversies
Having outlined the current mainstream approach
to money demand analysis and its evolution, we now
turn to matters that continue to be controversial. The
first of these concerns the role of uncertainty. In that
regard, one point has already been developed, i.e.,
that rate-of-return uncertainty on other assets cannot be used to explain why individuals hold money
in economies-such
as that of the United Statesin which there exist very short-term assets that yield
positive interest and are essentially riskless in nominal
terms. But this does not imply that uncertainty is
unimportant for money demand in a more general
sense, for there are various ways in which it can
affect the analysis. In the basic model outlined above,
uncertainty appears explicitly only by way of the
assumption that households view asset returns as
random. In that case, if money demand and consumption decisions for a period are made simultaneously then the portfolio-balance relation (1’2) will
be-as shown above-invariant
to changes in the
return distributions. But the same is not true for the
proper demand function (9). And the arguments ct
and Rt of (12) will themselves be affected by the
extent of uncertainty, for it will affect households’
saving-as well as portfolio-decisions.
The former,
of course, impact not only on ct but also on the
economy’s capital stock and thus, via the equilibrium real return on capital, on Rt. In addition, because
Rt is set in nominal
terms,
its level will
include a risk premium for inflation uncertainty (Fama
and Farber, 1979).
Furthermore,
the invariance of (12) to uncertainty breaks down if money must be held at the start
of a period to yield its transaction services during that
period. In this case, the money demand decision
temporally precedes the related consumption decision so the marginal service yield of money is random, with moments that depend on the covariance
matrix of forecast errors for consumption and the
price level. Thus the extent of uncertainty,
as
reflected in this covariance matrix, influences the
quantity of real balances demanded in relation to Rt
and plans for ct + 1.
BANK
OF RICHMOND
21
There is, moreover, another type of uncertainty
that is even more fundamental than rate-of-return
randomness. In particular, the existence of uncertainty regarding exchange opportunities available at
an extremely fine level of temporal and spatial
disaggregation-uncertainties
regarding the “double
coincidence of wants” in meetings with potential
exchange partners-provides
the basic ration d&-e
for a medium of exchange. In addition, the ready
verifiability of money enhances the efficiency of the
exchange process by permitting
individuals to
economize on the production of information when
there is uncertainty about the reputation of potential trading partners. Thus uncertainty is crucial in
explaining why it is that money holdings help to
facilitate transactions-to
save “shopping time” in our
formalization. In this way randomness is critically involved, even when it does not appear explicitly in
the analysis. (Alternative treatments of uncertainty
in the exchange process have been provided by
Patinkin, 1956; &mner and Meltzer, 1971; and King
and Plosser, 1986).
An important concern of macroeconomists
in
recent years has been to specify models in terms of
genuinely structural relationships, i.e., ones that are
invariant to policy changes. This desire has led to
increased emphasis on explicit analysis of individuals’
dynamic optimization problems, with these expressed
in terms of basic taste and technology parameters.
Analysis of that type is especially problematical in
the area of money demand, however, because of the
difficulty of specifying rigorously the precise wayat a “deeper” level than (Z), for example-in
which
money facilitates the exchange process. One prominent attempt to surmount this difficulty has featured
the application of a class of overlapping-generations
models-i.e.,
dynamic equilibrium models that
emphasize the differing perspectives on saving of
young and old individuals-to
a variety of problems
in monetary economics. The particular class of
overlapping-generations
models in question is one
in which, while there is an analytical entity termed
“fiat money,” the specification deliberately excludes
any shopping time or related feature that would represent the transaction-facilitating
aspect of money.
Thus this approach, promoted most prominently in
the work of Wallace (1980), tries to surmount the
difficulty of modeling the medium-of-exchange function of money by simply ignoring it, emphasizing
instead the asset’s function as a store of value.
Models
developed
under this overlappinggenerations approach typically possess highly distinctive implications, of which three particularly
striking examples will be mentioned. First, if the
22
ECONOMIC
REVIEW.
monetary authority causes the stock of money to
grow at a rate in excess of the economy’s rate of
output growth, no money will be demanded and the
price level will be infinite. Second, steady-state
equilibria in which money is valued will be Pareto
optimal if and only if the growth rate of the money
stock is nonpositive. Third, open-market changes in
the money stock wiU have no effect on the price level.
