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International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 3 - 16.

The Classical System

Robert A. Mundell

The distinction, vital to the classical system of international trade theory, between the short-run mechanism of balance-of-payments adjustment and the static theory of barter was an important dimension of the classical dichotomy between monetary theory and value theory. This dichotomy was a powerful tool of analytical abstraction that enabled a separation of long-run static analysis from short-run dynamics. In dynamical, short-run, disequilibrium theory, monetary elements assume a role of first-order importance in the adjustment process. But after the adjustment process is completed money is shown in its true light as a mere veil, with no influence upon the nature or position of long-run equilibrium. A major task of exposition in classical theory, therefore, was to demonstrate the automaticity of equilibrium through examination of the monetary adjustment process, and through this demonstration, the unimportance, in the long run, of monetary phenomena.

The demonstration of the automaticity of balance-of-payments adjustment in the field of international trade theory was a companion to, although it anteceded, the demonstration of a different kind of automaticity in value theory. In the theory of a closed economy the classical economists assumed the system tended automatically toward a full-employment equilibrium, on the premise that money wages were flexible, and it was an equilibrium not affected, in any fundamental way, by the amount of money in the system. Whatever the temporary effects of a change in central bank policy, the money supply had no influence upon the equilibrium rate of interest, which was identified with the rate of profit, or the real wage. Instead, money exerted its influence merely upon the price level and the level of money wages. Since money could not alter either the level of real wages or the rate of interest, it could not affect the equilibrium level of any real magnitude in the economic system, and the path was cleared for long-run analysis and abstraction from purely monetary phenomena.

In an open economy linked to the rest of the world by international trade and the gold standard, on the other hand, the central bank could not even affect the nominal quantity of money in the system unless the country was large enough to influence, by itself, the world price level. Whereas in a closed economy the central bank could determine the nominal quantity of money, and the public, through spending or hoarding it, could determine its real value, in an open economy any excess of new money creation over desired hoarding would escape down the foreign drain. An overissue of money by the banking system would quickly bring its own corrective: Specie would flow out and force the banks to take back the redundant currency, or else suffer a depreciation of the gold value of bank notes. The nominal quantity of money was thus determined in a single economy by international considerations, and the barter terms of trade could not be affected permanently by purely monetary disturbances.

To have perceived the validity of these propositions, which even today exhibit a fundamental truth, was the supreme intellectual achievement of classical economic analysis. Through this theory mercantilist fallacies could be refuted and the way paved for the emphasis on the doctrine of free trade and on other real phenomena, the only considerations that were supposed to matter in the long run. Ricardo's love was not the short-run dynamic mechanism but the long-run static theory of international barter.

We know today that this separation of statical, barter theory from dynamical, monetary theory was carried too far, in the sense that it cannot be maintained, as the classical school seemed to hold it could, that the trade equilibrium established under conditions in which money is used and the trade equilibrium reached under conditions of barter are identical. Indeed, it is difficult to conceive of a way in which the assertion can be given an operational meaning. What is valid in the separation is not the identical nature of the equilibrium that is achieved, but rather the universality of the principles established in the process of reaching trade equilibrium. The principles established would not be different and it is this that provides the justification for an extended treatment of the classical barter model.

The barter model is indeed the source of many propositions that form the body of modern international trade theory. Despite severe criticism of other aspects of classical theory the barter model has stood the test of time. Its survival can be attributed partly to its applicability to current policy issues in the country in which it originated, and partly to its internal consistency. It was logically immune to criticisms of general equilibrium and macroeconomic methods and was aggregative in scope.

The classical school was interested in establishing the direction in which the terms of trade would move as a result of exogenous disturbances to equilibrium such as would arise from tariffs, hoarding, harvest failures, income transfers (or other remittances) and productivity changes. More powerful methods today make it possible to derive additional implications from the model and to deduce, in cases where the relevant data are available, the probable magnitude of changes in the terms of trade. The purpose of this and the following two chapters 1 is to show how these results may most simply be obtained. The main focus of our attention will be on comparative statics rather than dynamics or monetary considerations.

