Currency Depreciation, Hoarding, and Relative Prices

Currency Depreciation, Hoarding, and Relative PricesAuthor(s): Rudiger DornbuschSource: Journal of Political Economy, Vol. 81, No. 4 (Jul. - Aug., 1973), pp. 893-915Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1831133 .

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Currency Depreciation, Hoarding, and Relative Prices

Rudiger Dornbusch University of Rochester

This paper investigates the effects of devaluation in a two-commodity, two-country, and two-money model with full employment and price flexibility. Primary emphasis is placed on the effect of a change in the real value of money on real expenditure and on the effects on relative prices of a redistribution of expenditure between countries. The stability properties of the model are related to the transfer problem in barter theory and to the Marshall-Lerner condition. Given stability, it is shown that a devaluation will improve the balance of payments.

Introduction

This paper investigates the effects of currency depreciation in a stationary two-country, two-commodity, and two-money model with full employment and price flexibility. While the spirit of the analysis is familiar from the work of Hahn (1959), Komyia (1966), Negishi (1968), Kemp (1969), Johnson (1971), and Mundell (1971), the present paper develops a novel and revealing formulation of the problem. Since, unlike in a "Keynesian" model, in a world of price flexibility it is not true that a devaluation in and of itself changes the terms of trade, it is important to demonstrate the channels through which a devaluation does generate its effects and the extent to which the disaggregation implicit in a two- commodity model does matter.

Submitted for publication January 9, 1972. Final version received July 28, 1972. This paper is a revised version of part of my dissertation, and I should like to acknow-

ledge the assistance and encouragement provided by my thesis committee: H. G. Johnson, S. Fischer, and R. A. Mundell. In preparing this revision, I have substantially benefited from the work of R. Jones, M. Kemp, and T. Negishi. My most particular indebtedness is to M. Mussa, with whom I have discussed this subject over an extended period and who gave me the benefit of insights derived from his own work on related matters. I should like to acknowledge, too, the extensive suggestions for revision I received from R. Gordon, an editor of this Journal.

893



894 JOURNAL OF POLITICAL ECONOMY

The approach taken here is to view devaluation primarily as a monetary phenomenon that operates via the real balance effect on absorption. A devaluation reduces the real value of domestic cash balances and raises the real value of foreign cash balances, thereby causing domestic residents to hoard in order to restore the real value of their money holdings and foreigners to dishoard to eliminate their excess real money holdings. The redistribution of the world money supply implicit in the home country's balance-of-payments surplus reduces the incentive for hoarding and dishoarding and causes the system in the long run to return to full equilibrium with all real variables remaining unchanged, in a manner that is familiar, from the specie flow mechanism.

The role of relative prices enters the analysis through two separate effects. Since a devaluation at constant terms of trade redistributes world expenditure, differences between countries in their marginal spending patterns leave commodity markets in disequilibrium and require adjustments in relative prices. Furthermore, given differences between countries in their demand functions for money, these changes in relative prices feed back on the equilibrium rates of hoarding and require further adjustments in relative prices.

The monetary approach to the balance of payments has frequently been criticized on the grounds that its predictions are essentially un- interesting-a statement that is primarily motivated by the long-run invariance of real magnitudes to a monetary change. That criticism, it is submitted, is misplaced since any structure that does yield long-run real effects as a consequence of a monetary change is difficult to reconcile with accepted thinking about the role of money, an obvious exception being a change in the rate of inflation. Furthermore, to the extent that the monetary approach does suggest that monetary changes do have short- run effects on real variables, it becomes an empirical issue to determine whether observed behavior is compatible with that theory or more readily agrees with the "Keynesian" variants of complete specialization and money prices that are fixed in terms of the producer's currency.

While both the Keynesian approach to devaluation and the monetary formulation of that problem are theoretically correct and can only be questioned with respect to the attractiveness of the underlying assumptions, this is not true of a large body of literature that discusses the effects of a devaluation in the framework of the standard barter model of trade. That discussion will typically revolve around the Marshall-Lerner criterion or relate devaluation implicitly to the transfer problem. This paper attempts to demonstrate the error involved in these exercises while at the same time demonstrating the manner in which elements, familiar from the barter model, may be usefully integrated in the analysis of devaluation.

The plan of this paper is to develop, in the first section, some familiar



CURRENCY DEPRECIATION 8cr

results of the standard barter model which illuminate the subsequent discussion, in section 2, of a monetary economy. In sections 3 and 4 the specific effects of currency depreciation are discussed.

1. The Two-Country, Two-Commodity Barter Model

Several features of the familiar barter model of trade prove useful for the subsequent discussion of the monetary model, in particular the stability conditions and the effects of income transfers.'

The following notation will be used throughout this paper:

Eb, Ei* = the excess demand for the ith commodity,

Ri = the world excess demand for the ith commodity,

q = the relative price of the first commodity-the home country's terms of trade, and

I, 1* = real income measured in terms of the second commodity.

An asterisk (*) denotes a foreign quantity or variable, while a circumflex (^') designates a relative change.

The model is characterized by the behavioral equations (1), the budget constraints (2), and the equilibrium condition (3). Given the factor endowment, production of the ith commodity and hence real income is a function of the relative price while consumption is a function of the relative price and real income, so that excess demand is a function of relative price and real income:

Ei= Ei(q, I), i 1, 2; (1)

E E *(q, *), i- 1, 2.

