Price and Output Effects of Monetary and Fiscal Policy Under Flexible Exchange Rates

Victor E. Argy; Joanne Salop

doi:10.5089/9781451946840.024.A002

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Price and Output Effects of Monetary and Fiscal Policy Under Flexible Exchange Rates

Author: Mr. Victor E. Argy¹ and Joanne Salop

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1979

eISBN:: 9781451946840

Language:: English

Keywords:: SP; mixed-citation publication-type; excess demand; output rise; Marshall-Lerner condition; exchange rate appreciation; oil price rise; output effect; Consumer price indexes; Real wages

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After a period of accelerating inflation in the early 1970s, the industrial countries in 1974–75 entered their most severe recession since the 1930s. The recession was brought on primarily by restrictive monetary and fiscal policies coupled with the dramatic rise in petroleum prices during 1973–74. Since early 1976 there has been some recovery, but unemployment continues to be a problem while inflation rates, although gradually moderating, remain at historically high levels. In this environment, governments have acted with caution in formulating their policies. In many of the industrial countries, monetary targets have been maintained at fairly modest levels, and fiscal policy, which was expansionary during 1975, reversed itself in 1976 and remains generally conservative. Over all, the desire to stimulate production has been tempered by concern over the inflationary consequences.

Abstract

This paper addresses itself to this central policy dilemma. To this end, it presents a formal analysis of the effects of monetary and fiscal policy under flexible exchange rates, with the main emphasis on the division of the effects between output and prices. It focuses on the relatively small industrial country and treats only unilateral adoption of more expansionary policies by that country, disregarding foreign repercussions.¹ Five alternative policies are contrasted: monetary expansion, a cut in income taxes, an increase in government expenditure, a balanced budget expansion, and, finally, an employment subsidy. ² Constraining each of these policies, where feasible, to secure the same addition to output, we then ask which of the policies will have the smallest impact on the price level.

Surprisingly, despite the evident importance of this issue, it has received little attention in the literature.³ Early literature on policy effectiveness under floating exchange rates generally abstracted from price changes induced by these exchange rate changes. In the classic papers by Mundell ⁴ and Fleming,⁵ the effects of expansionary monetary policy are analyzed under the assumption of constant wages and prices. In their analyses, with capital perfectly mobile, expansionary monetary policy increases output and employment, while expansionary fiscal policy does not. ⁶ In neither case are the price effects of the respective exchange rate changes pursued. More recently, economists ⁷ have focused their attention on the dynamic process by which the economy moves toward its post-policy-change equilibrium. This literature distinguishes markets by the speed at which they adjust to a shock, and assumes that asset markets clear more quickly than do goods markets, thereby giving rise to the possibility of exchange rate “overshooting.” In one paper, Dornbusch ⁸ imposes this assumption on the Fleming-Mundell fixed price framework and traces the path of the exchange rate and nominal aggregate demand in response to a monetary expansion. In another ⁹ he allows prices to vary but constrains output to return ultimately to its initial full-employment level. In this context, it is not surprising that monetary policy is found to have no real effects in the long run.

Our approach to the study of policy effectiveness under floating rates is different. We have sacrificed the elegant dynamics of this recent work for a clearer perspective on the relative effects of the various macroeconomic policy measures on prices and output via their differential impact on the marginal productivity of labor and wage demands. Hence, in our analysis, the effect of a policy change depends very much on its direct and indirect impact on the labor market.

The formal model consists of an aggregate demand sector and an aggregate supply sector. In essence, the aggregate demand sector is an amalgam of the conventional IS and LM schedules after appropriate allowances are made for international substitution effects and appropriate deflators. On the other hand, since it is the aggregate supply sector of the economy that ultimately determines the division of effects between prices and output for given variations in nominal demand, we have paid more careful attention to this sector in constructing our macromodel. First, we allow taxes to play a role in the determination of wages. With the size of the government sector as well as the tax rate increasing in nearly all industrial countries, workers and trade unions have become conscious of the real value of their aftertax increases. This relationship has been stressed in a number of contributions.¹⁰ Second, we emphasize the fact that, in their respective employment decisions, the relevant price to the producer is the price of domestically produced goods, while the relevant price to workers is the overall price level, which is itself influenced directly by the exchange rate.¹¹ Third, we modify the classical labor demand function to allow for the imposition of an employment subsidy. This serves to differentiate the wage received by the workers from the net wage paid by the employer. These three extensions mean that a tax cut will now directly affect wage demands and, hence, domestic prices,¹² while an employment subsidy will directly affect the demand for labor. At the same time, a change in the exchange rate will directly influence nominal wage demands without directly affecting the demand for labor.

Whenever a static construct is used to model a dynamic process, the formulation of the market-clearing equations largely determines the time period for which the analysis is relevant. To take account of the fact that economies differ in the speed with which their labor markets adjust fully to shocks as well as in the magnitude of the wage adjustment to price changes, we allow for different degrees of “money illusion” to characterize the labor supply response. Moreover, because significant adjustments to nominal income are forthcoming over the time frame of interest to us, roughly 12–18 months, the theoretical foundations for any exchange rate overshooting are seriously mitigated. This allows us to make the simplifying assumption that the prevailing exchange rate equals its expected future value. We further assume a degree of financial integration sufficiently high that interest rate differences are eliminated by arbitrage.¹³ On the other hand, we do not constrain our solutions so as to satisfy purchasing power parity, which we believe to be only weakly operative at the level of aggregation with which we are dealing. Finally, we assume that an improvement in the country’s price competitiveness improves its trade balance, despite possible perverse J-curve effects in the very short run.

The results of the model may be conveniently summarized according to whether or not money illusion is assumed. If there is no money illusion, monetary policy affects only prices and equivalently the exchange rate but has no output effects. Expansionary fiscal policy increases output ¹⁴ and decreases prices (i.e., below their trend path), while a balanced budget expansion in government spending, interestingly, reduces output and raises prices (i.e., generates stagflation).¹⁵ This suggests that a contractionary expenditure shock can induce unemployment that only pure fiscal expansion or a balanced budget contraction in spending can reverse. Attempts at real expansion via monetary policy will be futile and, if repeated, will take on the appearance of a vicious circle.

These results can be explained with reference to the effects of the various policies on real wage demands vis-à-vis the marginal product of labor. With the interest rate fixed, monetary policy leaves them both unchanged. On the other hand, fiscal expansion opens up a divergence between the change in the foreign price level and the change in the domestic price level, permitting both the real wage rate to be maintained in terms of the overall price level and the real demand for labor to increase. For example, where fiscal expansion produces exchange rate appreciation, as well as a rise in the domestic price level, the relevant real wage rate to workers can stay constant even while the real wage rate to employers falls, the latter inducing some increase in production. In the balanced budget case, these tendencies toward expansion are more than offset by the contractionary influence of the increased tax rate on the nominal wage.

As the degree of money illusion increases, the importance of real considerations in labor’s supply response wanes, and the effect of a policy on output tends to approach its effect on nominal aggregate demand. As a consequence, the familiar Fleming-Mundell results about policy effectiveness under floating rates are increasingly replicated. Moreover, in this instance, for the same output effect, we can rank the price effects of the various policy injections. For an increase in government spending, a decrease in the tax rate, and imposition of an employment subsidy, the resulting consumer price index will be the same, and uniformly less than that resulting from expansionary monetary policy. This is somewhat counterintuitive because it means that, even though tax cuts and employment subsidies will both act directly to reduce domestic prices, the ultimate overall price effect, for any given expansion in real output, is no different from that of an increase in government expenditure. The three fiscal policies, however, will differ in their impact on the components of the consumer price index. While we cannot rank the subsidy’s price effects a priori, we can say unequivocally that the producer price index as well as the exchange rate will be higher from an increase in government spending than from a cut in taxes.

The organization of the paper is as follows. Section I outlines a model that, we think, captures the current situation confronting small industrial economies with a minimum of excess baggage. Discussion of our particular specifications and their appropriateness is included in this presentation. Section II shows how the model can be solved graphically by requiring the simultaneous clearing of the goods market, the money market, and the labor market. Using the same apparatus, Section III examines the effects of the alternative policies on prices and output, assuming that exchange rates are fully flexible. Section IV summarizes our results and briefly considers some limitations of the analysis of the main text. Appendix A provides a mathematical solution to the model, and Appendix B casts the model is terms of the “assignment problem.”

I. The Model

The economy that we envisage produces a single composite good that is both “absorbed” domestically and exported. A different composite good is imported from abroad. These goods, being different, can trade at different prices. More importantly, however, this distinction causes the consumer price index and the producer price index to diverge in general, a phenomenon that will figure in each of the three markets that we consider.