Analytical Procedure

The nature of comparative statics analysis is a contrast between two positions, usually positions of equilibrium, distinguished from one another by a shift in some parameter such as that which would be brought about by a change in economic policy. The policy change disturbs the initial equilibrium by causing excess demand for one commodity and excess supply of another commodity. The disequilibrium must then be eliminated, if a new equilibrium is to be reached, by an adjustment in some other variable. The adjusting or equilibrating variable may be another policy change, or a process of adjustment that is sufficiently predictable to be considered automatic.

In classical international trade theory the adjustment mechanism was presumed to be automatic. A policy change would disturb balance-of-payments equilibrium, induce a gold flow and, through a change in relative price levels, a change in the terms of trade. Today this mechanism is not so automatic in the sense that central bank and government reaction to disequilibrium in the balance of payments is predictable. Besides the traditional inflation-deflation method of the gold standard, a disequilibrium may be corrected by borrowing (in the short run), trade controls, tax changes, technological changes (in the long run), or the exchange-rate adjustment. Most of these methods have been used2 by one country or another since the breakdown of the gold standard system to resolve balance-of-payments crises.

Because of this change in institutional response to disequilibrium, any analysis of policy change necessarily involves elements of taxonomy. Such questions as: "Do tariffs improve the balance of trade?" cannot be given an equivocal reply; the answer depends on the other policies followed by the government. A tariff disturbs the initial equilibrium and therefore requires, for a new equilibrium to be reached, a change in some other policy; it may involve changes in any or all of the policies listed above.

But exploring all conceivable policy alternatives would be tedious and unrewarding pedantry. For that reason it is convenient to assume that, for analytical purposes, the classical mechanism is operative, that the terms of trade "automatically" adjust to correct disequilibrium. The first step in the comparative-static analysis is therefore to determine the effect of policy changes on the terms of trade or domestic price ratios. It will be shown later that results thus obtained can be used to demonstrate the working of any alternative mechanisms of adjustment.

The Method of Comparative Statics

The most direct way to derive the effect of a policy change on the terms of trade is to differentiate a balance-of-payments equation with respect to the change in policy, and to substitute in the result the conditions necessary to satisfy the other conditions of equilibrium. A more intuitive way of getting the criterion, however, is to employ a device implicit in all comparative-statics analysis. This is to compute the excess demand caused by the policy change on the assumption that the adjusting variable is constant, and to equate this excess demand to the excess supply created by the actual change in the adjusting variable. If, for example, we wish to find the criterion for the effects of a tax on the terms of trade, we first determine the excess demand caused by the tax at constant terms of trade and translate the excess demand, which is the coefficient of the tax change, into the appropriate income or price elasticity; we then compute the excess supply of the same good created by a change in the terms of trade, translating its coefficient into the relevant elasticities. By equating the excess demand and the excess supply the criterion is established.

This procedure, which may be called the method of comparative statics, can be illustrated by two familiar-almost trivial-examples drawn from economic theory. In the Marshallian demand-supply system, with mnemonic terminology, we have at equilibrium the condition that demand equals supply:

where a is a parameter representing the position of the demand schedule. To determine the effect on price of a shift in the demand schedule, first determine the excess demand caused by the shift at constant price; this equals

The excess supply caused by an increase in price is equal to

At the new equilibrium the excess demand must be offset by an equal excess supply, so we get

which is the criterion we set out to find.

In the naive Keynesian system we have, at equilibrium, equality of saving (S) and investment (I), that is,

where y is income and (x is a parameter representing the level of autonomous investment. To find the effects of a shift in the investment schedule on income, first consider the excess demand for goods at constant income, that is,

and then the excess supply induced by a change in income, that is,

where s' is the marginal propensity to save. At the new equilibrium the excess demand caused by the shift in investment and the excess supply created by the change in income must be equal. Equating (6) and (7) and rearranging terms, we get the familiar multiplier

A second step in analysis is to utilize information from knowledge of stability. Any adjustment mechanism implies a type of dynamic behavior and thus a condition of dynamic stability-convergence to equilibrium over time. If an equilibrium is unstable, the system would not tend to approach the new equilibrium given by the comparative-statics analysis, and there would be little point in pursuing the comparative-statics analysis. On the other hand, if the system is stable, a useful clue may be obtained from the stability conditions about the sign of the elasticity coefficient of the adjusting variable, the terms of trade. The first step, then, is to examine the conditions of dynamic stability.