The budget constraint states that income equals expenditure in each country or, equivalently, that the sum of the excess demand for goods equals zero in each country as shown in equation (2):

qE1 (q, I) + E2 (q, I) = 0,

qEi * (q, I *) + E2* (q, I *) = 0. (2)

The equilibrium conditions of the model are that both commodity markets clear. By the budget constraints one of the equilibrium conditions is redundant, and without loss of generality the equilibrium conditions may be stated with respect to the market for the home country's

1 The structure of the barter model is developed in detail in various places (see, in particularJones [1961], Mundell [1968], and Kemp [1969]). Anticipating the develop- ment of the monetary model in section 2, we may note here that the barter model can be interpreted as the monetary model in long-run equilibrium or in a situation where nominal money supplies behave in such a manner as to keep hoarding equal to zero at all points in time.




exportable commodity. Accordingly, equation (3) states that in equilibrium the world excess demand for the first commodity is zero:

El = E1 (q, I) + El* (q, I*) = 0. (3)

The equilibrium of the model is shown in figure 1: a shows the foreign excess demand for the home country's exportables and the domestic excess supply as a function of the relative price of that commodity; b shows the corresponding world excess-demand schedule obtained by taking the horizontal distance between the schedules in a. The equilibrium relative price is q, at which the home country's excess supply of exportables equals the foreign excess demand for that commodity, and by the budget constraint the domestic excess demand for importables equals the foreign excess supply of that commodity. The equilibrium level of exports in physical terms equals OA, while the value of exports, measured in terms of importables, equals q x OA. The schedules are drawn on the assumption that equilibrium is unique.

To determine the stability condition of this model, assume a process according to which the relative price of exportables increases in proportion to excess demand with no trade taking place in disequilibrium. The stability condition on this dynamic assumption is that an increase in the relative price of exportables creates a world excess supply of that commodity. Accordingly, a negatively sloped world excess-demand schedule, as shown in figure lb, satisfies that stability condition. The algebraic statement of the stability criterion is the Marshall-Lerner condition

q dE1 = E2(q + s* + ml - ml*)4 < 0, (4)

where (i, t*) are the compensated elasticities of excess demand and are

-EI(q,I)

q --q

0 A 0 O A ~E* -E OE

(c) (Fb)

FIG. 1



CURRENCY DEPRECIATION 8Q7

negative quantities, (m1, m1*) are the marginal propensities to spend on the first commodity, and indicates a relative change.2 As is well known, the source of potential instability is the distribution effect of a relative price change since it raises the real income of the net exporter of the appreciating commodity.

Consider next the comparative statics application of this model to the effects of an income transfer, T, from the home to the foreign country. Expenditure in each country now is assumed to equal disposable income, and the latter equals I' = I - T and I*' = I* + T, respectively. Substituting the expressions for disposable income in (3) and differentiating the equilibrium condition yields the terms of trade effect of a transfer

q = 1 dT, (5)

where A E2(1 + I* + M1 - Ml*). Assuming stability, the home country's terms of trade will appreciate

or depreciate as the foreign marginal propensity exceeds or falls short of the domestic marginal propensity to spend on the home country's exportable good. The terms-of-trade effect of a transfer arises from a distribution effect since its source is the redistribution of income and hence expenditure between countries with different marginal spending patterns. Furthermore, since by assumption expenditure equals disposable income in each country, the effect of the transfer is to generate an identically equal trade-balance surplus. It is important, however, to recognize that the transfer and the trade-balance surplus are exogenously imposed.

In figure 2 we show the effect of a transfer on the terms of trade, assuming stability and a foreign marginal propensity to spend on the home country's exportables larger than the domestic marginal propensity to spend on that commodity. In a, at constant terms of trade the transfer causes foreign demand and hence excess demand to increase, domestic demand to decrease, and hence excess supply to increase. Since the foreign marginal propensity exceeds the domestic, at constant terms of trade there is a world excess demand for the home country's exportables, which in turn gives rise to an increase in the equilibrium terms of trade. In b, the relationship between the size and direction of the transfer and the equilibrium terms of trade or, equivalently, the combinations of transfers and terms of trade consistent with goods market equilibrium is illustrated. Recognizing that the transfer is identically equal to the home country's trade-balance surplus, an alternative view of figure 2b is that of a relationship between the home country's trade balance and the terms of trade.

We may now inquire into the relevance of the stability condition or the

2 The stability properties of this model and the decomposition of a price change into a substitution and income effect are developed inJones (1961) and Mundell (1971).




q q

? EE ? (qT)0

E

- - ~E q

(a) (b)

FIG. 2

transfer problem for the theory of currency depreciation. It should be perfectly obvious that in a barter model there is no sense whatsoever in viewing the terms of trade as the "exchange rate" and the transfer or the world excess demand for a commodity as the "balance of payments." Nevertheless, two popular misconceptions about this issue persist. The first approach gives the Marshall-Lerner condition as the criterion for a successful devaluation and may be interpreted in terms of figure lb. We may rewrite equation (3) by substituting from the budget constraint in the form

El = El*(q, I*) - E2(q, I) (3') q

which states that the world excess demand for the home country's exportables equals foreign excess demand for that commodity less domestic excess demand for imports measured in terms of exportables. Differentiat- ing that equation, we obviously wind up with the Marshall-Lerner condition. The misconception here is to identify the world excess demand for exportables with the balance of payments and the terms of trade with the exchange rate and the failure to recognize that only in equilibrium will foreign excess demand for exportables equal the domestic excess supply of that commodity and, conversely, for importables. 3

3 An alternative and correct interpretation of figure 1 is to assume the operation of a buffer stock that pegs the terms of trade at some level by purchasing the world excess supply of one commodity and sells off in exchange an amount equal to the world excess demand of the other commodity (see Jones 1961 and Mussa 1971).