The model of the economy that we use comprises markets for domestically produced goods, money, and labor. Our goods market, simply stated, requires that the total demand for the country’s production equal the supply. The sources of demand are consumption, investment, government spending, and net exports. Our money market is equally straightforward. The demand for real balances depends on income and the interest rate, the supply on the exogenous quantity of money and the price level. The labor market, which allows us to transform labor into the supply of output, completes the model. Here the demand for labor is derived from the aggregate production function, and labor’s real wage demands are generated under alternative assumptions about the degree of money illusion.

Symbols
Y	= real gross national product (GNP)
Y_d	= real disposable income
P_d	= price of domestic output
P	= consumer price index
P_f	= foreign price in foreign currency
e	= exchange rate (units of domestic currency per unit of foreign currency)
A	= real absorption
t	= rate of income tax
r	= interest rate
G	= real government spending
w	= nominal wage rate
a,b	= parameters of production function (See ^{footnote 17}.)
L	= nominal money supply
s	= employment subsidy
X	= quantity of exports
M	= quantity of imports

Symbols
Y	= real gross national product (GNP)
Y_d	= real disposable income
P_d	= price of domestic output
P	= consumer price index
P_f	= foreign price in foreign currency
e	= exchange rate (units of domestic currency per unit of foreign currency)
A	= real absorption
t	= rate of income tax
r	= interest rate
G	= real government spending
w	= nominal wage rate
a,b	= parameters of production function (See ^{footnote 17}.)
L	= nominal money supply
s	= employment subsidy
X	= quantity of exports
M	= quantity of imports

The equations comprising the goods market are as follows:

\begin{matrix} Y P_{d} = A P + X P_{d} - M P_{f} e & (1) \end{matrix}

\begin{matrix} A = C (Y_{d}) + I (r) + G & (2) \end{matrix}

\begin{matrix} Y_{d} = \frac{P_{d}}{P} [Y (1 - t) + (Y - Y_{0}) \frac{s b}{b - 1}] & (3) \end{matrix}

\begin{matrix} X = X (\frac{P_{d}}{P_{f} e}) X' < 0 & (4) \end{matrix}

\begin{matrix} M = M (\frac{P_{d}}{P_{f} e}, A) M_{1} > 0, M_{2} > 0 & (5) \end{matrix}

\begin{matrix} P = f (P_{d,} P_{f} e) & (6) \end{matrix}

Equation (1) says that the nominal value of domestic output must equal the nominal value of aggregate demand for domestic output. Nominal aggregate demand includes domestic absorption (A) times the consumer price index (P), plus exports (X) times the price of output (P_d), minus imports (M) times their price in domestic currency (P_f e). Equation (2) defines real absorption as the sum of real consumption (C), which is a function of real disposable income, plus real investment (I), which is a function of the interest rate, plus real government spending (G). Real disposable income (Y_d) is defined by equation (3). It equals the aftertax value of nominal GNP deflated by the consumer price index plus the total value of the employment subsidy to the private sector.¹⁶ Equations (4) and (5) indicate that exports and imports are functions of their relative prices; moreover, real imports vary directly with the level of domestic real absorption. Finally, equation (6) defines the consumer price index in terms of the price of domestic goods and imports.

The money market is given by equation (7).

\begin{matrix} \frac{L}{P} = L (r, Y) L_{r} < 0, L_{y} > 0 & (7) \end{matrix}

Equation (7) indicates that the supply of real balances equals the demand. The demand for real balances is negatively related to the interest rate and positively related to the level of real GNP. Note that the supply of nominal balances (L) is deflated by the consumer price index.

The labor market is represented by equations (8) and (9).

\begin{matrix} Y = a [\frac{w (1 - s)}{P_{d}}]^{b} & (8) \end{matrix}

\begin{matrix} \frac{w}{p} (1 - t) = \frac{(1 - n) (1 - t)}{P} + N & (9) \end{matrix}

These are key equations in the model. Since they represent the supply side of the economy, they are critical in determining the division of the effects of expansionary policies between prices and output. Equation (8) is the demand for labor. Production is assumed to be subject to diminishing marginal productivity, so that the real wage to the entrepreneur must fall if increased production is to be profitable.¹⁷ The employment subsidy (s) allows the wage paid to employees and the marginal cost to the firm of employing additional labor to differ. Equation (9) is the wage rate equation. As formulated, the model posits that labor supply is perfectly elastic at the “going” aftertax real wage.¹⁸Wages determined in this way are given to the employer who then decides on the volume of employment and production in terms of equation (8). Moreover, we allow for the possibility of money illusion to cause take-home real wages to vary with the price level and the tax rate. Hence, if n = 1 (i.e., no money illusion), aftertax real wages are invariant to the price level; alternatively, if n < 1, they vary inversely with the price level. Note that N = 0 is the Keynesian case in which the nominal wage is constant (i.e., w = 1—n). Labor uses the consumer price index to evaluate the real wage, whereas producers use the price of output. The latter is consistent with the theory of the firm, whereby profits are maximized by the hiring of labor until the marginal revenue product equals the nominal wage. For a perfect competitor, this entails equating the price of output (i.e., P_d) times the marginal physical product of labor with the nominal wage.

For completeness, we note that the model has nine equations that determine the nine endogenous variables (Y, Y_d, P, P_d, A, X, M, w, e) for given values of the exogenous variables (r, P_f, t, s, G, L).

Several aspects of the model deserve further explanation. First, the interest rate is assumed to be exogenous. This is due to our small-country perspective in conjunction with our medium-term time frame. For a small country whose securities are perfect substitutes for foreign issues, interest rate equality need not hold at every moment because of expectations of exchange rate changes. In fact, interest rate equalization cannot occur immediately after a monetary expansion, for example, because with prices and output fixed in the very short run, the interest rate is the only variable free to clear the money market. Our time horizon, however, is the more medium run of some 12–18 months after a policy injection, over which substantial adjustments to output and prices can and do take place. Hence, we posit interest rate equality and its corollary, the equality of actual and expected exchange rates.

A second aspect concerns the relevance of a model that treats only price level changes to a world in which policy is concerned primarily with altering its rate of change. The policy changes that we consider are of the “one-shot” variety. Hence, the stock of money or the rate of government spending is increased. The rate of growth of the money supply is left as it would be otherwise, except at the instant of the change. And, because we accept the view that the rate of money growth ultimately determines the inflation rate, our policy injections will not affect its long-run value. Nevertheless, our policy changes do alter the price level, and, in a continuous time framework, would affect the rate of inflation, over our time horizon. Thus, an increase in the price level corresponds to an increase in the rate of change of prices, whereas a decrease in the price level connotes a decrease in the rate of change of prices.

Third, and most important, is our formulation of the labor supply side of the economy. As noted earlier, our equation describes the supply of labor as perfectly elastic at the going real wage. We chose the perfectly elastic specification because of its simplicity in depicting the existence of involuntary unemployment. Hence, our model is valid only in analyzing the effects of contractionary policies, starting from some arbitrary initial definition of full employment, or expansionary policies in a less than full-employment environment. And we have formulated the wage equation in real rather than nominal terms, in deference to the inflationary environment, which has reputedly heightened labor’s awareness of purchasing power considerations.

II. Graphical Apparatus

In this section, we represent the three markets graphically. For each market a relationship may be derived between output and domestic prices for every value of the exchange rate. The equilibrium exchange rate then is that value for which all three markets simultaneously clear at a common level of output and domestic prices.

Solving the goods market, that is, equations (1)–(6), for given values of government spending, the tax rate, and the exchange rate, and setting the initial values of P, P_d, P_f, and e equal to one and s equal to zero, we find the slope of the IS relation.

\begin{array}{l} \frac{d Y}{d P_{d}} |_{I S} = \\ \frac{- Y (1 - C') (1 - t) (1 - f_{1}) (1 - M_{2})) + f_{1} A + X' - M_{1} + X}{1 - C' (1 - t) (1 - M_{2})} & (10) \end{array}

Because the marginal propensity to consume (C^’) and to import (M₂) are traditionally assumed to be less than one, the denominator of equation (10) can be taken to be positive. The numerator will be negative if the Marshall-Lerner condition holds and the marginal propensity to consume is less than or equal to the average propensity to consume.¹⁹

The slope of the LM curve is much easier to ascertain. Combining equations (6) and (7), differentiating, and setting initial values equal to unity, we have

\begin{matrix} \frac{d Y}{d P_{d}} |_{L M} = \frac{L (r, Y) f_{1}}{L_{y}} & (11) \end{matrix}

Since f₁ > 0 and L_y > 0, its sign is clearly negative.