It has been shown, however, that these implications
result from the models’ neglect of the medium-ofexchange function of money. Specifically, McCallum
(1983) demonstrates that all three implications vanish
if this neglect is remedied by recognition of shoppingtime considerations as above. That conclusion suggests that the class of overlapping-generations models
under discussion provides a seriously misleading
framework for the analysis of monetary issues. This
weakness, it should be added, results not from the
generational structure of these models, but from the
overly restrictive application of the principle that
assets are valued solely on the basis of the returns
that they yield; in particular, the models fail to reflect
the nonpecuniary return provided by holdings of the
medium of exchange. On these points also see Tobin
(1980).
Recognizing this problem but desiring to avoid
specifications like (Z), some researchers have been
attracted to the use of models incorporating a cashin-advance constraint (e.g., Lucas, 1980; Svensson,
1985). In these models, it is assumed that an
individual’s purchases in any period cannot exceed
the quantity of money brought into that period.
Clearly, imposition of this type of constraint gives
a medium-of-exchange role to the model’s monetary
asset and thereby avoids the problems of the Wallacestyle overlapping-generations
models. Whether it
does so in a satisfactory manner is, however, more
doubtful. In particular, the cash-in-advance formulation implies that start-of-period money holdings place
a SD$Yupper limit on purchases during the period.
This is a considerably more stringent notion than that
implied by (Z), which is that such purchases are
possible but increasingly expensive in terms of time
and/or other resources. Thus the demand for money
will tend to be less sensitive to interest-rate changes
with the cash-in-advance specification than with one
that ties consumption and money holdings together
less rigidly. More generally, the cash-in-advance
specification can be viewed as an extreme special case
of the shopping-time function described in (Z), in
much the same way as a fixed-coefficient production
function is a special case of a more general neoclassical technology. For some issues, use of the
special case specification will be convenient and not
JANUARY/FEBRUARY
1988
misleading, but care must be exerted to avoid inappropriate applications, It seems entirely unwarranted, moreover, to opt for the cash-in-advance
specification in the hope that it tiill be more nearly
structural and less open to the Lucas critique (1976)
than relations such as (2). Both of these specificational devices-and
probably any that will be
analytically tractable in a macroeconomic contextshould be viewed not as literal depictions of technological or social constraints, but as potentially useful
metaphors that permit the analyst to recognize in a
rough way the benefits of monetary exchange. (On
the general topic, see Fischer, 1974).
A final controversy that deserves brief mention pertains to an aspect of money demand theory that has
not been formally discussed above, but which is of
considerable importance in practical applications.
Typically, econometric estimates of money demand
functions combine “long-run” specifications such as
(12) with a partial adj,,t,,,t
process that relates
actual money holdings to the implied “long-run”
values. Operationally, this approach often results in
a regression equation that includes a lagged value of
the money stock as an explanatory
variable.
(Distributed-lag formulations are analytically similar.)
Adoption of the partial adjustment mechanism is
justified by appeal to portfolio-adjustment
costs.
Specifically, some authors argue that money balances
serve as a “buffer stock” that temporarily accommodates unexpected variations in income, while
others attribute sluggish adjustments to search costs.
From the theoretical perspective, however, the
foregoing interpretation for the role of lagged money
balances (or distributed lags) appears weak. It is
difficult to believe that tangible adjustment costs are
significant, and in their absence there is no role for
lagged money balances, in formulations such as (1 Z),
when appropriate transaction and opportunity-cost
variables are included. Furthermore, typical estimates
suggest adjustment speeds that are too slow to be
plausible.
These points have been stressed by Goodfriend
(1985), who offers an alternative explanation for the
relevant empirical findings. A model in which there
is full contemporaneous
adjustment
of money
holdings to transaction and opportunity-cost variables
is shown to imply a positive coefficient on lagged
money when these determinants
are positively
autocorrelated and contaminated with measurement
error. Under this interpretation, the lagged variable
is devoid of behavioral significance; it enters the
regression only because it helps to explain the dependent variable in a mongrel equation that mixes
together relations pertaining to money demand and
other aspects of behavior. (This particular conclusion is shared with the buffer stock approach described by Laidler (1984), which interprets the conventional regression as a confounding of money demand
with sluggish price-adjustment behavior.) Furthermore, the measurement error hypothesis can account
for positive autocorrelation of residuals in the conventional regression and, if measurement errors are
serially correlated, the magnitua?of the lagged money
coefficient typically found in practice.