CURRENCY DEPRECIATION 899

A more sophisticated error can be interpreted in terms of figure 2b. Again the terms of trade are viewed as the exchange rate, writing disposable income as I' = I - B and I*' = I* + B, respectively, where B equals the home country's balance-of-trade surplus. Substituting in (3) and differentiating, we obtain the following result:'

dB = q. (6) ml - ml*

The appropriate and correct interpretation of (6) is to assume a change in the terms of trade and ask what is the size and direction of the transfer that will make the new terms of trade an equilibrium-relative price in the sense that markets clear.

There is, however, a sense in which transfer analysis is relevant to the theory of currency depreciation. If a devaluation induces changes in expenditure relative to income of equal size and opposite direction in both countries, then a devaluation would operate with respect to the terms of trade in a manner similar to an exogeneously imposed transfer. It thus remains to be shown how a change in the relative price of monies gives rise to changes in expenditure, a problem that naturally presupposes a monetary economy as the framework of analysis.

2. The Monetary Model

TIhe present section develops the monetary extension of the two-country, two-commodity barter model. That extension is achieved by assumptions relating to the stock and flow demand and supply of money. On the demand side, we assume a stock demand for nominal balances and hoarding as a function of the stock excess demand for money. On the supply side, we will assume that money is the only marketable asset, that each country has its own currency, and that the exchange rate is pegged by a central pool that does not engage in sterilization operations. Under these assumptions, the balance-of-payments surplus (the trade-balance surplus) equals the rate of increase in the domestic money supply and the rate of decrease in the foreign money supply measured in terms of domestic currency. The plan of this section is to develop first the behavioral assumptions, proceed then to describe the conditions of equilibrium and the distinction between short- and long-run equilibrium, and finally discuss the effects of changes in relative and absolute prices.

4 This procedure is implicit in Pearce (1961) and Mundell (1968, p. 40).




We require the following additions to our notation, nominal quantities being measured in terms of the respective country's currency:

Pi, Pi* = the money price of the ith commodity,

L, L* = the stock demand for nominal balances,

M, M * = the nominal quantity of money,

H, H* = hoarding,

H = world real hoarding,

e = the domestic currency price of foreign exchange, and

Z. Z* = real expenditure.

A tilde (-) over a variable designates that a monetary quantity is deflated by the money price of the second commodity and accordingly is measured in real terms in units of the second commodity.

The central behavioral assumption of this section relates to the stock demand for money. We will assume that, given the endowment, the reduced form stock demand for nominal balances is a linear homogeneous function of the money prices of goods:

L = L(P1, P2); L* = L*(P1*, P2*) (7)

We furthermore assume that the stock demand for money is an increasing function of either money price. Given these assumptions, the excess demand for money is an increasing function of either money price, a decreasing function of the stock of money, and is homogeneous of degree one in money prices and the nominal quantity of money.

Consider next the adjustment of cash balances in the presence of stock disequilibrium. Each individual believes himself to be able to add to or subtract from his actual cash holdings at current prices by hoarding or dishoarding or, equivalently, spending less or more than his income. Since hoarding, however, implies foregoing current consumption, the individual has to weigh the costs and benefits of alternative time paths of adjustment. We will assume that the solution of that investment problem implies a finite rate of adjustment and hence a hoarding function that is an increasing function of the stock excess demand for money. At the aggregate level, we will accordingly have a hoarding function that is an increasing function of the stock excess demand for money.

We may thus write the hoarding functions as in (8):

H = H(P1, P2, M); H* = H*(P1*, P2*, M*). (8)

Given our assumptions about the stock excess demand for money, it follows that a rise in either money price raises hoarding since it creates a stock excess demand for money, while an increase in the nominal

' See Dornbusch 1971.



CURRENCY DEPRECIATION 90I

quantity of money reduces hoarding since it creates a stock excess supply. Furthermore, hoarding is linear homogeneous in money prices and the nominal quantity of money, so that an equiproportionate increase in prices and the quantity of money changes nominal hoarding in the same proportion but leaves real hoarding, measured in terms of either commodity, unchanged.

Since the hoarding functions are homogeneous of degree one, we may write (8) in real terms, choosing the second commodity as numeraire:

H = H (q M) H H - H*(q, M*) (8') P 2 P 2*

where M M/P2 and M* _ */P_*. The assumptions about the derivatives of (8) imply that the derivatives of (8') have the following signs:

q > 0A ; M a-- < 0; aq am

q fl* > 0; M* _*< 0. (9) aq aM*

The budget constraint in each country implies that planned expenditure equals income less the planned rate of hoarding:

Z= I-H; Z* = I* -H*. (10)

The excess-demand functions for goods are functions of money prices and nominal expenditure. Since the functions are homogeneous of degree zero in these variables, we may write the excess-demand functions as functions of the terms of trade and real expenditure as in (11):

E = Ei(q, I - ), i = 1, 2; (11)

E = E *(q, 1* -H*), i = 1, 2.

