The quantification of the efficiency loss of the tax.

Predescu, Antoniu ; Predescu, Iuliana ; Toader, Stela 等

1. INTRODUCTION

The stimulus given to a real economy by the fiscal policy (Mishkin, 2004), when the latter amplifies the 'area' and the 'depth' of the total fiscal debt acts as a deterrent not only for economic growth (generally speaking), but even for the effectiveness of fiscal policy itself.

This effect, known as efficiency/deadweight loss of the tax, can be measured: as such, the formulae used for this must take into account the influence of demand, respective supply elasticity over the real economy, since those elasticities practically materialize the (increased) fiscal pressure, modifying, consequently, the real economy (Lipsey&Chrystal, 1999).

In this paper, we employed the method of treating the efficiency loss of the tax, and, in a certain degree, the elasticities themselves as 'functions' of price, e.g. of the price paid by the consumers and received by the producers whenever a certain product is sold--and bought--, using a geometric framework for the economic dynamics we are quantifying.

What remains to be researched, in the future, is the size, on one side, of a given elasticity for which this loss is at a minimum, and, on the other side, of the period of time during which a given dimension of the efficiency/deadweight loss of the tax is not bearable.

2. AGGREGATE DEMAND AND AGGREGATE SUPPLY

The elasticity of both demand and supply relative to the price, when a tax having a significant impact on the real economy is introduced, represent nothing less than a lever 'linking' that tax with the future dynamics of the real economy (McConnell et al., 2003), assuring its functionality in the short and long terms.

From the perspective of the aggregate demand, the starting point of the analysis is the following: we can consider aggregate demand is, in essence, inelastic, on both the short term and the long one. In fact, as regards certain products, demand, even aggregate demand, is, at least on short term, inelastic when the price is on the rise (Schiller, 2003).

But, also in practice, the aggregate demand of certain goods (e.g. bread--in Romania), in the long term, is surely elastic.

As such, the assumed constant rise of the financial effort of taxpayers for paying the fiscal debt is under no circumstance coupled with, as complement of, the continual rise, and at least in the same proportion, of the size of the taxpayers' incomes (e.g. wages), as a response to the (general) surge of the prices. Therefore, the conclusion is even if a certain product is, practically, indispensable to the consumer (that is, the buyer), if its price is on the rise in the long term the demand will become elastic; for all the products (of the real economy), the aggregate demand is a fortiori elastic, in the long term (Maddala&Miller, 1989).

The elasticity of the aggregate supply is likewise important here. First of all, this latter elasticity cannot be conceived, the (general) level of prices being raised by the fiscal policy or not, but in an environment of increasing prices. And yet, the rise of the aggregate demand, and of the production capacity cannot be realised over night, so that aggregate supply is, in such conditions, in the short term, inelastic: larger profits are surely wanted, but--without expanding production--unreachable.

In the long term, the aggregate supply is inextricably linked with the aggregate demand. And, even if it can be assumed the aggregate demand is, in the long term, even inelastic (with far more probability, that it is at least 'a little' elastic), the consumers will buy (practically) as much as before the rise of the price level, or, more likely, almost as much, respective substantially less after the prices soared, while the firms will produce an equal, or, more likely, slightly smaller quantity than the quantity obtained, and sold, before the introduction/rise of the tax, respective substantially less after the prices soared.

The arguments which prove correct that, in the long term, the aggregate demand is elastic were exposed theretofore. But, even if, in extremis, this statement would be false, it is clear the aggregate supply is itself, in the long term, elastic.

In our analysis, quantifying the size of the incomes of the taxpayers after the tax is needed: and also to emphasize a new fiscal pressure determines a drop in the aggregate output, and of the equilibrium (quantitative) level of the real economy (Goolsbee, 1997), both the aggregate demand and supply leaving their mark in the process.

3. THE PRICE--LINK BETWEEN THE REAL ECONOMY AND THE FISCAL POLICY

The sum paid that accounts for the tax is quantifiable starting from the observation the efficiency loss of the tax presumes a drop in the aggregate output, on one side--the size of its initial level is larger than after the introduction/increase of a tax--, and the rise of the (general) level of prices, on the other side.