This procedure is an application of the correspondence principle. Thus in the demand-supply example just given, on the dynamic hypothesis that excess demand induces an increase in price, say, according to the law

Therefore the change in demand has the same sign as the resulting change in price.

In the second example, on the dynamic hypothesis that income rises when there is excess demand for goods, stability requires that

s' > 0

so an increase in investment induces an increase in income.

The Free-Trade Model

Let us now construct a simplified classical trade model and examine its stability conditions. Assume two countries, A and B, in full employment, producing two commodities --X, which is exported by A, and Y, which is exported by B. Let capital letters denote production, small letters consumption, and subscripts countries. Let T represent the capital exports (lending) of country A expressed in terms of X; let P denote the terms of trade, the price of Y in terms of X; and let D represent domestic expenditure.

The system can then be described by the following equations:

Domestic expenditure in A (in terms of X) equals national income minus net capital exports:

Domestic expenditure in B (in terms of Y) equals national income plus net capital imports:

The demand for Y in A depends on domestic expenditure and the terms of trade:

The demand for X in B depends on domestic expenditure and the terms of trade:

Figure 1-1.

The dimensions of the box represent world output of the two goods. The endowment point shows how production is distributed between the two countries before trade or transfers. The point Q Illustrates post-trade equilibrium on that assumption that country A makes a transfer to country B and that there is free trade

It is left for the reader to translate the symbols used in the text into distances in the diagram, to develop an alternative statement of the equilibrium conditions using community indifference curves and the contract locus, and to show that, in the variable production case, A's and B's production possibility curves, referred to origins OA and OB respectively, would be tangent to one another at the pre-transfer point.

In subsequent diagrams the endowment point will be regarded as the origin for trade.

The production of X and Y in A depends on the terms of trade:

The production of X and Y in B depends on the terms of trade:

The net capital exports of country A equal the balance of trade of country A:

Variations in domestic expenditure in each country are assumed to depend on changes in policy. In the free-trade case the system is completed by the following equations:

We then have eleven independent equations in the twelve unknowns xa, xb, ya, yb, Xa, Xb, Ya, Yb, Da, Db, P, and T, so there is 1 degree of freedom. Knowing the rate at which A is lending to B (that is, T), we can solve for the equilibrium terms of trade (P); or, assuming that the terms of trade are fixed, we can find the rate of lending that will establish equilibrium.

There are other, equivalent ways of writing the equilibrium conditions of the system. Equations (9) and (10) could be replaced by conditions stating that world production and world consumption of each good must be equal -- these alternatives imply each other when combined with equation (15), expressing balance-of-payments equilibrium. Equations (11) and (12), the demand functions for the good that is imported in each country, could be replaced by the demand functions for the good that is exported, since all income is spent; the part of domestic expenditure that is not spent on one good must be spent on the other good.

It will be convenient to define an import demand function for each country. The demand for imports is the difference between the quantities of the imported good demanded and supplied, that is, Ia = ya - Ya and Ib = xb -Xb, where Ia and Ib are, respectively, the demands for imports in A and B. Then, because the demand and supply functions depend only on domestic expenditure and the terms of trade, the import demand functions must also depend on these variables. Thus we have two more equations and two more unknowns:

If we now substitute (16) in the balance-of-payments equation (15) we obtain

Conditions of Stability

Now let us consider the question of stability. An equilibrium is stable if a small displacement of a variable from its equilibrium level is followed by a return to equilibrium. In the context of the classical trade model, the equilibrium is stable if a displacement of the terms of trade from equilibrium sets in motion forces inducing a return to that equilibrium. The system is stable only if a fall in the price level or exchange rate of the deficit country causes an improvement in its balance of payments. To find the criterion for stability we have to compute the excess supply caused by a change in the terms of trade. This criterion will then give us the coefficient of a change in the terms of trade for use in the comparative-statics analysis.