Finally, we have the labor market. Combining equations (6), (8), and (9), differentiating, and again setting initial values of P, P_d, P_f, and e equal to one and s equal to zero, we have

\begin{matrix} \frac{d Y}{d P_{d}} |_{A S} = - a b (1 - n + \frac{N}{1 - t})^{b - 1} [\frac{N f_{2}}{1 - t} + 1 + n] & (12) \end{matrix}

The sign of $\begin{matrix} \frac{d Y}{d P_{d}} |_{A S} \end{matrix}$ is positive because b > 0, f₂ > 0, n < 1.

The three markets are now shown in Figure 1. IS, LM, and AS represent the goods, money, and labor markets, with their respective slopes given by equations (10)—(12).²⁰ As drawn, the three curves intersect at a common point. This implies that the exchange rate used as a parameter is consistent with equilibrium in all three markets. The corresponding domestic price and output levels are P_d₀ and Y₀.

The position of each of the three curves changes when a different value for the exchange rate is used. Consider first the IS curve.

\begin{matrix} \frac{d Y}{d e} |_{A S} = \frac{f_{2} A - f_{2} C' Y (1 - t) (1 - M_{2}) - X' - M_{1} - M}{1 - C' (1 - t) (1 - M_{2})} & (13) \end{matrix}

In general, this will be positive. ²¹ Hence, the IS curve shifts to the right as the exchange rate rises (i.e., devaluation). Performing a similar operation on the money market, we find

\begin{matrix} \frac{d Y}{d e} |_{L M} = \frac{- L (r, Y) f_{2}}{L_{y}} & (14) \end{matrix}

Because f₂ > 0, L_y > 0, the LM curve is shifted to the left by devaluation. In the labor market we have

\begin{matrix} \frac{d Y}{d e} |_{A S} = a b (1 - n + \frac{N}{1 - t})^{b - 1} • \frac{N f_{2}}{(1 - t)} & (15) \end{matrix}

whose sign is negative because b < 0, f₂ > 0. Hence, the AS curve also shifts leftward.

III. Policy Exercises

We now consider the effects of changes in monetary and fiscal policy on the level of output, prices, and the exchange rate. Our starting point is the equilibrium depicted in Figure 1, that is, P_d_o and Y₀. In each case the policy to be considered has a direct impact on one or two of our markets. This disturbs the overall equilibrium and induces an exchange rate change to restore equilibrium. The results reported in the text can be verified by referring to the mathematical appendix.

an increase in government spending

An increase in government expenditure initially causes the IS schedule to shift to the right. ²² With the interest rate assumed given, the emerging excess demand for money causes the exchange rate to appreciate. As noted earlier, revaluation shifts the LM and the AS schedules to the right and the IS schedule to the left. The final solution with all three markets once again in equilibrium is shown in Figure 2 with P_d1 and Y₁ the new price and output levels.²³ Although the price is shown to have risen, it is possible for the price level to have fallen in the hew equilibrium, that is, if AS shifts sufficiently to the right. This is more likely, the less money illusion there is.

That output increases from an increase in government expenditure can easily be verified by reference to the requirements for equilibrium in each of the three markets. Suppose that output has increased, the exchange rate has appreciated, and the domestic price level has increased. This is consistent with equilibrium in the goods market, since the effects of increased government expenditure on net demand can more than offset the deflationary effects of both appreciation and the increase in domestic prices. Increased output is also consistent with the money market if the appreciation is of sufficient magnitude to more than offset the restrictive effects of the higher domestic price level on the consumer price index. Finally, the labor market can also be in equilibrium: If the wage rate rises by less than the domestic price, entrepreneurs will employ more labor; at the same time, the real wage to labor need not fall, since imports are now cheaper.

The rationale for the solution is easily explained when there is no money illusion. Increased aggregate demand tends to push up the domestic price level; at the same time, there is upward pressure on domestic interest rates, and the excess demand for money forces an appreciation of the exchange rate. In turn, this will ease real money balances and lower wage demands, both of which are linked to the overall price level. The domestic price level is, therefore, subject to two opposing influences: the excess demand for goods tends to raise it, but the appreciation and the correspondingly lower wage demands tend to push it down. In the final equilibrium, increased output is possible because the real wage rate has fallen from the point of view of the entrepreneurs, for whom the relevant deflator is the domestic price level, and yet has remained the same from the point of view of the suppliers of labor for whom the relevant deflator is the overall price level. In short, with full wage indexation, or simply no money illusion, wages rise in proportion to the overall price level but rise proportionately less than the increase in domestic prices.

This result may be compared with the familiar Fleming-Mundell result. In their analyses, fiscal expansion has no effect on GNP. Concomitant currency appreciation checks any expansion in aggregate demand and leaves the domestic price and output unchanged. Our model differs from theirs in two respects. First, we allow for pass-through effects of exchange rate changes on wages and prices. Hence, the appreciation leads to a decrease in nominal wages that causes producers to expand output. As money illusion is increasingly admitted, however, this effect is diminished, and the Fleming-Mundell result is increasingly approximated. ²⁴ Second, even if we allow for constancy of the money wage rate, ²⁵ fiscal policy still affects real aggregate demand and output in our model through the money market. In the Fleming-Mundell analysis, money balances are implicitly deflated by the price of domestic output; in ours, the deflator includes both domestic goods and imports. Hence, even with the nominal stock of money unchanged, output and the domestic price can rise in response to fiscal expansion because the prices of imports fall, thereby maintaining money market equilibrium.

a reduction in taxes

In the first instance, a cut in taxes shifts both the AS ²⁶ and IS ²⁷ schedules to the right. The former is due to the tax cut’s impact on the real value of labor’s take-home pay; the latter occurs because of the injection of purchasing power into the economy. Again, the exchange rate will change and cause all three schedules to shift until they intersect at a common point.

As in the previous case, output rises and the domestic price may rise or fall. In contrast, however, the exchange rate does not necessarily rise in response to a cut in taxes. More specifically, if the exchange rate appreciates, domestic prices may rise or fall.²⁸ If the exchange rate depreciates, domestic prices definitely fall. The exchange rate is more likely to fall, the less money illusion there is (causing the AS curve to shift further initially) and the smaller the income elasticity of the demand for money (causing the LM schedule to be flatter than the IS schedule). Figure 3 depicts the effect of a cut in taxes; panel (a) illustrates an appreciation, panel (b) a depreciation.

It is worth highlighting the result that a tax cut can cause depreciation. In the usual academic approach, pure fiscal expansion is viewed as producing appreciation under conditions where capital is perfectly mobile. The possibility of depreciation in our case arises from the fact that, with the interest rate given, a tax cut may on balance produce an incipient excess supply of money, if the positive effect on output is more than offset by the initial negative effect on the price level.

balanced budget expansion

Suppose that the government tried to achieve an increase in output by increasing its spending, while at the same time raising tax rates to ensure that the size of its deficit remained unchanged. The effect of this kind of expansion depends critically on the degree of money illusion posited. In particular, with no money illusion, output falls and prices rise. ²⁹ The exchange rate appreciates if the IS schedule is steeper than the LM schedule, but may depreciate if the LM curve is steeper. Figure 4 illustrates the latter case. At the other extreme, that is, with money wages invariant to purchasing power considerations, output rises ³⁰ and the currency appreciates. In each instance, however, the balance of trade deteriorates and the flow of net indebtedness rises.

These results are easy to explain. Under normal Keynesian assumptions, balanced budget expansion generates a positive real output response because the effect on real demand of the increase in government expenditure exceeds the restrictive effects on real demand of the increase in taxes (provided, of course, that the marginal propensity to spend is less than unity). Where there is no money illusion, however, the increase in tax rates, by forcing up nominal wages, imposes an additional restrictive impact that, as it happens, is decisive for the net outcome. It also follows from our money market equilibrium that if output should fall, the overall price level must rise. As for the effect on the exchange rate, it depends on the net impact on the demand for money, given the initial interest rate. Since output and domestic prices move in opposite directions, the effect on the excess demand for money is clearly ambiguous.

the employment subsidy

This policy entails subsidizing firms for employing additional workers. In terms of the model, the government rebates the proportion “s” of the nominal wage for workers hired to produce at output levels in excess of the initial output level Y₀. Its implementation causes the relevant portion of the AS schedule to shift to the right, ³¹ since the demand for labor and employment increases for every wage level. It also imparts a kink to the IS schedule. This reflects the fact that disposable income via profits is higher for every output level above Y₀.

The effect of the subsidy is to raise output and employment and to put downward pressure on domestic prices. The exchange rate may rise or fall, depending on whether the IS or LM curve is steeper. Figure 5 illustrates a steeper IS schedule that leads to depreciation.

an expansionary monetary policy

An increase in the money supply directly affects the LM schedule by shifting it to the right. This causes the exchange rate to depreciate and, in so doing, alters the positions of the IS and AS schedules. The effect on output and prices depends on the degree of money illusion in the economy. With none, the system is homogeneous of degree zero in money, the domestic price level, and the exchange rate. Thus, under these circumstances, output does not change, and the domestic price level and the exchange rate change by the same percentage as the change in money. This situation is illustrated in Figure 6.