Equations (11) are identical with the excess-demand functions in the barter model, with the single additional element of endogenously deter- mined hoarding which makes absorption an endogenous variable.6

The first equilibrium condition in this monetary model is given by the arbitrage equations (12) which state that a commodity commands the

6 The difference between the present treatment and that of Hahn (1959), Negishi (1968), and Kemp (1969) lies in an implicit assumption about the underlying utility function. Our analysis, making expenditure rather than income and the nominal quantity of money the argument in the excess-demand functions, assumes a separable utility function (see Komyia [1966] and Negishi [1972] on this point). The assumption is adopted here for two reasons. On one hand, it permits one to emphasize more forcefully the relationship with the transfer problem in the barter model. On the other hand, a more general treatment might be deceptive in that it overemphasizes the role of money in the utility function which, after all, is a shortcut that dispenses with a more elaborate macroeconomic theory of the demand for money.




same money price in both countries, money prices being measured in terms of either currency, or

P* Pi i= 1, 2. (12) e

The market clearing conditions given in equations (13) state that in equilibrium the world excess demand for each commodity is zero and world hoarding is zero:

Ri = Ei(q, I-H + Ej* (q, I* - H_ = 0 =1 2; ( H = H(q, M) + H*(q, M*) = 0.

There are two implications of the budget constraints that deserve emphasis and further our understanding of the nature of equilibrium. First, we wish to establish that one of the equilibrium conditions in (13) is redundant. For that purpose, we rewrite the budget constraints in (10) in terms of the excess demands:

qEl + E2 + H= 0; qEl* + E2* + H* = 0, (10')

and adding the two constraints we have q(E, + E1*) + (E2 + E2*) + (H + H*) = 0, which proves the above assertion and is nothing but a statement of Walras' Law. Next, it is important to note that the equilibrium conditions in (13) define flow equilibrium in that they constrain goods markets to clear and world income to equal world expenditure; they do not, however, constrain the balance of payments to equal zero or hoarding to equal zero in each country. Short-run equilibrium obtains when flow markets clear and planned equals actual hoarding in each country, but the world money supply is being redistributed to eliminate monetary stock disequilibrium. In the long run, on the other hand, both flow and stock equilibrium obtain, and accordingly hoarding and the balance of payments are zero in each country. The distinction between short-run and long-run equilibrium is useful for purposes of comparative statics since it permits us to distinguish the impact effect of a policy change from its steady-state effects. In the short run, the balance of payments is an endogenous variable; in the long run, the distribution of the world money supply.

The flow equilibrium defined by equations (13) is shown in figure 3 for the case of gross substitution. The market-equilibrium schedules are drawn for a given nominal quantity of money in each country and a given exchange rate. Flow equilibrium obtains at point A where both commodity markets clear and world income equals world expenditure. The equilibrium terms of trade are given by the slope of the ray OQ.

Consider now the effects of changes in money prices and relative prices, given the nominal quantity of money in each country and the exchange rate. It is first useful to emphasize the distinction between the effects of a



CURRENCY DEPRECIATION

P

E2= 0 /

\<,,. ~~E, = O

0 P?

FIG.

change in the "price level " as opposed to the effects of a change in "relative prices." A change in the price level is unambiguously defined when relative prices remain constant. Accordingly, a lnovement

along OQ corresponds to an increase in the price level. Such an increase in the price level reduces the real value of cash balances, raises real

hoarding in both countries, and, given positive marginal propensities to

spend on both goods, creates a world excess supply of both commodities. Conversely, an equiproportionate decline in money prices raises real balances, creates a stock excess supply of money, and hence raises real

expenditure relative to real income in both countries thereby creating an excess demand for both commodities. An alternative graphical inter-

pretation of the real balance effect is provided in figure 4, where we show domestic real hoarding and foreign real dishoarding as a function of the domestic currency price of the second commodity, given the equilibrium terms of trade, qO, the nominal quantity of money in each country, and the exchange rate.

Initial equilibrium obtains at a domestic currency price of importables, P2', at which real hoarding is zero in both countries. An increase in the

price level to P2' reduces domestic and foreign real balances and causes both domestic residents and foreigners to hoard in order to reattain the initial real value of their money balances. The real rate of domestic hoarding rises to IT and the foreign rate of hoarding to H7*', thus creating a world excess supply of goods equal to AB.




W < ->-H HH(q ,M)

-H 0 H H,-H

FIG. 4

Consider a movement along the world-income-equals-expenditure locus H = 0 in figure 3. Given that along the locus world hoarding is zero, the world excess demand for one commodity equals the world excess supply of the other goods. A movement from initial equilibrium at point A to a point such as C may be decomposed into two effects. First, the terms of trade change, holding income equal to expenditure in each country, inducing a substitution effect and a real income effect in exactly the manner in which we analyze the effect of a relative price change in the barter model in figure 1. The effect of the terms of trade change on the excess demand for the first commodity and the excess supply of the second is accordingly given by the Marshall-Lerner criterion.