References
Barro, R. J., and S. Fischer. “Recent Developments in Monetary
Theory.” JoumaL of Monetary Economics 2 (April 1976):
133-67.
Fama, E. F., and A. Farber. “Money, Bonds, and Foreign Exchange.” American EconomicRevim 69 (September 1979):
639-49.
Baumol, W. J. “The Transactions Demand for Cash: An Inventory Theoretic Approach.” Quarter&Journalof Economics66
(November 1952): 545.56.
Feige, E., and M. Parkin. “The Optimal Quantity of Money,
Bonds, Commodity Inventories, and Capital.” American
EconomicReview 61 (June 1971): 33549.
Brunner, K., and A. H. Meltzer. “The Uses of Money: Money
in the Theory of an Exchange Economy.” AmericanEconomic
Rtiena, 61 (December 1971): 784-805.
Fischer, S. “Money and the Production Function.”
Inqui~ 12 (December 1974): 517-33.
Cannan, E. “The Application of the Theoretical Apparatus of
Supply and Demand to Units of Currency.” Economic
Joumal31 (December 1921): 453-61.
Dutton, D. S., and W. P. Gramm. “Transactions Costs, the
Wage Rate, and the Demand for Money.” Amaican Economi
Review 63 (September 1973): 652-65.
Fama, E. F. “Banking in the Theory of Finance.” Journal of
MonetaryEconomics6 (January 1980): 39-57.
FEDERAL
RESERVE
Economic
Fisher, I. The PurchasingPowerofMonq. New York: Macmillan,
1911.
. The Theoryof Zntemst.New York: Macmillan,
1930.
Friedman, M. ‘The Quantity Theory of Money: A Restatement.”
In Studies in the Quantio Theory of Money, edited by M.
Friedman. Chicago: University of Chicago Press, 1956.
Friedman, M., and A. J. Schwartz. MonetaryStatink of the United
States. New York: National Bureau of Economic Research,
1970.
BANK
OF RICHMOND
23
Goodfriend, M. “Reinterpreting Money Demand Regressions.”
Came*-Rochester Confmce &es on PubhkPolicy2 2 (Spring
1985): 207-42.
Meltzer, A. H. “The Demand for Money: The Evidence From
the Time Series.” Journal of Politial Economy 71 (June
1963): 219-46.
Hicks, J. R. “A Suggestion for Simplifying the Theory
Money.” Ihnomica 2 (February 1935): 1-19.
Mill, J. S. Principles of Political Economy, 2 ~01s. London:
John W. Parker, 1848.
Value and Capital. London:
Press; 1939.
Oxford
of
Miller, M. H., and D. Orr. “A Model of the Demand for
Money by Firms.” Quatidy Journal of Economic 80 (August
1966): 413-35.
University
Karni, E. “The Transactions Demand for Cash: Incorporation
of the Value of Time into the Inventory Approach.”
JournolofPoliticalEconomy 81 (September/October
1973):
1216-2.5.
Niehans, J. Th Theooryof Money. Baltimore:
University Press, 1978.
Patinkin, D. Money, Interest, and Pties. New York: Harper
and Row, 1956.
Keynes, J. M. A Treatise on Money, 2 ~01s. London: Macmillan,
1930.
Pigou, A. C. “The Value of Money.” Quart&y Journal of Economics 32 (November 1917): 38-65.
Th General Thory of Employment, Interest, and
Money. London: Macmillan, 1936.
King, R. G., and C. I. Plosser. “Money as the Mechanism of
Exchange.” Jounral of Monetary Economics 17 (January
1986): 93-l 15.
F. Th English Capital Madet. London:
Lucas, R. E., Jr. “Econometric
Carnegie-Rochester
Confme
1976): 19-46.
Svensson, L. E. 0. “Money and Asset Prices in a Cash-inAdvance Economy.” Journalof Poliiticalhmomy93 (October
1985): 919-44.