It is easy to show that this result is consistent with equilibrium in our three markets. With the increase in domestic prices exactly offset by the depreciation, real demand for goods will be unchanged. Again, with the overall price level rising in proportion to the increase in the money supply, money market equilibrium is consistent with a constant real output level. Finally, since the real wage rate will not have changed from the point of view of workers or employers, there is no inducement to produce more. If, on the other hand, there is money illusion, output rises, and the domestic price level rises by a smaller percentage than does the exchange rate.

IV. Summary and Conclusions

Table 1 presents our qualitative findings on the effects of the various policies on output, the consumer price index, the price of domestic goods, and the exchange rate. Because the results are sensitive to the degree of money illusion assumed, we have classified them accordingly. Column (1) represents zero money illusion; column (2), complete money illusion, that is, money wage demands are invariant to the price level and the tax rate; and column (3), the intermediate case of some money illusion.

Table 1.

Effects of Various Fiscal and Monetary Policies on Output, Consumer Prices, Domestic Prices, and the Exchange Rate for a Small Industrial Country

^¹If Y rises, P falls; if Y falls, P rises.

^²A plus sign indicates depreciation.

Table 1.

Effects of Various Fiscal and Monetary Policies on Output, Consumer Prices, Domestic Prices, and the Exchange Rate for a Small Industrial Country

	No Money Illusion		Full Money Illusion	Some Money Illusion
		dY
dL	0		+	+
dG	+		+	+
-dt	+		+	+
dBB	–		+	?
ds	+		+	+
		dP
dL	+		+	+
dG	–		–	–
-dt	–		–	–
dBB	+		–	?¹
ds	–		–	–
		dP_d
dL	+		+	+
dG	?		+	?
-dt	?		+	?
dBB	+		+	+
ds	–		–	–
		de²
dL	+		+	+
dG	–		–	–
-dt	?		—	?
dBB	?		—	?
ds	?		?	?

^¹If Y rises, P falls; if Y falls, P rises.

^²A plus sign indicates depreciation.

Table 1.

Effects of Various Fiscal and Monetary Policies on Output, Consumer Prices, Domestic Prices, and the Exchange Rate for a Small Industrial Country

	No Money Illusion		Full Money Illusion	Some Money Illusion
		dY
dL	0		+	+
dG	+		+	+
-dt	+		+	+
dBB	–		+	?
ds	+		+	+
		dP
dL	+		+	+
dG	–		–	–
-dt	–		–	–
dBB	+		–	?¹
ds	–		–	–
		dP_d
dL	+		+	+
dG	?		+	?
-dt	?		+	?
dBB	+		+	+
ds	–		–	–
		de²
dL	+		+	+
dG	–		–	–
-dt	?		—	?
dBB	?		—	?
ds	?		?	?

^¹If Y rises, P falls; if Y falls, P rises.

^²A plus sign indicates depreciation.

Table 1 is a convenient starting point for discussing some of the policy implications of our analysis. In the first place, the model can be used to analyze the impact of the price increases imposed by the Organization of Petroleum Exporting Countries on an oil importing nation and to demonstrate the possibility of a “vicious circle” type of response in the case of no money illusion. Second, the model permits us to compare the price effects of the various policies when constrained to yield equal output effects. The latter is discussed under the assumption of some money illusion. This choice reflects the presumption that, in general, the policies considered are used to stabilize cyclical fluctuations in the economy. For this reason, the policies are apt to be temporary, and some degree of money illusion is likely to prevail over their duration.

Returning to the first point, we note that the oil price rise reduced aggregate demand as well as the market-clearing real wage in the oil importing nations. In terms of our model, all three schedules were shifted to the left by the shock. With downward inflexibility in the real wage, the new output level is characterized by unemployment. ³² No change in the exchange rate need have accompanied the shock if all importers are affected to the same degree. The exchange rate used herein is implicitly between industrial economies; and, with all suffering the same shock, their mutual depreciations tend to offset each other.

Now consider the possible policy responses by one country. Essentially, there are three: (1) patience on the part of the government to endure the unemployment until real wage demands are reduced to their new lower market-clearing level; (2) expansionary monetary policy; and (3) some form of fiscal stimulus. About the first, this paper has little to offer other than some support for its effectiveness. ³³ With respect to expansionary monetary policy, however, our analysis is particularly relevant. With wage demands fixed in real terms, monetary policy will only increase prices and depreciate the exchange rate, even though there is initially unemployment. ³⁴ Moreover, continued attempts at expansion via this route will repeat this process, which will take on the appearance of a vicious circle. On the other hand, fiscal policy can relieve the employment situation. A cut in taxes or an increase in spending, if financed by new bond issues, ³⁵ will raise output, although it may cause the trade balance to deteriorate. A balanced budget contraction in government spending or the imposition of a wage subsidy will similarly increase employment. Conversely, and somewhat perversely, a balanced budget expansion in spending will serve to reduce employment.

The model can also be used to rank the price effects of the policies in generating the same increase in output. If there is complete money illusion, then monetary expansion, a decrease in the tax rate, and an increase in government spending all increase the domestic price equally. ³⁶ They do differ, however, in their impact on the consumer price index and the exchange rate. Specifically, monetary expansion induces a depreciation, while both the tax cut and the increase in fiscal spending lead to an exchange rate appreciation of equal size. With less money illusion, the two fiscal policies continue to have a common effect on the consumer price index, ³⁷ but their impact on its components diverges. In particular, with an injection of spending, the domestic price level will always be higher than it would for a tax cut, given that both yield the same expansion in output. Conversely, the exchange rate appreciates more in the former case and may even depreciate in the latter. As the degree of money illusion declines, the domestic price effect of monetary policy is enlarged, while that of both types of fiscal policy is decreased. Because the subsidy entails no change in the money supply, its effect on the consumer price index is identical to that of the tax cut and the increase in spending; yet, as indicated in Table 1, the subsidy always yields a decrease in the producer price. Hence, for high degrees of money illusion, the subsidy lowers this price more than does any other policy. As the degree of money illusion declines, the subsidy’s price effect relative to the tax cut and the increase in spending becomes increasingly ambiguous.

In terms of the model, the subsidy has much to recommend it. Its qualitative effect on output and employment is invariant to the degree of money illusion in the economy, and it exerts downward pressure on the price of domestic goods as well as on the consumer price index. Nevertheless, of the policies being compared, it may be the one most subject to criticism on administrative or longer-term considerations. ³⁸ Despite the strong claims by advocates of this policy, its impact and workings remain uncertain. It is possible that, in anticipation of the introduction of an employment subsidy, employers would lay workers off, thus frustrating the major objective of the subsidy. Subsidies presumably are paid on all increments to employment, including those that are due to influences other than the employment subsidy, which means that the claimed saving in net cost to the government may be, at least in part, spurious. The administrative costs and complexities of implementing an employment subsidy could be substantial, while its eventual removal may recreate unemployment problems in the future. ³⁹

An important caveat is also attached to those policies involving a cut in taxes. In general, our analysis treats the responsiveness of wages to price and tax changes as symmetric, although it is amenable to allowing for money illusion on the downside and no money illusion with respect to price and tax increases. If tax cuts are to be translated expeditiously into wage cuts, this must emerge from some kind of agreement between the trade unions and the government, of which there have been several recent examples in the industrial countries. In this same spirit, we need to highlight again our particular results that a balanced budget expansion of government expenditure may produce stagflation. The reverse of this, a balanced budget contraction of expenditure, may therefore increase real output and put downward pressure on the inflation rate. The success of this policy depends, however, on the degree to which the tax cut lowers wage demands.

It goes without saying, of course, that in order to arrive at a balanced judgment about alternative expansionary policies, several additional considerations would become relevant. For example, the size of the budget deficit, over which there is so much concern in the current situation, as well as the level of foreign indebtedness, would need to be taken into account. Budget as well as current account deficits, the latter implying a higher level of foreign indebtedness, carry implications for asset creation, wealth, and interest-rate servicing in the longer run that have been passed over in our analysis. The importance of these considerations remains a matter of some controversy; in any event, the time span over which they would become at all significant is beyond that envisaged in our study.

