Working capital finance and the balanced budget multiplier.

Wen-ya Chang ; Ching-chong Lai

I. Introduction

The macroeconomic literature has long agreed that the balanced budget multiplier is positive. More specifically, the standard belief |Wallich (1944), Haavelmo (1945), Dornbusch and Fischer (1990)~ indicates that an increase in government spendings, accompanied by an equal increase in taxes, will generate an expansion in the national income.(1) The purpose of this paper is to question this conventional wisdom by explicitly taking the status of working capital finance on the production process into consideration.

The role of working capital finance on economic activities has received increasing attention in the literature, particularly in the so-called structuralist macromodel. This strand of research emphasizes that in most developing countries the working-capital cost is an expense of doing business, since it should be paid in advance as the production process is initiated. In the context of working-capital finance consideration, Shaller (1983) and Mitchell (1984) reevaluate the performance of fiscal policy, and find that an expansion in government expenditure will actually depress the domestic output. Sauernheimer (1987) as well as Chang, Lai and Chu (1990) apply the role of working capital finance to the open economy, and find that the Shaller-Mitchell conclusion may not hold in the context of flexible exchange rates. On the other hand, Taylor (1983, ch. 5) and van Wijnbergen (1983) demonstrate that monetary contraction may lead to stagflation should the cost-push effect created by working capital be substantially dominant. In line with these studies, this paper turns its attention to explore the implication of working-capital cost on the balanced budget multiplier. It can be found that the balanced budget multiplier may be negative depending on the extent of working-capital cost.

The remainder of the paper is organized as follows. The theoretical framework characterized by the working-capital cost is presented in section II. Section III examines the balanced budget multiplier as well as derives a graphical illustration. Finally, the concluding remarks are given in section IV.

II. The Theoretical Framework

Except for the fact that the government will maintain a balanced budget via changes in the income tax rates and that the aggregate supply function embodies the feature of working capital finance, the analytical framework is basically that of the standard aggregate demand and aggregate supply (AD-AS) as model. The model consists of the following set of equations:

y = C(y - |Tau~y) + I(r) + G, (1)

M/p = L(r, y), (2)

y = S(p, r), (3)

G = |Tau~y; (4)

where y = national income, C = consumption expenditure, |Tau~ = a proportional income tax rate, I = investment expenditure, r = interest rate, G = government expenditure, M = nominal money supply, p = domestic price level, L = real money demand, S = aggregate supply function. As customary, we impose the following restrictions on the behavioral functions: 1 |is greater than~ c |equivalent to~ dC/d(y - |Tau~y) |is greater than~ 0, |I.sub.r~ equivalent to~ dI/dr |is greater than~ 0, |L.sub.r~ |equivalent to~ |Delta~L/|Delta~r |is less than~ 0, |L.sub.y~ |equivalent to~ |Delta~L/|Delta~y |is greater than~ 0.

Equations (1) and (2) are the equilibrium conditions for the commodity market and money market, respectively.(2) Equation (3) represents the economy's aggregate supply function. Since the aggregate supply function will play a significant role on evaluating the balanced budget multiplier, we now turn to derive this function in detail.

Define labor employed as N, the aggregate short-run production function can then be written as

y = y(N), (5)

where |y.sub.N~ |equivalent to~ dy/dN |is greater than~ 0 and |Y.sub.NN~ |equivalent to~ |d.sup.2~Y/d|N.sup.2~ |is less than~ 0.

Empirical studies, such as Morley (1971), suggest that in most developing countries, supplier of inputs are too financially constrained to allow their payments to wait. Therefore, entrepreneurs must possess money on hand to pay in advance for the services of current inputs into the production process. Consequently, following Taylor (1983, ch. 5) and Mitchell (1984), we specify that partial workers' payments should be paid in advance, so that the working-capital expense for the labor is

V = |Alpha~WN, (6)

where |Alpha~ is the portion of the wage bill which is paid in advance, and W denotes the money wages of labor.