We may have a second and subsidiary influence, however, that stems from the effect of changed money prices on hoarding. Since by definition of that locus world hoarding is zero, it must be true that either hoarding is zero for both countries and for all relative prices along H = 0 or one country's rate of hoarding equals the other country's rate of dishoarding. In the former case, the change in relative prices will not change expenditure relative to income, and the Marshall-Lerner criterion exhausts the effects of the relative price change on excess demands. The second case, however, is more complicated and may prove a source of instability, as we will show in section 4 below. For the second possibility to obtain, it must be true that a given change in money prices has an asymmetric effect on the respective countries' stock excess demand for money and hence hoarding. Thus, a given increase in the money price of the first commodity and a decrease in the money price of the second commodity might cause the home country to hoard and the foreign country to




dishoard, which obviously assumes that the demand functions for money differ between countries. Such a result would obtain if the home country was relatively more sensitive to a change in the money price of the first commodity and the foreign country relatively more sensitive to a change in the money price of the second commodity.

The effect on excess demands for goods brought about by these induced changes in expenditure relative to income will then depend on the direction in which expenditure changes in each country and the differences in marginal spending patterns. In particular, if an increase in the terms of trade along I- = 0 raised domestic absorption and reduced foreign absorption, we would get an excess demand for the home country's exportables if the domestic marginal propensity to spend on that good exceeded the foreign marginal propensity. We conclude that a relative price change along H = 0 generates in the commodity markets a substitution effect, an income effect, and an absorption effect. The latter two effects are akin to a transfer: the effect of the former on excess demand depends only on the relative size of the marginal propensities to spend, while the effect of the latter depends both on the differences between marginal propensities and differences in hoarding functions. The gross- substitute case shown in figure 3 is suitable as a benchmark of analysis since in that case an increase in the terms of trade (along H = 0) creates an excess supply of the first commodity and an equal excess demand for the second commodity, so that the potentially destabilizing effects induced by a relative price change either do not obtain or are dominated by the substitution effect.

3. The Effects of Devaluation: Two Special Cases

In this section, we discuss the effects of devaluation for two special cases that deserve attention because of their simplicity and historical interest- the gross-substitute and Bickerdike-Robinson-Metzler case, respectively. We are interested in determining the effect of a currency depreciation on the terms of trade, money prices, and the balance of payments, given the nominal quantity of money in each country. We are thus conducting a comparative statics analysis to determine the impact effect of a devaluation.

It will be convenient to follow the standard practice of comparative statics and consider first the effect of a devaluation at constant terms of trade on the price level and the balance of payments. Given these results, we can then inquire whether a change in relative prices is required to clear individual commodity markets.

First, we want to show that a devaluation, at constant terms of trade, acts in the manner of a capital levy on real balances in the home country and a capital gain on real balances abroad, and that these changes in the




real value cause foreigners to dishoard to reduce the real value of their cash balances and domestic residents to hoard to recover the initial real value of their money holdings. To establish these effects, we use figure 5 and assume that both countries are initially in long-run equilibrium with terms of trade q0 and a domestic currency price of importables P20. The home country is assumed to devalue in the proportion (P2" - P20) / P20 = e'. At an unchanged domestic currency price of goods, the foreign currency price of goods would decline in the same proportion as the rate of currency depreciation. That decline in the foreign price level raises foreign real balances and therefore induces foreigners to raise real expenditure relative to real income such as to decumulate their capital gains. If, however, the domestic price level rose in the same proportion as the exchange rate, the foreign price level and foreign real balances would remain unchanged, and accordingly foreign hoarding or dishoarding would remain zero. The argument establishes that the foreign dishoarding schedule shifts upward to intersect the vertical axis at P2".

Next, we inquire into the magnitude of the domestic price level change required to maintain the equality of world income and expenditure. Since the equality of world income and expenditure implies that one country's rate of hoarding equals the other country's rate of dishoarding, it is readily seen from figure 5 that the price change is indicated by the intersection of the respective country's hoarding schedules and equals (P2' - P20)/P20, implying a decline in the foreign price level equal to

(P2" - P2')/P20. If the domestic currency price of goods were to increase by less, there would be a world excess demand for goods and conversely

P2

P~~s /~H(q rM) P2ie P2N

-H (q0,M

0 B H,-H

FIG. 5




for a change in the domestic price level in excess of that magnitude. The first effect of a devaluation, then, is to change the actual relative to the desired stock of real balances in both countries, thereby inducing hoarding and dishoarding as residents attempt to restore the real value of their cash holdings. The equilibrium real balance-of-payments surplus is equal to OB.

Since the equality of world income and expenditure only implies that the world excess demand for goods is zero and not necessarily the world excess demand for each commodity, we inquire in figure 6 whether the redistribution of real expenditures shown in figure 5 is consistent with equilibrium in individual goods markets. The proportionate rate of depreciation is given by (A" - A')/OA'. The previous argument establishes that at constant terms of trade, the world-income-equals-expenditure locus shifts upward to intersect the ray OQ at A'.