Methuen,
Tobin, J. “The Interest-Elasticity
of Transaction Demand for
Cash.” Review of EconomicsandStatistics 38 (August 1956):
241-47.
Policy Evaluation: A Critique.”
Se& on Public Poky 1 (Autumn
. “Equilibrium in a Pure Currency Economy.” In Mod&
of Monetav Economies, edited by J.H. Kareken and N.
Wallace. Minneapolis: Federal Reserve Bank of Minneapolis,
1980.
Marshall, A. Ofid Papers by A&d Ma&d..,
Keynes. London: Macmillan, 1926.
edited by J.M.
McCallum, B. T. “The Role of Overlapping-Generations Models
in Monetary Economics.” Canregie-Rdester Gmjhttce Se&
on Public Policy 18 (Spring 1983): 9-44.
. “Bank Deregulation, Accounting Systems of Exchange, and the Unit of Account: A Critical Review.”
Came@-Rochesterconferee series on public Pohy 23 (Autumn
1985): 13-45.
24
ECONOMIC
REVIEW,
Saving, T. R. “Transactions Costs and the Demand for Money.”
American Economic Rehw 61 Uune 1971): 407-20.
Sidrauski, M. “Rational Choice and Patterns of Growth in a
Monetary Economy.” Am&an Economic Rev&~ 57 (May
1967): 534-44.
Laidler, D. ‘The ‘Buffer Stock’ Notion in Monetary Economics.”
EconomicJoumaf 94 (Supplement 1984): 17-34.
Lavington,
1921.
Johns Hopkins
Rev&
“Liquidity Preference as Behavior Toward Risk.”
of Economic Studies 25 (February 1958): 65-86.
. “Discussion.”
In Mod& of Monetav
Economic,
edited by J.H. Kareken and N. Wallace. Minneapolis:
Federal Reserve Bank of Minneapolis, 1980.
Wallace, N.
Money.”
Kareken
Bank of
“The Overlapping Generations Model of Fiat
In MoaUs of MonetaryEconomies, edited by J.H.
and N. Wallace. Minneapolis: Federal Reserve
Minneapolis, 1980.
Whitaker, J. K., ed. TireEhz’y Economic W’titingsof A&d Marsba~l, 1867-2890, 2 ~01s. New York: Free Press, 1975.
Wicksell, K. L.ectures on Pohical Economy, Vol. 2 (1906).
Translated by E. Classen. London: Routledge & Kegan
Paul, 1935.
JANUARY/FEBRUARY
1999
AGRICULTURALSUMMARYANDOUTLOOK
Raymond E. Owens
After deteriorating rapidly in the early 198Os, the
financial condition of agriculture leveled off by the
middle of the decade. Since then, most measures of
the sector’s financial condition have strengthened.
In 1987, total farm income was higher and production expenses were lower than in the previous year.
The improved financial condition of farmers was also
apparent in the expanded equity position of their
balance sheets, which resulted from a combination
of increased asset values and reduced debt burdens.
The turnaround in the agricultural sector was
discussed recently at the annual Outlook Conference
sponsored by the United States Department
of
Agriculture (USDA) in Washington, D.C. There,
analysts from the public and private sectors assessed the current condition of agriculture and gave
their views of its future. Most analysts at the conference believed that the recent financial turnaround
was likely to be the start of a longer-term economic
improvement for U.S. agriculture. What follows summarizes their consensus view.
World Supply and Demand
Conference analysts cited tightened world supply
and demand conditions for agricultural products as
a primary reason for an improved farm income picture. Worldwide grain production fell short of consumption of some commodities in 1987, leading to
reductions in carryover stocks. Worldwide production was lower due to fewer planted acres and lower
yields for some grains. Lower planted acreage
resulted from larger acreage set-asides in the United
States and the withdrawal of some crop land in other
nations. Crop yields held up well in the United States
in 1987, but dry weather and storm damage curtailed yields in some other parts of the world.
While production was lower, world coarse grain
usage rose in 1987 as the expansion of meat production raised feed usage. Wheat consumption was flat
and rice usage was down slightly. Oilseed production matched usage.
World red meat and poultry production rose 1 percent in 1987. Consumption increased by a similar
amount so that carryover stocks were unchanged.