APPENDICES

A. Mathematical Supplement

Equations (l)–(9) reduce to the following three equations in P_d, Y, and e:

\begin{matrix} {\begin{matrix} Y P \end{matrix}}_{d} = f (P_{d}, P_{f} e) [\frac{C (P_{d} [Y (1 - t) + (\frac{s b}{b - 1}) (Y - Y_{0})])}{f (P_{d}, P_{f} e)} + I + G] \\ + P_{d} X (\frac{P_{d}}{P_{f} e}) - P_{f} e M (\frac{P_{d}}{P_{f} e}, \frac{C (P_{d} [Y (1 - t) + (\frac{s b}{b - 1}) (Y - Y_{0})]}{} + I + G) & (16) \end{matrix}

\begin{matrix} L = L (r, Y) f (P_{d}, P_{f} e) & (17) \end{matrix}

\begin{matrix} Y = a {[\frac{(1 - s) (1 - n + \frac{N}{1 - t}) f (P_{d}, P_{f} e)}{P_{d}}]}^{b} & (18) \end{matrix}

Setting initial values of s equal to zero and P, P_d, e, and P_f equal to one, we solve for the determinant of the coefficients of the endogenous variables.

\begin{matrix} D = - (1 - C' (1 - t) (1 - M_{2})) L (r, Y) b Y f_{2} + L_{y} a b {[1 - n + \frac{N}{1 - t}]}^{b - 1} (1 - n) \\ [- f_{2} A + C' Y (1 - t) f_{2} (1 - M_{2})] + L (r, Y) [f_{2} Y (1 - (1 - t) C' (1 - M_{2})) \\ + M_{1} - X' - f_{2} X - f_{1} M] & (19) \end{matrix}

The sign of D is positive because the parameters C’, t, M₂, s, f₁ and f₂ all lie between zero and one. In addition, a is positive and b is negative. This can be verified with reference to footnote 17. The last two terms contain proxy expressions for the Marshall-Lerner condition. In the former, it appears as X’ – M₁ + M and in the latter, as –X’+ M₁, –f₂X – f₁ M. It is assumed that this condition holds, and that the former expression is negative and the latter positive.

Differentiating the system, we ascertain how output is affected by the various policies. BB is used to denote a balanced budget expansion.

\begin{matrix} \frac{d Y}{d L} = {(1 - n) a b {(1 - n + \frac{N}{1 - t})}^{b - 1} (\frac{1}{1 - t}) (- f_{2} A + C' Y (1 - t) \\ f_{2} (1 - M_{2}) + X' - M_{1} + M)} / D \geq 0 & (20) \end{matrix}

\begin{matrix} \frac{d Y}{d G} = \frac{- b Y L (r, Y) f_{2} (1 - M_{2})}{D} \geq 0 & (21) \end{matrix}

\begin{matrix} \frac{d y}{d t} = {C' Y^{2} (1 - M_{2}) L (r, Y) b f_{2} + \frac{N}{{(1 - t)}^{2}} a b {(1 - n + \frac{n}{1 - t})}^{b - 1} L (r, Y) \\ [f_{2} Y (1 - (1 - t) C' (1 - M_{2})) + M_{1} - X' - f_{2} X - f_{1} M]} / D \leq 0 & (22) \end{matrix}

\begin{matrix} \frac{d Y}{d B B} = {- b Y^{2} f_{2} (1 - M_{2}) (1 - C^{'}) + \frac{N}{{(1 - t)}^{2}} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ [f_{2} Y (1 - (1 - t) C^{'}) (1 - M_{2})) - X^{'} - f_{2} X - f_{1} M]} \\ / {b Y f_{2} [(1 - M_{2}) (t + (1 - t) C^{'}) - 1] + \frac{L_{y}}{L (r, Y)} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ (\begin{matrix} 1 - n \end{matrix}) [- f_{2} A + C^{'} Y (1 - t) f_{2} (1 - M_{2}) + f_{2} Y (1 - (1 - t) C^{'} (1 - M_{2}))] \\ + M_{1} - X^{'} - f_{2} X - f_{1} M]}. ≷ 0 & (23) \end{matrix}

\begin{matrix} \frac{d Y}{d s} = {- (1 - n + \frac{N}{1 - t}) a b {[(1 - s) (1 - n + \frac{N}{1 - t})]}^{b - 1} L (r, Y) \\ [f_{2} Y (1 - (1 - t) + \frac{s b}{b - 1} C^{'} (1 - M_{2})) \\ + C^{'} Y_{0} \frac{s b}{b - 1} f_{2} (1 - M_{2}) + M_{1} - X^{'} - f_{2} X - f_{1} M] \\ - f_{2} C^{'} (1 - M_{2}) \frac{b^{2}}{b - 1} Y L (r, Y) (Y - Y_{0})} / D \geq 0 & (24) \end{matrix}

In each case except for monetary policy and the balanced budget expansion, output increases with expansionary policy regardless of the degree of money illusion. Equation (20) indicates that if there is no money illusion, that is, n = 1, output is invariant to the money supply. Moreover, in this case the numerator of equation (23) reduces to

\frac{L (r, Y)}{1 - t} b Y [Y f_{2} (1 - (1 - M_{2}) (1 - t)) + M_{1} - X^{'} - f_{2} X - f_{1} M] < 0

Hence, the “balanced budget multiplier” is negative.

In view of the Fleming-Mundell analysis of fiscal policy under floating exchange rates, it is especially interesting to see how the effectiveness of fiscal policy varies with the degree of money illusion. To this end, we differentiate equation (21) with respect to n. Simplifying a rather cumbersome expression, we get

\begin{matrix} \frac{\begin{matrix} d (\frac{d Y}{d G}) \end{matrix}}{d n} = \frac{{a b}^{2} (1 - M_{2}) f_{2} {(1 - n + \frac{N}{1 - t})}^{b - 2}}{D^{2}} \\ {{Y L}_{y} (- f_{2} A + C^{'} Y (1 - t) f_{2} (1 - M_{2})) (\frac{- N}{1 - t} L (r, Y) + {b Y L}_{y} (1 - n)) \\ + L {(r, Y)}^{2} (1 - n + \frac{N}{1 - t}) (M_{1} - X^{'} - f_{2} X - f_{1} M) \\ - Y^{2} L (r, Y) f_{2} L_{y} b (1 - n) C^{'} (1 - t) (1 - M_{2})} & (25) \end{matrix}

whose sign is positive. Hence, as the degree of money illusion rises (n falls), the expansionary impact of fiscal policy diminishes. However, in a world of no money illusion, fiscal policy clearly has output effects.

We now present the effects on the domestic price of the various changes.

\begin{matrix} \frac{{d P}_{d}}{d L} = - [(1 - C^{'} (1 - t) (1 - M_{2})) (\frac{{N f}_{2}}{1 - t}) a b {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ + (- f_{2} A + C^{'} Y (1 - t) f_{2} (1 - M_{2}) + X^{'} - M_{1} + M)] / D > 0 & (26) \end{matrix}

\begin{matrix} \frac{d P_{d}}{d G} = (\frac{1 - M_{2}}{D}) [L_{y} (\frac{N f_{2}}{1 - t}) a b {(1 - n + \frac{N}{1 - t})}^{b - 1} + f_{2} L (r, Y)] ≶ 0 & (27) \end{matrix}

\begin{matrix} \frac{{d P}_{d}}{d t} = {C^{'} Y (1 - M_{2}) [- L_{y} \frac{{N f}_{2}}{(1 - t)} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} + f_{2} L (r, Y)] \\ \frac{- N}{{(1 - t)}^{2}} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} [f_{2} L (r, Y) (1 - C^{'} (1 - t) (1 - M_{2})) \\ - L_{y} (- f_{2} A + X^{'} - M_{1} + M + C^{'} Y (1 - t) f_{2} (1 - M_{2}))]} / D ≷ 0 & (28) \end{matrix}

\begin{matrix} \frac{{d P}_{d}}{d s} = {C^{'} (1 - M_{2}) \frac{b}{b - 1} (Y - Y_{0}) L_{y} (1 - s) \frac{{N f}_{2}}{1 - t} a b [(1 - s) \\ {\begin{matrix} (1 - n + \frac{N}{1 - t})] \end{matrix}}^{b - 1} + b Y [L (r, Y) f_{2} (1 - C^{'} (1 - M_{2}) \\ (1 - t + \frac{s b}{b - 1} + \frac{Y - Y_{0}}{Y (b - 1)})) - L_{u} (- f_{2} A + X^{'} - M - M_{1} + C^{'} Y \\ (1 - t + \frac{s b}{b - 1}) (1 - M_{2}) - C^{'} Y_{0} \frac{s b}{b - 1} f_{2} (1 - M_{2}))]} / D \leq 0 & (29) \end{matrix}