The balance of trade surplus of country A, expressed in terms of home goods, can be written, given the level of domestic expenditure in each country, as

The terms in parentheses are the elasticities of demand for imports in A and B respectively. Write these terms, with a change of sign, as etaa and etab. Then we have

If trade is initially in balance, Ib = PIa, so that a fall in A's terms of trade (an increase in P) will improve or worsen A's trade balance, depending on whether

where I = Ia = Ib, on the assumption of initially balanced trade and choice of commodity units to make P initially equal to 1. Stability requires that a fall in A's terms of trade improve A's trade balance, so the system is stable or not

Figure 1-2.

The offer curves OA and OB intersect an initial equilibrium Q. A change in the terms of trade in the proportion TQ/QM in favor of A creates an excess demand for B's good and a deficit in A's balance of payments equal to RW (in terms of Y). Deflationary pressures in A and inflationary pressures in B will therefore reverse the terms of trade change restoring equilibrium. The system is therefore stable.

The stability conditions are derived as follows: Define the elasticities of demand for imports in each country.

depending on whether the sum of the elasticities of demand for imports is greater or less than 1.

This criterion can be derived directly from the dynamic behavior of the system along the lines that Samuelson, writing in the early 1940s, made famous.

Let us approximate the dynamic behavior of the system by the following differential equation:

which states that the speed of the change in the terms of trade is proportional to the discrepancy between foreign exchange payments and receipts. Expanding this equation in a Taylor series in the neighborhood of equilibrium, omitting nonlinear terms, and choosing time units to make the "speed of adjustment" k = 1, we obtain

where P0 denotes the terms of trade at equilibrium. This equation has a solution

The equilibrium point is stable only if ; this can be the case only if the exponential term disappears, that is, only if etaa + etab -1 > 0.3

This discussion has been restricted to the stability of an equilibrium rather than to the stability of a system. John Stuart Mill recognized the possibility of multiple equilibria without reference to stability ([66], pp. 15-63), but his treatment was in error in certain respects. Marshall, in 1879, was aware ([52], pp. 24-25) that a point of unstable equilibrium must be flanked by points of stable equilibria, that the number of equilibria must be odd, and that (therefore) if an equilibrium were unique it would be stable.

There are alternative ways of expressing the stability condition. For example, it can be expressed in terms of one good only. To see this. recall equation (1), which expresses the equality of income (plus borrowing) and expenditure in country A. With lending zero this equation can be written

That is, offers of exports equal the value of imports demanded. Substituting in (18) and making a similar substitution for Ib, we can write the balance of payments (with no lending) as

where X is world production and consumption at equilibrium, and the arguments in the bracket are, respectively, the world elasticity of demand for X and the world elasticity of supply of X:

where units are chosen so that P is, at equilibrium, equal to unity. By similar reasoning from the balance-of-payments equation,

we find that

where etay and epsilony are the elasticities of world demand for, and supply of, Y.4

The elasticities of demand for X and Y are defined to be positive provided these goods are not Giffen goods; and the elasticities of supply of X and Y are defined to be positive provided opportunity costs are not decreasing. It may then be seen that the system is necessarily stable if neither good is a Giffen good in world consumption and opportunity costs are not decreasing. But even if the goods are Giffen goods, positive supply elasticities may yet make the system stable.