FEDERAL
RESERVE
The U.S. Agricultural Trade Position
One of the most encouraging developments of
1987 was the rebound in agricultural exports. The
total value of agricultural exports rose to $27.5 billion
in 1987, an increase of over $1 billion from 1986.
The volume of agricultural exports rose by 20 million
metric tons to 129.2 million metric tons. Both wheat
and corn exports rose sharply, although lower prices
dampened increases in export values. Increased crop
sales were primarily responsible for the higher export value, but additional meat and horticultural exports accounted for about 40 percent of the value
increase. The increase in value for agricultural exports was the first since 1980, when a peak value
of $43.8 billion was reached. The value of agricultural
imports fell $875 million in 1987 to $20.0 billion.
The decrease was the first since 1981/82.
A higher value of exports combined with a lower
value of imports to widen the 1987 agricultural trade
surplus to $7.2 billion, almost $2.0 billion above the
1986 figure. While improved from 1986, the trade
surplus nevertheless remains low by historical standards. As recently as 1981, the agricultural trade
surplus stood at $26.5 billion.
Farm Income
Analysts from USDA reported that farm cash
income totaled about $57 billion and net farm income
reached about $45 billion in 1987. As shown in Table
I, the income measures were boosted by higher cash
receipts from the sale of livestock, record levels of
government payments, and lower production expenses (lines 1, 2, and 7). Farm production expenses
fell in 1987 primarily due to decreased usage of crop
inputs and lower costs for feed used by livestock producers. After adjusting for inflation, net farm income
reached a record level in 1987.
Crop sales were buoyed by larger than expected
domestic usage and exports. A total of 129.2 million
tons of grains moved out of U.S. ports in 1986/87
compared to just 109.5 million tons in 198.5186. The
higher tonnage figures translated into a higher world
market share for U.S. agricultural products. Lower
export
prices, a weaker dollar, and government
BANK
OF RICHMOND
25
Table I
FARM INCOME STATISTICS
(Billions of dollars)
Item
1.
Farm receipts
............
Crops .................
(incl.
..............
Farm related’
Direct
...........
Government
payments
Cash payments
.
..........
Value of PIK commodities
3.
1982
144.1
147.1
1983
1984
1985
1986
1987F
1988F
137
58
138
62
72.5
72.3
141.1
67.1
146.7
69.4
149.2
74.4
140.2
63.6
69.2
2.5
70.3
4.5
69.4
4.5
72.9
4.4
69.8
5.0
71.6
5.1
74
5
71
5
1.9
1.9
0.0
3.5
3.5
0.0
9.3
4.1
5.2
8.4
4.0
4.5
7.7
7.6
0.1
11.8
8.1
3.7
17
9
9
15
7
8
166.3
163.5
153.1
174.7
166.0
159.5
163
162
146.0
150.6
150.4
155.1
156.9
152.0
155
153
13.8
6.5
14.3
-1.4
13.5
- 10.9
13.4
6.2
11.8
-2.7
10.8
-3.3
10
-1
8
1
113.2
139.4
112.5
140.0
113.3
140.4
116.3
142.7
109.6
133.7
100.1
122.1
97
118
99
118
32.8
26.9
28.6
38.1
23.5
23.5
37.1
12.7
12.2
38.8
32.0
29.7
47.3
32.3
29.1
52.0
37.5
32.9
58
45
39
52.5
42.5
36
35.8
36.4
37.0
38.3
42.5
44.7
48
49
9.4
6.2
4.0
3.4
2.5
1.0
-0.8
-0.8
- 5.6
-9.2
-7.3
- 10.5
-6
-9
-6
-5
6.4
16.8
6.3
13.3
5.3
12.7
8.9
12.5
8.8
9.6
7.8
8.6
7
7
37.9
38.4
33.6
33.6
31.6
33.4
44
net CCC loans)
Livestock
2.
1981
Total gross farm
. .
income
....
(4+5+6)*
4.
Gross cash income
........
(1+2)
5.
6.
Value of inventory
7.
8.
Total expenses
Nonmoney
incomea.
Cash expense9.
9.
10.
...
..........
...........
Net cash income
(4 - 7) ....
Net farm income
(3 -8)
Deflated
11.
.......
change
Off-farm
(1982$)
income
....
......
..........
Loan changes?
12.
13.