The exchange rate changes in accord with the following:

\begin{matrix} \frac{d e}{d L} = {[(1 - C^{'} (1 - t) (1 - M_{2})) (1 - n + \frac{{N f}_{2}}{1 - t}) a b {(1 - n + \frac{N}{1 - t})}^{b - 1}] \\ - [Y - f_{1} A - X - X^{'} + M_{1} - C^{'} Y (1 - t) f_{2} (1 - M_{2})]} / \geq 0 & (30) \end{matrix}

\begin{matrix} \frac{d e}{d G} = (\frac{1 - M_{2}}{D}) (L_{y} b Y - f_{1} L (r, Y)) \leq 0 & (31) \end{matrix}

\begin{matrix} \frac{d e}{d G} = {- C^{'} Y (1 - M_{2}) (L_{y} b Y - f_{1} L (r, Y)) + \frac{N}{{(1 - t)}^{2}} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ [L (r, Y) f_{1} (1 - C^{'} (1 - t) (1 - M_{2})) - L_{y} (Y - f_{1} A - X^{'} + M_{1} - X - C^{'} Y \\ (1 - t) (1 - M_{2}) f_{2})]} / D ≷ 0 & (32) \end{matrix}

\begin{matrix} \frac{d e}{d s} = {C^{'} (1 - M_{2}) \frac{b}{b - 1} (Y - Y_{0}) (L_{y} b Y - L (r, Y) f_{1} - b Y \\ [L (r, Y) f_{1} (1 - C^{'} (1 - t) + \frac{s b}{b - 1}) (1 - M_{2}) \\ - L_{y} (Y - f_{1} A - X - X^{'} + M - C^{'} Y (1 - t + \frac{s b}{b - 1}) f_{2} (1 - M_{2}) \\ + C^{'} Y_{0} \frac{s b}{b - 1} (1 - M_{2}) f_{2}]} / D ≶ 0 & (33) \end{matrix}

Now we proceed to calculate the impact of the various policies on the domestic price for a given output effect. As noted in the text, inspection of the money equation indicates the relative rankings of effects on the overall price index, so that algebraic manipulation is unnecessary. For the individual components, however, such a route is not open, so that explicit consideration of the algebra is required.

First, we note that the actual change in Y (ΔY) for a finite change in policy variable (ΔL, ΔG, Δt, Δs) can be calculated as follows:

\begin{matrix} {\begin{matrix} Δ Y \end{matrix}}_{L} = \frac{d Y}{d L} \cdot Δ L & (34) \end{matrix}

\begin{matrix} {\begin{matrix} Δ Y \end{matrix}}_{G} = \frac{d Y}{d G} \cdot Δ G & (35) \end{matrix}

\begin{matrix} {\begin{matrix} Δ Y \end{matrix}}_{t} = \frac{d Y}{d t} \cdot Δ t & (36) \end{matrix}

\begin{matrix} {\begin{matrix} Δ Y \end{matrix}}_{s} = \frac{d Y}{d s} \cdot Δ s & (37) \end{matrix}

Since we want to compare price effects for equal output effects, we set ΔY_i = ΔY_j, and arbitrarily set ΔG = 1. Now we can calculate the actual policy change required to increase output by the same amount as an increase of one unit in fiscal spending.

\begin{matrix} Δ L = \frac{d Y}{d G} / \frac{d Y}{d L} & (38) \end{matrix}

\begin{matrix} Δ t = \frac{d Y}{d G} / \frac{d Y}{d t} & (39) \end{matrix}

\begin{matrix} Δ s = \frac{d Y}{d G} / \frac{d Y}{d s} & (40) \end{matrix}

Next, we calculate the actual price changes induced by the policy changes calculated in equations (38) to (40), which yield equal output effects. Hence,

\begin{matrix} Δ P_{d L} = \frac{d P_{d}}{d L} \cdot \frac{d Y}{d G} / \frac{d Y}{d L} & (41) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d G} = \frac{d P_{d}}{d G} & (42) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d t} = \frac{d P_{d}}{d t} \cdot \frac{d Y}{d G} / \frac{d Y}{d t} & (43) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d x} = \frac{d P_{d}}{d s} \cdot \frac{d Y}{d G} / \frac{d Y}{d s} & (44) \end{matrix}

Filling in the derivations from equations (26) to (29), we can expand equations (41) to (44):

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d L} = [\frac{(1 - C^{'} (1 - t) (1 - M_{2}))}{D} (\frac{{N f}_{2}}{1 - t} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ + (- f_{2} A + X^{'} - M_{1} + M + C^{'} Y (1 - t) f_{2} (1 - M_{2})))] \cdot \\ [\frac{(1 - M_{2}) f_{2} (1 - n + N) L (r, Y)}{(1 - n) (- f_{2} A + C^{'} Y (1 - t) f_{2} (1 - M_{2}) + X^{'} - M_{1} + M)}] > 0 & (45) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d G} = (\frac{1 - M_{2}}{D}) [L_{y} \frac{F f_{2}}{1 - t} a b {(1 - n + \frac{N}{1 - t})}^{b - 1} + f_{2} L (r, Y)] ≶ 0 & (46) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d t} = {- {Y f}_{2} (1 - M_{2}) [- C^{'} Y (1 - M_{2}) (L_{y} \frac{{N f}_{2}}{1 - t}) {(1 - n + \frac{N}{1 - t})}^{b - 1} \\ + f_{2} L (r, Y)] - \frac{N a b}{{(1 - t)}^{2}} {(1 - n + \frac{N}{1 - t})}^{b - 1} [L (r, Y) f_{2} \\ (1 - C^{'} (1 - t) (1 - M_{2})) - L_{y} (- f_{2} A + X^{'} + M - M_{1} \\ + C^{'} Y (1 - t) f_{2} (1 - M_{2}))]} / D {C^{'} Y^{2} (1 - M_{2}) f_{2} + \frac{N}{{(1 - t)}^{2}} \\ a {(1 - n + \frac{N}{1 - t})}^{b - 1} L (r, Y) [f_{2} Y (1 - (1 - t) \\ C^{'} (1 - M_{2})) + M_{1} - X^{'} - f_{2} X - f_{1} M]} ≶ 0 & (47) \end{matrix}

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d s} = f_{2} (1 - M_{2}) (1 - s) {C^{'} (1 - M_{2}) \frac{b}{b - 1} (Y - Y_{0}) L_{y} (1 - s) \\ \frac{{N f}_{2}}{1 - t} a b {[(1 - s) (1 - n + \frac{N}{1 - t})]}^{b - 1} + b Y \\ [L (r, Y) f_{2} (1 - C^{'} (1 - M_{2}) (1 - t + \frac{s b}{b - 1} + \frac{Y - Y_{0}}{Y (b - 1)}) \\ - L_{y} (- f_{2} A + X^{'} - M - M_{1} + C^{'} Y (1 - t + \frac{s b}{b - 1}) (1 - M_{2}) \\ - C^{'} Y_{0} \frac{s b}{b - 1} f_{2} (1 - M_{2})]} / D [f_{2} Y (1 - (1 - t) C^{'} (1 - M_{2})) \\ + M_{1} - X^{'} - f_{2} X - f_{1} M + f_{2} C^{'} \\ (\begin{matrix} 1 - M_{2} \end{matrix}) \frac{b}{b - 1} (Y - Y_{0}) (1 - s)] < 0 & (48) \end{matrix}

It remains only to rank the price effects given by equations (45) to (48). A convenient starting place is to consider the relative Δ P_ds for complete money illusion. This is represented by setting N = 0. In this case, ΔP_dL = ΔP_.dG = ΔP_dt. This is so because the AS schedule is invariant to price and tax considerations; hence, a given ΔY requires a common ΔP_d. As the degree of money illusion is reduced, ΔP_dL rises while ΔP_dG and ΔP_dt get smaller. Moreover, it can be shown that, except with complete money illusion, ΔP_dt < ΔP_dG.

\begin{matrix} {\begin{matrix} Δ P \end{matrix}}_{d t} - {\begin{matrix} Δ P \end{matrix}}_{d G} = \frac{- N}{{(1 - t)}^{2}} a {(1 - n + \frac{N}{1 - t})}^{b - 1} L (r, Y) \\ [f_{2} Y (1 - (1 - t) C^{'} (1 - M_{2})) + M_{1} - X^{'} - f_{2} X - f_{1} M] \\ + {Y f}_{2} (1 - M_{2}) \frac{N a b}{{(1 - t)}^{2}} {(1 - n + \frac{N}{(1 - t)})}^{b - 1} [L (r, Y) f_{2}] \\ (1 - C^{'} (1 - t) (1 - M_{2})) - L_{y} (- f_{2} A + X^{'} + M - M_{1} \\ + C^{'} Y (1 - t) f_{2} (1 - M_{2}))] < 0 & (49) \end{matrix}

This expression is negative in general, but equals zero if N = 0. Thus, our ranking is ΔP_dL > ΔP_dG > ΔP_dt, for all cases except complete money illusion.