The task of Chapter 2 is to introduce into the balance-of-payments equation various parameters representing economic policies, and to show how the equilibrium values of the variables are affected by changes in these policies. Unless it is explicitly stated to the contrary, the equilibrium point will be assumed to be stable.5

Price and Income Effects

Before going on to a consideration of changes in economic policies, it will be useful to introduce a relationship between income propensities and price elasticities based on Slutsky's separation of price effects into income and substitution effects. A price elasticity of demand can always be written as the sum of a compensated (pure substitution) price elasticity and an income propensity. Consider any demand function of the form I = I(D, P) and differentiate with respect to P. This yields

after multiplying by P/I. Now -(P/I) deltaI / deltaP is the (money-income constant) elasticity of demand,  eta, and P deltaI / deltaD is the marginal propensity to spend, m. Thus

A change in price can be associated with a change in real income approximately equal to the change in cost of the initial amount bought, IdP. If expenditure is adjusted to compensate for this change in real income, that is, if dD = IdP, then -(P/I)(dI/dP) becomes the compensated elasticity of demand, eta', and we get eta  =  m + n' .6 If indifference curves are convex, all

Figure 1-3

Initial equilibrium is at Q on A's offer curve OA. Suppose that the terms of trade change in the proportion TQ/QM, and that at the new terms of trade A trades at the point Q'. The effect on income of this change in the terms of trade can be approximated by OD in terms of X or TQ in terms of Y, where DQ is drawn parallel to OT.

To prove the relation between compensated and ordinary elasticities: Define the elasticity of demand for imports in A, by

which is the elasticity of demand for imports with the income effect removed, i.e., the compensated elasticity of demand for imports, eta'a .

substitution effects in the two-good case under consideration are positive, so eta > 0. From this it follows that the elasticity of demand for imports is always greater than the marginal propensity to import. A fortiori the sum of the elasticities of demand for imports is greater than the sum of the marginal propensities to import, so that if ma + mb is equal to, or exceeds, 1, the exchange market is necessarily stable. Conversely, an unstable exchange market implies that the sum of the marginal propensities to import is less than unity.


l Adapted from: Amer. Econ. Rev., 50, 68-110 (March, 1960).

2 Often, perhaps usually, to the detriment of economic efficiency. We are concerned now, however, with "positive," rather than "normative," aspects of international trade theory.

3 The elasticity criterion just derived was first developed by Alfred Marshall. It is important, however, to notice that Marshall's dynamic postulates differ from that described in (20) above. The latter assumes that the budget equations in each country are satisfied (each country is always at a point on its offer curve) but that markets are not necessarily cleared. Marshall's postulates are based on adjustments of offers toward the budget equations (offer curves). Marshall's adjustment process, which can be justified on the basis of varying profitability of export industries, admits richer solutions, including the possibility of complex roots and an oscillatory path to equilibrium (see Samuelson [90], pp. 266-268).

4 Mosak ([68], chap. 4) derived stability conditions in terms of one good only; see also Johnson ([30], p. 98). See Hirschman [25] for a development of the stability criterion when trade is not initially in balance.

5 With respect to instability Marshall ([51], p. 354) wrote: ". . . it is not inconceivable but it is absolutely impossible," a statement I find understandable if not comprehensible ! More complicated aspects of stability in the classical system are explored in Chapters 3 and 7.

6 Meade [54] has made extensive use of this relation, his stability condition is split into income and substitution effects and, in my notation. is eta'a + eta'b + ma + mb - 1 > 0.


Literature Cited

[25] A. O. HIRSCHMAN, "Devaluation and the Trade Balance: A Note," Rev. Econ. Stat., 31, 50-53 (Feb.1949).

[30] H . G . JOHNSON, " Economic Expansion and International Trade," Manchester School Econ. Soc. Stud., 23, 95-112 (May 1955).

[51] A. MARSHALL, Money Credit and Commerce. London: Macmillan, 1923.

[54] J. E. MEADE, "A Geometrical Representation of Balance-of-Payments Policy," Economica, 16, 305-320 (Nov. 1949).

[68] J. L. MOSAK, General Equilibrium Theory in International Trade. Bloomington: Indiana University Press, 1944.

[90] P. A. SAMUELSON, " The Transfer Problem and Transport Costs: I, The Terms of Trade When Impediments Are Absent, II, Analysis of Effects of Trade Impediments," Econ. Jour., 57, 278-304 (June 1952); 59, 264 290 (June 1954).


© Copyright Robert A. Mundell, 1968