Real estate ...........
Non-real estate ........
14.
Rental
income
monetary
plus
change.
15.
Capital
16.
Net cash flow.
........
expenditure9
......
...........
(9+12+13+14-15)
1 Income from machine hire, custom work, sales of forest products, and other misc. cash sources.
2 Numbers in parentheses indicate the combination
3 Value of home consumption
of self-produced
4 Excludes capital consumption,
of items required to calculate a given item.
food and imputed gross rental value of farm dwellings.
prerequisites to hired labor, and farm household expenses.
* Excludes farm households.
F =
midpoint of forecast range.
Note:
Source:
26
Totals may not add due to rounding.
U. S. Department of Agriculture,
Economic Research Service.
ECONOMIC
REVIEW,
JANUARY/FEBRUARY
1988
8
8
42.5
subsidies were, in part, responsible for the increase
in export usage. A second factor spurring crop sales
was increased domestic usage for livestock. Domestic
grain sales were boosted by low feed prices and increased livestock production in 1987.
The net effect of generally lower grain prices
dominating higher grain usage was a reduction of crop
cash receipts in 1987. Cash receipts totaled just $58
billion, down from the 1986 total of $63.6 billion.
Total farm production expenses fell in 1987. Cash
expenses were pressured downward by reduced crop
plantings by farmers attempting to qualify for government price support programs. Cash expenses
totaled $97 billion in 1987, down $3 billion from
1986.
Balance Sheet
Farmers’ total equity, as shown in Table II, rose
in 1987 for the first time in the 1980s. Stable to
slightly higher farm real estate values (line 1) and
lower farm debt burdens (line 10) contributed to the
increase.
The value of farm real estate peaked at $785 billion
in 1981 but then declined steadily to $510 billion
in 1986. According to the Department of Agriculture
estimates, this decline was reversed in 1987 when
the total value of farm real estate rose to $530 billion.
Improved farm income prospects and lower interest
Livestock cash receipts were up moderately in
1987, as higher production and strong prices coincided. Strong demand for meat led to expanded production and generally higher prices for producers.
Livestock cash receipts rose to a record $74 billion
in 1987, up from $71.6 billion in 1986. Direct
government payments totaled $17 billion in 1987
compared to $11.8 billion in 1986. Both figures are
large by historical standards. As recently as 1981,
direct government payments were only $1.9 billion.
Table
II
BALANCE SHEET OF THE U. S. FARMING
Item
1981
Assets
1. Real estate’.
2.
Non-real
. . . . . . . . . . . . .
3.
4.
Livestock
5.
Crops stored’
6.
Financial
7.
1983
1984
1985
1986P
1987F
558.9
510.1
181.5
47.6
80.4
18.4
35.0
691.6
530
179.5
48.5
76
19
36
709.5
$ billion
estate
Machinery
1982
SECTOR
. . . . . . . . . . .
and poultry
. . . . .
and motor vehicles
. . . . . . . . . . .
assets
. . . . . . . . .
Total farm assets
. . . . . .
784.7
212.0
53.5
101.4
29.1
28.0
996.7
748.8
212.2
53.0
102.0
27.7
29.5
961.0
205.4
49.7
100.8
23.7
31.3
945.0
32.8
848.5
191.2
46.3
87.7
23.1
34.2
750.1
98.7
83.6
182.3
814.4
102.5
87.0
189.5
771.5
104.8
87.9
192.7
752.3
103.7
87.1
190.8
657.7
97.7
77.5
175.2
574.9
88.1
66.8
155.0
536.6
83
58
141
568.5
23.4
30.5
370
22.4
28.9
298
20
25
245
739.6
639.6
208.9
49.6
96.9
29.6
Liabilities
8.
9.
Real estate2. . . . . . . . . . . . . .
Non-real estatea. . . . . . . . . . .
10.
11.
Total farm equity
Selected
ratios
Total farm liabilities
. . . .
. . . . . .
Percent
12.
Debt-to-assets
. . . . . . . . . . . .
13.
Debt-to-equity
. . . . . . . . . . , .
14.
Debt-to-net
cash income
. . . .
18.3
22.4
556
19.7
24.6
497
20.4
25.6
519
22.5
29.0
’ Non-CCC crops held on farms plus value above loan rates for crops held under CCC.