If the domestic price level remained unchanged at A', domestic real expenditure would remain unchanged but foreign real expenditure would rise and create an excess demand for both goods. Conversely, if the domestic price level rose to A", foreign real expenditure would remain at the initial level, but the decline in domestic real balances would cause domestic real expenditure to decline, thereby creating a world excess supply of both commodities. The argument establishes that an inter- mediate price change is required, and we may ask whether A' is the

H 90X

X ~ ~~~~~~~~~ 0

P P2

FIG. 6




appropriate price level. The movement to A' involves changes in real expenditure of equal magnitude and opposite direction-a transfer so that the excess demand for the first commodity is given by7 (M1 * -m 1) dH and the excess demand for the second commodity by (M2* - M2) dH. If the marginal propensities to spend on each commodity are identical between countries these terms are zero, and accordingly all three schedules will intersect at A' and the real expenditure effects of a devaluation leave relative prices unchanged.8

The case shown in figure 6, however, does assume distribution effects, and in particular it assumes that the foreign marginal propensity to spend on the second good exceeds the domestic propensity to spend on that commodity. It follows that at A' we have an excess demand for the second commodity and an excess supply of the first commodity, requiring a relative price change and movement to point W, where both commodity markets clear.9 The gross-substitute assumption implies that the required price adjustment is a decrease in the relative price of exportables.

Some further results may be derived from the gross-substitute case shown in figure 6. We observe that both goods' prices rise in terms of domestic currency and that they rise less than proportionately to the rate of depreciation. This implies in turn that prices decline in terms of foreign currency and decline less than proportionately to the rate of devaluation.10 Given our assumptions about the hoarding functions, the rise in both domestic currency prices and the decline in both foreign currency prices imply unambiguously that the home country will be hoarding or running a balance-of-payments surplus, and the foreign country will be dishoarding and running a balance-of-payments deficit.

The redistribution of the world money supply implied by the home country's balance-of-payments surplus will cause, over time, domestic nominal balances to rise and foreign nominal balances to decrease, thereby making the short-run equilibrium at W obsolete. The increase in the domestic nominal money supply at constant prices lowers the domestic rate of hoarding and the decrease in the foreign money supply

7 The marginal propensities are defined with respect to expenditure so that ml_ q(aEllaZ) = 1 - os2, and similarly for the foreign country.

8 This particular outcome justifies the aggregation of traded goods into a composite commodity, a convention that proves particularly convenient in models that emphasize the distinction between traded and nontraded goods (see Dornbusch 1972).

9 The shifts of the various schedules along OQ are obtained by differentiating the equilibrium conditions in (13) holding relative prices and the nominal money supplies constant and noting that P2* = P2 - e. Performing that operation yields:

P2 - m** ** P2LE2=0 = m m2** e;

P21I = O

+De mJOC + MJ1O aM20 + m2 *O* aC + OC*

where it should be noted that the constancy of the terms of trade implies that both money prices change in the same proportion.

10 This result is due to Hahn 1959.



CURRENCY DEPRECIATION BOO

Q

P P

f'o

FIG. 7

reduces the foreign rate of dishoarding, thereby reversing the initial expenditure effects of the devaluation. The process continues until the initial real equilibrium is reattained with an increase in the domestic nominal quantity of money and price level and a decrease in the foreign quantity of money and price level.

The Bickerdike-Robinson-M~etzler model is the second case we propose to analyze here. " It will be recalled that the model assumes that the total cross-price elasticities of excess demand are zero, an assumption that has been criticized as leading to a partial equilibrium approach to devaluation. Negishi and Kemp have pointed out, however, that the model may be interpreted to reflect a monetary economy in which substitution and income effects of a relative price change are exactly offset by its hoarding effects.. " Maintaining our assumptions about the hoarding

K~~~~~~~~~

functions, we show in figure 7 the market-equilibrium schedules for the case of zero cross-price effects in the commodity markets. Given the nominal quantity of money in each country and the exchange rate, there is only one domestic money price at which the respective commodity markets are in equilibrium.

Initial long-run equilibrium obtains at point A'. The effect of a devaluation, assuming M2* - M2 > O. is shown by the shifts in the market- equilibrium schedules, and the new short-run equilibrium obtains at

I See Metzler 1948. 12 See Kemp 1969 and Negishi 1968.




point W where all flow markets clear. Since the analysis follows exactly that of the gross-substitute case, we confine ourselves to pointing out that in this case, too, both domestic currency prices of goods increase less than proportionately to the rate of depreciation, the terms of trade improve or deteriorate as the foreign exceeds or falls short of the domestic marginal propensity to spend on the home country's exportable commodity, and the home country's balance of payments unambiguously improves.

These strong results obtained here are due to our assumption that hoarding is an increasing function of either money price, which, together with the assumption of a zero total cross-price elasticity of excess demand, amounts to the implicit assumption that the own price elasticity of excess demand is larger than unity in absolute value for both goods in both countries, which is, in turn, a sufficient condition in the Bickerdike- Robinson-Metzler model for a devaluation to improve the balance of payments. 1 3

4. The Effects of Devaluation: The General Case

While the previous section showed a devaluation to improve the balance of payments and to raise domestic currency prices of goods, we consider here the more general case and ask whether it is possible that a currency depreciation could deteriorate the balance of payments and whether the conditions that give rise to such an outcome are consistent with stability. To the extent that instability is closely related to the distribution effects associated with a relative price change, the discussion will establish a relationship with the analysis of the barter model developed earlier. We will continue to assume the properties of the hoarding functions in (8) and (9), a constant nominal quantity of money in each country and initial long-run equilibrium.