Letting K denote the fixed cost, the profit of the representative firm, |Pi~, can then be specified as follows:(3)

|Pi~ = py(N) - WN - rV - K. (7)

The objective of the representative firm is to choose N so as to maximize its profit. Therefore, the first-order condition can be expressed as

p|y.sub.N~ - (1 + |Alpha~r)W = 0. (8)

In conformity with the conventional specification, we assume that nominal wages are set to be rigid by the labor union and actual employment is determined by labor demand. Then from equations (5) and (8) we have

y = S(p, r),

where |Mathematical Expression Omitted~. Without loss of generality, it is assumed that initially p = 1 throughout the paper. As is evident, if |Alpha~ = 0, then |S.sub.r~ = 0 will result and equation (3) degenerates to the standard Keynesian aggregate supply function in which the interest-sensitive effect on aggregate supply is neglected. On the other hand, if |Alpha~ |is not equal to~ 0, then |S.sub.r~ |is less than~ 0 and equation (3) is characterized by the negative effect of the interest rate on aggregate supply, from the viewpoint that wage payments are financed by working capital.

Finally, equation (4) describes that the government keeps a balanced budget through the method of tax finance. More specifically, following the analysis of Smyth (1970), Decaluwe and Steinherr (1976) and Argy and Salop (1979), the government increases its expenditures and at the same time chooses the income tax rates to vary in order to maintain G = |Tau~y. This implies that |Tau~ is an endogenous variable if G is treated as a policy parameter.

III. The Balanced Budget Multiplier

We are now in a position to reevaluate the balanced budget multiplier. The system of equations (1)-(4) can be simultaneously solved to determine y, r, p, and |Tau~. Total differentiation of the system gives

|Mathematical Expression Omitted~

By Cramer's rule, from equation (9) the effects of an equal increase in government spendings and taxes on domestic output are given by:

|Mathematical Expression Omitted~

where |Delta~ = |S.sub.p~|(1-c)|L.sub.r~ + |I.sub.r~|L.sub.y~~ + M||I.sub.r~ + |S.sub.r~(c-1)~ |is less than~ 0 due to the stability condition proposed by Shaller (1983).

Equation (10) can lead to some interesting results. First, under the conventional wisdom the role of working capital on aggregate supply is ignored (|S.sub.r~ = 0), equation (10) can then be reduced to

|Delta~y/|Delta~G = |S.sub.p~|L.sub.r~(1 - c)/|S.sub.p~|(1 - c)|L.sub.r~ + |I.sub.r~|L.sub.y~ + |I.sub.r~M |is greater than~ 0. (11)

Obviously, equation (11) is exactly the conclusion of the conventional Keynesian AD-AS analysis. It indicates that an increase in government expenditures fully covered by taxes will raise the national income, that is, the balanced budget multiplier is positive.

Secondly, if the working capital effect on aggregate supply is brought into the analysis (|S.sub.r~ |is less than~ 0), equation (10) then turns out to be

|Mathematical Expression Omitted~

Consequently, an expansion in government spending constrained by a balanced government budget will create a negative impact on domestic output if the effect of working capital on production is substantially dominant. This result runs in sharp contrast with the conventional analysis.

The sharp distinction between the conventional belief and that of this paper can be clearly illuminated by means of graphical presentation. In figure 1, the ADS curve traces the locus of the income tax rate and the national income that will fulfill the equilibrium conditions of the goods and money markets as well as the aggregate supply function for a given level of government expenditure. It can be easily inferred from equations (1)-(3) that the ADS curve can be either upward or downward sloping depending on the extent of the interest-sensitive aggregate supply effect. If the interest-sensitive supply effect is absent (i.e., |S.sub.r~ = 0), the ADS curve unambiguously has a negative slope, indicated as AD|S.sup.1~ in figure 1. However, the ADS schedule will have a positive slope provided that the interest-sensitive supply effect is substantially large (i.e., - |S.sub.r~ |is greater than~ - |S.sub.p~|L.sub.r~/M), denoted as AD|S.sup.2~ in figure 1.(4) On the other hand, the BG curve represents the pairs of |Tau~ and y that will maintain the government budget in balance for a given government expenditure. Apparently, BG is a rectangular hyperbola and in equilibrium the BG schedule is flatter than the AD|S.sup.1~ schedule.(5)