* Excludes debt on operator dwellings, but includes CCC storage and dryng facilities
loans.
’ Excludes debt for nonfarm purposes.
P =
preliminary
F =
midpoint of forecast range.
Source:
U. S. Department of Agriculture,
Economic Research Service.
FEDERAL RESERVE BANK OF RICHMOND
27
rates may have assisted the rebound. While the 1987
increase in farmland value is not large in percentage
terms, it accounts for the rise in total farm asset values
from $692 billion in 1986 to around $710 billion in
1987.
Farm liabilities were lower in both the real estate
and non-real estate categories in 1987. Lower debt
loads resulted from loan paydowns by farmers with
available cash and further farm debt writedowns by
financial institutions. Real estate liabilities fell an
estimated $3 to $7 billion to about $83 billion and
non-real estate liabilities declined $8 to $10 billion
to about $58 billion.
Total farm equity reached an estimated $568
billion in 1987, up from $537 billion the year before.
While far short of the $829 billion equity peak
reached in 1980, the 1987 figure is encouraging:
stabilization in the farm balance sheet is one of the
most important developments of 1987.
OUTLOOK
FOR THE FARM SECTOR IN 1988
Trade
The outlook for agriculture in 1988 bears some
similarities to the summary for 1987. A primary
similarity is that agricultural trade should continue
to improve. Agricultural exports are projected to
reach $31 billion in 1988, up sharply from last year’s
$27.9 billion. The higher export value is anticipated
to result from a combination of increased volume and
higher prices. Export volume is expected to reach
137.0 tons in 1988, up from 129.2 tons in 1987.
Volume growth should be centered in larger quantities of grains and cotton. Demand for these commodities will be helped by the Export Enhancement
Program that subsidizes U.S. agricultural exports to
qualifying purchasers. Higher prices are anticipated
in grains, cotton, and soybeans as world supply
tightens relative to demand.
Imports of agricultural commodities are expected
to remain level or decline slightly. In 1987, $20.6
billion of agricultural commodities were imported into
the United States. The Department of Agriculture
is forecasting this value to fall to $20.5 billion in
1988.
Income
Farm income prospects are bright in 1988. Net
farm income is projected to range between $40 and
$45 billion, only a little below the record $45 billion
of 1987. Total government payments are likely to
contribute significantly to net income in 1988, ac-
I
28
ECONOMIC
REVIEW,
counting for about $13 billion. Production
should remain about even with 1987.
expenses
Balance Sheet
If all goes as predicted, the farm balance sheet
should be stronger by the end of 1988. Asset values
are projected to rise further provided farmland values
increase in response to strong farm income prospects,
as most analysts believe they will. Further, debt
reductions are anticipated as farmers pay down more
of their existing debt and financial institutions continue to charge off some of their uncollectible farm
loans.
Farm Policy
The provisions of the 1985 Farm Bill remain in
effect in 1988. Under these provisions, farmers will
continue to operate under programs which provide
crop price supports in exchange for reduced plantings. Smaller crop plantings should reduce production and pressure crop prices upward. Since direct
government payments are the difference between the
target and actual market prices farmers receive,
rising grain prices should reduce the differential and
thus also direct government payments.
Livestock producers will also feel the effects of
these government programs. Such programs, which
push grain prices up, affect livestock producers’
profit margins. Rising grain prices, for example,
translate into higher feed costs, which reduce the
profit margins of livestock producers.
The cost of farm policy has risen dramatically in
recent years. While USDA expects these costs to
fall somewhat in 1988, they still will remain high by
historical standards. The increasing concern over the
federal budget deficit has focused attention on farm
program outlays and many analysts warn that the current expenditures may be subject to reductions in
the next several years.
Food
Prices
Conference analysts look for only modest food
price increases in 1988. Stronger grain prices will
place some upward pressure on cereal-based foods,
but expected expansion in meat production and
only slight increases in the prices of fresh fruit and
vegetables should limit the overall increase in food
prices.
Nonfarm factors, including processing, packaging,
and distribution costs should show only modest increases in 1988. The net effect of farm and nonfarm
influences on food prices should be a 2 to 4 percent
increase.
JANUARY/FEBRUARY
1988
@FedFRASER