The AS schedules shift with the imposition of a subsidy even if labor has full money illusion. Hence, for high degrees of money illusion ΔP_ds is below the others. As money illusion decreases, and ΔP_dt and ΔP_dG become negative, it is possible that the always negative ΔP_ds will come to exceed one or both of them.

B. The Assignment Problem

In the light of our finding that monetary and fiscal policies have different inflationary effects for a given expansion in output, the question may now be asked whether this result implies anything about the assignment of our instruments to our two targets—output and inflation.

Figure 7 illustrates the assignment problem. The PP schedule combines the volume of money and tax rates in such a way as to maintain a constant overall price level.⁴⁰ Since an expansion in money raises the overall price level while a reduction in the tax rate lowers the price level, the slope of PP must be negative. The YY schedule reflects the combinations of monetary and fiscal policies that keep real output constant. Its slope is positive, since an increase in money requires an increase in tax rates if output is to be maintained. In the extreme case where there is no money illusion, the slope will be infinite (YY will be vertical), since an infinitely large increase in the volume of money will be required to offset any reductions in output from an increase in the tax rate.

Following convention, four zones are identified corresponding to recession/inflation (stagflation), excess demand/inflation, excess demand/deflation, and recession/deflation. These are derived as follows. The area to the right of the PP schedule represents a situation of relatively high prices (inflation): with the volume of money given, tax rates are higher than required to ensure the short-term price target. The area to the left of the PP schedule represents relatively low prices (deflation): tax rates are below those required to meet the price target. The area to the right (left) of YY represents recession (excess demand), since, at a given volume of money, tax rates are now higher (lower) than those required to meet the short-term demand target.

In the conventional assignment literature, which is concerned with the appropriate assignment of the monetary and fiscal instruments to the targets of internal and external balance,⁴¹ the assumption is made that both surpluses and deficits in the balance of payments are undesirable and hence need to be corrected by an appropriate mix of policy instruments. It is not quite so evident, when the price level is the target, why the areas to the left of PP, where the price level is below “target,” should be considered undesirable. For obvious reasons, we feel it would not be meaningful to have a government authority manipulate one of its instruments so as to push the price level up toward its target. Hence, we assume in what follows that the instrument assigned to the price level is activated only when the price level is too high and, asymmetrically, not when it is too low. In any event, it is evidently only the area to the right of PP that is of interest to us.

Now consider the case where there is some money illusion, and assume that fiscal policy is assigned to the output target while the money supply is assigned to the price level. This particular assignment is shown in the form of broken arrows in each of the four zones. For example, in the zone labeled recession/inflation (stagflation), this would require that the volume of money be reduced (to reduce the inflation) at the same time that taxes are reduced (to stimulate output). It is evident from the diagram that this particular assignment is stable in the sense that, starting from any disequilibrium situation, either the point of intersection of PP and YY or some point on YY to the left of this point would ultimately be reached.

The alternative assignment, gearing the volume of money to output and the tax rate to the price level, is shown by the unbroken arrows. Now, in the face of the same stagflation conditions, the volume of money would be allowed to increase (to combat the unemployment) while the tax rate would be lowered to combat the inflation. It turns out, as the diagram clearly demonstrates, that this assignment is also stable. The conclusion, then, is that either assignment appears to be stable in terms of the model.⁴²

The diagram shows that if an economy finds itself in the stagflation zone (the most relevant in today’s world), it would be possible to reduce the volume of money and lower the tax rate so as to maintain the level of output while lowering the overall price level, or, alternatively, to raise the volume of money and lower the tax rate so as to stimulate output while leaving the overall price level unchanged.

Mr. Argy, Consultant in the Fund’s Research Department when this paper was prepared, is Professor of Economics at Macquarie University, Sydney, Australia.

Ms. Salop, economist in the Special Studies Division of the Research Department, is a graduate of the University of Pennsylvania and Columbia University.

For an analysis of the large-country case, see Victor Argy and Joanne Salop, “Price and Output Effects of Monetary and Fiscal Policy in a Two-Country World Under Flexible Exchange Rates” (unpublished, International Monetary Fund, May 1979).

An employment subsidy, in a variety of forms, has recently been adopted by a large number of industrial countries. It has been viewed as a means of simultaneously increasing employment, reducing prices, and reducing the budget deficit. See John Burton, “Employment Subsidies—The Cases For and Against,” National Westminster Bank, Quarterly Review (February 1977), pp. 33–43.

Among the few contributions in the area are Robert A. Mundell, The Dollar and the Policy Mix: 1971, Essays in International Finance, No. 85, International Finance Section, Princeton University (May 1971); Thomas F. Dernburg, “The Macroeconomic Implications of Wage Retaliation Against Higher Taxation,” Staff Papers, Vol. 21 (November 1974), pp. 758–88; Francisco R. Casas, “Capital Mobility and Stabilization Policies under Flexible Exchange Rates: A Revised Analysis,” Southern Economic Journal, Vol. 43 (April 1977), pp. 1528–37; Rudiger Dornbusch and Paul Krugman, “Flexible Exchange Rates in the Short Run,” Brookings Papers on Economic Activity: 3 (1976), pp. 537–75. A very recent and relevant exception to the statement in the text is J. Sachs, “Wage Indexation, Flexible Exchange Rates, and Macroeconomic Policy.” (This is scheduled for publication in the Quarterly Journal of Economics.)

Robert A. Mundell, “Flexible Exchange Rates and Employment Policy,” Canadian Journal of Economics, Vol. 27 (November 1961), pp. 509–17.

J. Marcus Fleming, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates,” Staff Papers, Vol. 9 (November 1962), pp. 369–80.

It is evident that with the interest rate and the price level unchanged, monetary expansion must generate a proportionate effect on real output. At the other extreme, with prices, interest rates, and the money supply all fixed, fiscal expansion cannot change output—the associated revaluation fully offsetting the fiscal stimulus. These results are of interest because they replicate some monetarist propositions (including complete real crowding out for fiscal policy) with what is basically a Keynesian model.

Stanley Warren Black, International Money Markets and Flexible Exchange Rates, Princeton Studies in International Finance, No. 32, International Finance Section, Princeton University (1973); William H. Branson, “Asset Markets and Relative Prices in Exchange Rate Determination,” Sozialwissen schaftlich Annalen, Vol. 1 (1977); Rudiger Dornbusch, “The Theory of Flexible Exchange Rate Regimes and Macroeconomic Policy,” Scandinavian Journal of Economics, Vol. 78 (No. 2, 1976), pp. 255–75; Pentti J.K. Kouri, “The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach,” Scandinavian Journal of Economics, Vol. 78 (No. 2, 1976), pp. 280–304.

Rudiger Dornbusch, “Exchange Rate Expectations and Monetary Policy,” Journal of International Economics, Vol. 6 (August 1976), pp. 231–44.

Rudiger Dornbusch, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, Vol. 84 (December 1976), pp. 1161–76.

See Dernburg, op. cit.; Dudley Jackson, H.A. Turner, and Frank Wilkinson, Do Trade Unions Cause Inflation? Two Studies: With a Theoretical Introduction and a Policy Conclusion (Cambridge University Press, 1974); Alan S. Blinder, “Can Income Tax Increases Be Inflationary? An Expository Note,” National Tax Journal, Vol. 26 (June 1973), pp. 295–301; G. Brennan and D.A.L. Auld, “The Tax Cut as an Anti-Inflationary Measure,” Economic Record, Vol. 44 (December 1968), pp. 520–25.

This asymmetry is emphasized in Joanne Salop, “Devaluation and the Balance of Trade Under Flexible Wages,” in Trade, Stability, and Macroeconomics: Essays in Honor of Lloyd A. Metzler, ed. by George Horwich and Paul A. Samuelson (New York and London, 1974), pp. 129–51.

This is also true in the contribution by Dernburg, op. cit. Dernburg’s paper deals only with the closed economy case; moreover, he allows wages to be influenced by taxes but not by prices.

It is sometimes argued that the degree of capital market integration will itself be reduced by flexible exchange rates. It is not, however, clear what meaning should be attached to this. Is it that the response to the uncovered interest differential is weaker? Or to the covered differential? Or is it simply that the speculator’s schedule in the forward market is now less elastic?

The evidence on capital market integration remains somewhat inconclusive. While it is generally agreed that integration is very nearly perfect as between Eurocurrencies, it appears to be less than perfect as between national markets. See Eurocurrencies and the International Monetary System, ed. by Carl H. Stem, John H. Makin, and Dennis E. Logue, American Enterprise Institute for Public Policy Research (Washington, 1975).

In the two-country version, fiscal expansion raises output at home but reduces it abroad. Without money illusion, the system as a whole functions in the classical manner. Thus, total output cannot rise, but its distribution among countries can change. See Argy and Salop, op. cit.