The comparative static properties of the model will be developed in terms of the market for the home country's exportables and the world- income-equals-expenditure equality. The equilibrium conditions are repeated here for convenience:

El = EI(q, I-H) + El*(q, I* H*) = 0, (14)

H = H(q, M) + H*(q, M*) = 0, (15)

where M = NI/P2 and M* = M*(e/P2). If the equilibrium conditions in (14) and (15) hold, the home country's actual balance of payments or

13 The reader may wish to verify this statement by differentiating the budget constraints in (10') above.



CURRENCY DEPRECIATION 9II

rate of increase in the money supply, M, measured in terms of importables, equals the planned rate of hoarding:

M = H = H(q, M). (16)

The first relationship we propose to derive is one between the terms of trade and the equilibrium balance-of-payments surplus such that commodity markets clear. Differentiating the equilibrium condition in (14), we obtain the expression

q dEj = 0 = Aqj - ml dH - m1* dH*, (17)

where the first term on the right-hand side is again the Marshall-Lerner criterion, while the second and third terms arise from changes in hoarding or, equivalently, from changes in expenditure relative to income. Since we are interested in the relationship between the terms of trade and the equilibrium balance of payments, we have to impose the further restriction that -dH = dH*, since only in equilibrium one country's rate of dishoarding equals the other country's rate of hoarding. Given that substitution in (17), we have

q dE1 = 0 = Aq- + (ml* -m ) dH. (18)

This equilibrium relation is shown in figure 8 as the locus E1 = 0 on the assumption that A < 0 and ml* - ml > 0. We note that neither restriction is necessarily satisfied and that accordingly the schedule may be positively sloped, negatively sloped, or horizontal. Figure 9 acknowl- edges this possibility. The market-equilibrium schedule in that figure exhibits multiple long-run equilibria, and its slope changes sign.

So far, we have only obtained a relationship between the terms of trade and the equilibrium balance of payments, and it remains to determine the equilibrium balance of payments itself. Differentiating equation (15)

q eai ^j

H H

FIG8 /

FIG. 8



9I2 JOURNAL OF POLITICAL ECONOMY

q q

__H

FIG. 9

yields a relationship between terms-of-trade changes, price-level changes, and exchange-rate changes such that world income equals world expenditure:

dH = 0 =3+ /)q - (?C + a*)P2 + oCt. (19)

Differentiating (16) and substituting from (19) gives us the change in domestic hoarding as a function of the change in the terms of trade and in the exchange rate: 1 4

dH= ( - 3*)q + Ye, (20)

where - /1[oc/(a + x*)] > 0; P* = /3*[c/(x + x*)] > 0; y -4c*/(cx + a*)] > 0. The second term in (20) is the balance-of-payments effect of a devaluation at constant terms of trade, an effect that is unambiguously positive, as was shown in figure 5. The first term arises from the asymmetric effects of a relative price change on the respective countries' rates of real hoarding. The sign of that term is ambiguous since there is no theoretical presumption as to the specific bias of the demand functions for money in the two countries.1 5

I The reader should recognize that from the derivation of (20) the expression for the change in domestic hoarding is at the same time the formula for foreign dishoarding.

15 The reader may find it helpful to derive this effect in fig. 4 by investigating the change in equilibrium hoarding brought about by an increase in the terms of trade. At a constant domestic price of the second good, the increase in the money price of the first commodity raises domestic hoarding and lowers foreign dishoarding. The new equilibrium obtains at the intersection of the shifted hoarding schedules, and while the equilibrium price of the second commodity will decrease, domestic hoarding will increase or decrease as the domestic hoarding schedule shifts more or less than the foreign dishoarding schedule.




We can now proceed to solve (18) and (20) for the terms of trade and balance-of-payments effect of a devaluation to obtain' 6

q e (21)

and

dH = (1 ? i) y, (22)

where X [(ml - ml*)(6 - 6*)]/[A - (ml - ml*)(6 - 0*)] C 0. These solutions highlight the role of distribution effects which are

captured in the term 2A. They may arise either from differences in the marginal propensities to spend, ml - ml*, or from differences in the hoarding functions, 6 - 6*. A particularly strong and attractive result obtains when the latter effect is absent so that 6 = 3* In that event we have a strong separation between the role of the real balance effect in determining absorption and the role of relative prices in clearing commodity markets. The balance-of-payments effect may be analyzed as in a one-commodity world and the terms-of-trade effect in the manner of the transfer problem in the barter model.

In general, such a separation between the real and monetary aspects of the problem is not possible, and changes in relative prices have feed- back effects on the equilibrium rate of hoarding as shown in figures 8 and 9. The locus HH indicates the equilibrium rate of domestic real hoarding consistent with the equality of world income and expenditure, given the exchange rate and the nominal quantity of money in each country, and can be interpreted as a movement along H = 0. The slope is the reciprocal of the first term in (20), and the figures are drawn on the assumption that 6 - b* > 0. A change in the exchange rate at constant terms of trade increases the equilibrium rate of domestic real hoarding and accordingly, shifts the HR locus to the right to Hl'H'. The new equilibrium is deter- mined by the intersection of the commnodity market equilibriuin schedule with the shifted equilibrium boarding schedule. It is readily apparent that in figure 8 a devaluation improves the terms of trade and the balance of payments while the converse obtains in figure 9.

Figure 9 interprets the circumstances that may lead to a deficit. The essential ingredients are low substitutability between goods combined with strong differences in the hoarding functions. Given these ingredients, substantial relative price adjustments are required to equilibrate the goods market, and these relative price adjustments in turn cause expenditure changes sufficiently strong to outbalance the favorable effect

16 The solutions for the changes in nioney prices can be derived by substituting (21) in (19) to solve for the relative change in the price of importables and then by using the fact that q = PI - P2 and Pi* = Pi - Ca to solve for the remaining price changes.