In figure 1, the initial equilibrium for a given |G.sub.0~ is at point |E.sub.0~ where AD|S.sup.1~, AD|S.sup.2~, and BG intersect, and initial output is |y.sub.0~. As G increases from |G.sub.0~ to |G.sub.1~, AD|S.sup.1~, AD|S.sup.2~ and BG shift upward to |Mathematical Expression Omitted~, |Mathematical Expression Omitted~ and |BG.sub.*~. As indicated in figure 1, irrespective of whether the role of working capital finance is brought into consideration, the |ADS.sup.1~ schedule shifts the same vertical distance as the |ADS.sup.2~ schedule does, but both |ADS.sup.1~ and |ADS.sup.2~ shift by more than BG shifts.(6), 7 As is evident in figure 1, the domestic output will increase from |y.sub.0~ to |y.sub.1~ if the interest-sensitive supply effect is neglected and will decrease from |y.sub.0~ to |y.sub.2~ if the negative effect of interest rate on aggregate supply is substantially dominant.

These opposite results can be intuitively illuminated by examining the aggregate supply function. An expansion in government spending accompanied with an equal increase in taxes will stimulate both domestic price and interest rate. If the effect of supply-side interest rate is ignored, in response to the increased domestic price, the output will be expanded. In contrast, if the interest rate effect on aggregate supply is introduced, the increased interest rate will create an additional contractionary impact on production. Provided that the interest rate effect of the latter surmounts the price effect of the former, an expansion in government spending with a balanced government budget will definitely have a negative impact on domestic output.

IV. Concluding Remarks

By extending the standard AD-AS analysis, this paper reexamines the conventional belief concerning the balanced budget multiplier through introducing the role of working capital on production, which usually receives wide attention in the structuralist macromodel. It is found that the conventional conclusion may not be valid if the negative interest-rate effect on aggregate supply enters the picture. More specifically, a tax-financed expansion in government spending will contribute a negative impact on income, provided that the interest-sensitive effect on aggregate supply is substantially dominant. This result is sharply contrary to the conventional belief.

Notes

1. To our knowledge, the only exception is Holmes and Smyth (1979), in which the balanced budget multiplier may be negative if the effects of the stock of bonds on expected income and liquidity are taken into the analysis.

2. Holmes and Smyth (1972) argue that the transactions demand for money should be a function of disposable income rather than national income based on the ground of theoretical and empirical viewpoints. It can be easily shown that the conventional belief will be reinforced by considering the argument of Holmes and Smyth (1972). For simplifying the analysis and emphasizing the role of the interest-sensitive effect on aggregate supply, we abstract this effect from the analysis.

3. As is conventional in simple macro models, our model is a one-commodity model. The economy's aggregate price level (p) thus is also used to denote the price of a representative firm's output. This point is raised by an anonymous referee.

4. Combining the first three equations in (9) and deleting r as well as p, we can obtain

|Mathematical Expression Omitted~

Thus, the slope of the ADS curve is

|Mathematical Expression Omitted~

Moreover, it can be easily derived from the above equation that

|Mathematical Expression Omitted~

5. From the fourth equation in (9), we have

|Mathematical Expression Omitted~

Comparing |Mathematical Expression Omitted~ with |Mathematical Expression Omitted~ in footnote 4,

it gives

|Mathematical Expression Omitted~

6. It follows from footnote 4 that

|Mathematical Expression Omitted~

And from the fourth equation in (9), one obtains

|Mathematical Expression Omitted~.

7. It is obvious from footnote 6 that the shifts of the AD|S.sup.1~, AD|S.sup.2~, and BG curves depend on y. Therefore, in figure 1, the shifts upward from AD|S.sup.1~, AD|S.sup.2~, and BG should not be parallel.

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