For an argument along these lines applied to the United Kingdom, see Robert Bacon and Walter Eltis, “How Growth in Public Expenditure Has Contributed to Britain’s Difficulties,” Ch. 1 in The Dilemmas of Government Expenditure: Essays in Political Economy by Economists and Parliamentarians, Institute of Economic Affairs (Sussex, 1976), pp. 1–21.

The subsidy affects disposable income in the following way. As output increases above some initial value Y₀, the value of the subsidy will equal the subsidy (s) times labor’s share in the increase in GNP. Because our production function is of the form

$Y = α_{10} K^{α 1} L^{α 2}$

labor’s share equals ɑ₂. The exponent b, to be used in equation (8), equals $- \frac{α_{2}}{α_{1}} .$ Hence $\frac{b}{b - 1}$ represents labor’s share of output. Even though labor income at any level of output will be invariant to the subsidy, profits (also a part of disposable income) are higher if the subsidy is on. Moreover, the increase in aftertax profits is the value of the subsidy.

Equation (8) can be derived from the profit-maximizing conditions for the competitive firm and the Cobb-Douglas production function Y = ɑ₀K^ɑ1L^ɑ2 for which case,a = K ɑ⁰(ɑ₂/ɑ₁)² and b = –ɑ₂/ɑ₁

For some econometric work supporting this hypothesis, see Michael Parkin, “The Causes of Inflation: Recent Contributions and Current Controversies,” in Current Economic Problems: The Proceedings of the Association of University Teachers of Economics, Manchester 1974, ed. by Michael Parkin and A.R. Nobay (Cambridge University Press, 1975), pp. 243–74, especially pp. 254–55; Robert J. Gordon, “Recent Developments in the Theory of Inflation and Unemployment,” Journal of Monetary Economics, Vol. 2 (April 1976), pp. 185–219, especially p. 212.

Rewriting the numerator, assuming that the average and marginal propensities to consume are equal, we have

$- Y (1 - C^{'} (1 - t) (1 - M_{2}) (1 - f_{1})) + f_{1} G + f_{1} I + X^{'} - M_{1} + X$

The coefficient of C’ is less than one, as is From equation (1) we know that

$Y (1 - C^{'} (1 - t) (1 - M_{2}) (1 - f_{1})) - f_{1} G - f_{1} I - X > - M$

This implies that the numerator is less than X^’ –M₁, + M. The negative of this expression is a proxy for the Marshall-Lerner condition. Following convention in assuming this to hold, we find that the numerator is less than some negative quantity.

To minimize the amount of graphical presentation, we show only the case where the slope of LM is steeper than the slope of IS, except where the reverse situation is critical to the argument.

See footnote 19 and equation (2).

That is,

$\frac{d Y}{d G} = \frac{1 - M_{2}}{1 - C' (1 - t) (1 - M_{2})} > 0$

As drawn, the IS schedule shifts to the right from the combined effects of the increase in government spending and the revaluation. It is less likely, but conceivable, that it will shift to the left. In that event, Y rises and P_d f falls.

See equation (25).

This entails setting N = 0.

$\frac{d Y}{d t} |_{A S} = a b \frac{N}{(1 - t)^{2}} [1 - n + \frac{N}{(1 - t)}]^{b - 1} < 0$

$\frac{d Y}{d t} |_{I S} = - \frac{C' Y (1 - M_{2})}{1 - C' (1 - t) (1 - M_{2})} < 0$

This follows directly from the money market condition.

$\begin{array}{l} \frac{d Y}{d t} |_{Δ G = Δ T} = [\frac{d Y}{d G} Y + \frac{d Y}{d t}] / [(1 - t) \frac{d Y}{d G}] = \\ L \frac{(r, Y)}{(1 - t)} b Y {\frac{Y f_{2} (1 - (1 - M_{2}) (1 - t) + M_{1} - X' - f_{2} X - f_{1} M)}{(1 - t) \frac{d Y}{d G}}} < 0 \end{array}$

In this case, $\frac{d Y}{d t} |_{Δ G = Δ T} = \frac{- L (r, Y) f_{2} b Y^{2} (1 - M_{2}) (1 - C')}{(1 - t) \frac{d Y}{d G}} > 0$

$\frac{d Y}{d s} |_{A S} = \frac{- b Y}{1 - s} > 0$

With sticky prices, Keynesian unemployment would result even if real wages were rigid. Essentially, the demand component of the shock would cause producers to be “demand constrained” in their production and sales decisions. Hence, they would employ fewer workers than their marginal productivity conditions would admit. With diminishing marginal productivity, labor’s marginal revenue product will exceed the wage. With both prices and real wages sticky, unemployment occurs on two counts—Keynesian unemployment and rigid real wage unemployment.

A decrease in real wage demands shifts the AS schedule to the right. The exchange rate appreciates if LM is steeper than IS and depreciates if IS is steeper. In either case, output rises and unemployment falls.

Note that expansionary remedies can eliminate the portion of unemployment that is Keynesian in origin. By relaxing the demand constraint, such remedies allow producers to expand and to hire more workers. The marginal revenue product falls as this happens, until it equals the wage. Once this point is reached, however, further expansion goes into prices.

If financed by money creation, then a vicious circle will ensue at a higher level of output. In the first period, the monetary and fiscal effects on the exchange rate tend to offset each other. In subsequent periods, however, the money created would still be in circulation and unmatched by additional fiscal stimulus.

Because the AS schedule is stationary, the change in P_d for a given change in Y is invariant to the source of the expansionary impulse.

Since neither fiscal policy alters the money supply, for the same output, the consumer price index must be the same to satisfy LM.

See Burton, op. cit. See also Towards Full Employment and Price Stability: A Report to the OECD by a Group of Independent Experts, Organization for Economic Cooperation and Development (Paris, June 1977). While this Report says it is “attracted” by such schemes, it warns against the administrative complexities and possible “displacement” effects. (See paragraph 349 of the Report.)

Since the employment subsidy has taken many different forms in different countries, these objections clearly do not apply in equal degree to all variations of this subsidy. For a good discussion, see George F. Kopits, “Wage Subsidies and Employment: An Analysis of the French Experience,” Staff Papers, Vol. 25 (September 1978), pp. 494–527.

As far as the assignment issue is concerned, there is no difference between the three fiscal policies, since we have shown that they have the same overall price effect for any given expansion in output.

See Robert A. Mundell, “The Appropriate Use of Monetary and Fiscal Policy for Internal and External Stability,” Staff Papers, Vol. 9 (March 1962), pp. 70–79; Jay H. Levin, “International Capital Mobility and the Assignment Problem,” Oxford Economic Papers, Vol. 24 (March 1972), pp. 54–67.

As the degree of money illusion decreases, however, this assignment becomes increasingly inappropriate. At the limit where YY is vertical, the assignment is clearly less efficient than the reverse assignment.

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IMF Staff papers: Volume 26 No. 2

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1979: Issue 002

Publisher:: International Monetary Fund

ISBN:: 9781451946840

ISSN:: 1020-7635

Pages:: 226

DOI:: https://doi.org/10.5089/9781451946840.024

Keywords
I. The Model
II. Graphical Apparatus
III. Policy Exercises
IV. Summary and Conclusions
APPENDICES
- A. Mathematical Supplement
- B. The Assignment Problem

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Equilibrium in Three Markets

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Effects of an Increase in Government Expenditure

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Reduction in the Tax Rate

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Balanced Budget Expansion with Output Falling and Exchange Rate Depreciating

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Employment Subsidy Increasing Output, Decreasing Prices, and Leading to Exchange Depreciation

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Expansionary Monetary Policy, with No Money Illusion

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The Assignment Problem, with Some Money Illusion

Table 1.

Effects of Various Fiscal and Monetary Policies on Output, Consumer Prices, Domestic Prices, and the Exchange Rate for a Small Industrial Country

	No Money Illusion		Full Money Illusion	Some Money Illusion
		dY
dL	0		+	+
dG	+		+	+
-dt	+		+	+
dBB	–		+	?
ds	+		+	+
		dP
dL	+		+	+
dG	–		–	–
-dt	–		–	–
dBB	+		–	?¹
ds	–		–	–
		dP_d
dL	+		+	+
dG	?		+	?
-dt	?		+	?
dBB	+		+	+
ds	–		–	–
		de²
dL	+		+	+
dG	–		–	–
-dt	?		—	?
dBB	?		—	?
ds	?		?	?

^¹If Y rises, P falls; if Y falls, P rises.

^²A plus sign indicates depreciation.

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Abstract

I. The Model

II. Graphical Apparatus

III. Policy Exercises

an increase in government spending

a reduction in taxes

balanced budget expansion

the employment subsidy

an expansionary monetary policy

IV. Summary and Conclusions

APPENDICES

A. Mathematical Supplement

B. The Assignment Problem

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