9I4 JOURNAL OF POLITICAL ECONOMY

of a devaluation at constant terms of trade. The conditions for the devaluing country to enjoy a surplus, > - 1, implies that we require the equilibrium hoarding schedule to have a slope larger in absolute value than the goods-market equilibrium schedule. Furthermore, if the slopes are of opposite sign a surplus is ensured, though the relative price change dampens the balance-of-payments effect of a devaluation at constant terms of trade.

Next, we propose to inquire into the stability conditions of the model to determine whether a devaluation-induced deficit is consistent with stability. The dynamic system appropriate for questions of stability is given by equations (14), (15), and (16) together with the world monetary constraint, M = M + M*. The system will be considered stable if a redistribution of the world money supply leads to a deficit in the recipient country, or dM/dM = -2y(l + A) < 0, where dM = -dM*. The stability condition then implies that a devaluation must improve the balance of payments of the devaluing country. The close similarity between the stability condition and the balance-of-payments effect of a devaluation derives from the fact that a devaluation is equivalent to an increase in the foreign money supply.

While it is only reasonable to assume global stability, since otherwise it becomes possible for the deficit country to run down its cash balances to zero, we have nevertheless to recognize the possibility of local instability that arises from a multiplicity of long-run equilibria. Such a situation is shown in figure 9 where we have multiple long-run equilibria and where the initial equilibrium at terms of trade q0 is unstable.' 7 For that con- stellation a devaluation causes, in the short run, a deficit: the reduction in domestic balances and the increase in the foreign money supply implied by the deficit shift the equilibrium hoarding schedule over time down and along the goods-market equilibrium schedule until a new long-run equilibrium is attained at terms of trade q'. There is nothing in the present structure that would rule out this possibility. Moreover, the fact that a devaluation in this instance has long-run real effects is solely due to the local instability and multiplicity of long-run equilibrium.

We may conclude this section by a summary of our results. Given a unique and stable long-run equilibrium, a devaluation will improve the balance of payments. If, in addition, the Marshall-Lerner condition holds, the home country's terms of trade will improve or deteriorate as the foreign marginal propensity to spend on the home country's exportables exceeds or falls short of the domestic propensity to spend on that commodity. If there is a multiplicity of long-run equilibria and initial equilibrium is unstable, a devaluation will cause a deficit; the terms of trade

17 The entire discussion assumes that short-run equilibrium is unique, since without such an assumption the dynamics of the system become intractable.



CURRENCY DEPRECIATION

providing the Marshall-Lerner condition holds will behave as des- cribed above.

Conclusion

The present paper has been devoted to the analysis of devaluation in what must be considered a nicely behaved framework. We may question at this point some of the assumptions and suggest extensions that would enrich the analysis. There are two main shortcomings. The first relates to the costless adjustment in commodity and factor markets that allows instantaneous movements along the transformation curve and thus disregards both the specificity of factors and the existence of contracts fixed in nominal terms. In a model that inquires into the time path balance of payments, these factors should prove important and accordingly should be incorporated into the structure. The second limitation arises from the absence of assets alternative to money. The implication of that restriction is that too much weight of the analysis rests on the effect of a change in real balances on expenditure.' 8

References

Dornbusch, R. "Aspects of a Monetary Theory of Currency Depreciation." Ph.D. dissertation, Univ. Chicago, 1971.

. "Devaluation, Money and Nontraded Goods." A.E.R. (in press). Hahn, F. "The Balance of Payments in a Monetary Economy." Rev. Econ.

Studies 26, no. 70 (February 1959): 149-58. Johnson, H. G. "The Monetary Approach to Balance of Payments Theory."

Mimeographed. Dept. Econ., Univ. Chicago, 1971. Jones, R. "Stability Conditions in International Trade: A General Equilibrium

Analysis." Internat. Econ. Rev. 2, no. 2 (May 1961): 199-209. Kemp, M. The Pure Theory of International Trade. Englewood Cliffs, N.J.: Prentice-

Hall, 1969. Komiya, R. "Monetary Assumptions, Currency Depreciation and the Balance of

Trade." Econ. Studies Q. 27, no. 2 (December 1966): 9-23. Metzler, L. "The Theory of International Trade." In A Survey of Contemporary

Economics, edited by Howard S. Ellis. Philadelphia: Blackiston, 1948. Mundell, R. A. International Economics. New York: Macmillan, 1968.

. Monetary Theory. Englewood Cliffs, N.J.: Goodyear, 1971. Mussa, M. "A Simple General Equilibrium Model of Trade and the Balance of

Payments." Mimeographed. Dept. Econ., Univ. Chicago, 1971. Negishi, T. "Approaches to the Analysis of Devaluation." Internat. Econ. Rev. 9,

no. 2 (June 1968): 218-27. . General Equilibrium Theory and International Trade. New York: Elsevier,

1972. Pearce, I. "The Problem of the Balance of Payments." Internat. Econ. Rev. 2,

no. 1 (January 1961): 1-28.

18 An approach that remedies this deficiency is proposed in Mussa (1971).



Documents

Currency Depreciation, Hoarding, and Relative Prices