Both producers and consumers will bear, price-based, their share of the total fiscal debt, forcefully imposed (on the latter, e.g. with V.A.T.) or not, income taxation being direct (when the prices will surely rise) or indirect--if, like today, in addition, the consumer bear the brunt of the fiscal debt. In other words, charging/paying those prices acquits, in the market economy, the fiscal debt, by the means of the real economy itself (Romer, 1996), which yields to the Treasury what can be named the net price paid by consumers.

The price paid by the consumers can be named demand enforced price ([P.sub.D]): from the unit price they pay, as tax, a share of that price--labelled [DELTA][P.sub.D]--, with which the firms raise the price, to the respective government authorities (McConnell et al., 2003). The price paid by the producers can be labelled supply enforced price ([P.sub.S]): less than the (nominal) value of the unit price can be used by them, giving the deduction from it of the sum charged by the fiscal authorities--labelled [DELTA][P.sub.S]. Thus, the unit value of the newly imposed tax is equal with:

[T.sub.ax] = [P.sub.D] - [P.sub.S] = (P + [DELTA][P.sub.D]) - (P - [DELTA][P.sub.S]) = [DELTA][P.sub.D] + [DELTA][P.sub.S] (1)

For the aim of the quantification of the paid tax, the size of this index ([T.sub.axT]) can be computed using the following simple formula ([XI] stands for output, and [[XI].sub.1] is the value of the output produced after the introduction, or the rise, of the tax/taxes):

[T.sub.axT] = [[XI].sub.1] x [DELTA][P.sub.D] + [[XI].sub.1] x [DELTA][P.sub.S] = [[XI].sub.1] x ([DELTA][P.sub.D] + [DELTA][P.sub.S]) (2)

Since a share of the tax is paid by the consumers and the other part of the tax is paid by the producers, the sum computed as financing the budget this way is the sum of those two payments: geometrically, the area composed by adding the two rectangles (from the graph below).

4. EFFICIENCY LOSS OF THE TAX-QUANTIFICATION

In order to quantify, further on, the efficiency loss of a tax we need to compute the value of the above mentioned deadweight loss (of the real economy too), for which we use the following graph:

[FIGURE 1 OMITTED]

To quantify the area of these two triangles we use, as basis of our calculations, the formula used for quantifying the area of a triangle: (base x height) /2. The base of the two triangles is equal with [DELTA][XI]; the height is equal with [DELTA][P.sub.D], respective [DELTA][P.sub.S]. From this, the value of the deadweight loss of the tax (denoted here as [L.sub.otax]) is obtained using the following formula:

[L.sub.otax] = [DELTA][XI] x [DELTA][P.sub.S]/2 + [DELTA][XI] x [DELTA][P.sub.D]/2 = [DELTA][XI] x ([DELTA][P.sub.S] + [DELTA][P.sub.D])/2 (3)

[??][L.sub.otax] = [DELTA][XI] x [T.sub.ax]/2 (4)

The elasticities of demand, respective supply are required for computing the size of the variation in the demand/supply enforced prices ([DELTA][P.sub.D] and [DELTA][P.sub.S]); once inserted in the equation [L.sub.otax] can be quantified, these, of course, being not identical. As a result, firstly, we quantified the size of elasticity of demand, using the well known variables:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Similarly, the elasticity of supply is computed like this:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

It is known that [T.sub.ax] = [DELTA][P.sub.D] + [DELTA][P.sub.S]. It can be, thus, quantified the value of the efficiency/deadweight loss of the tax depending on the elasticities of demand and supply (relative to the price):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[??] [DELTA][XI] = [T.sub.ax] x [XI] x [[eta].sub.D] x [[eta].sub.S]/P x ([[eta].sub.D] + [[eta].sub.S]) (8)

5. CONCLUSIONS

The main mathematical conclusion is that the efficiency/deadweight loss of the tax can be quantified in the following manner:

[L.sub.otax] = 1/2 x [T.sub.ax] x [XI]/P x [[eta].sub.D] x [[eta].sub.S]/[[eta].sub.D] + [[eta].sub.S] x [T.sub.ax] (9)

[??][L.sub.otax] = 1/2 x [T.sub.ax.sup.2] x [XI]/P x [[eta].sub.D] x [[eta].sub.S]/[[eta].sub.D] + [[eta].sub.S] (10)

The second conclusion is an economic principle that can be labelled "focus on the number": the loss quantified here grows one more time whenever the fiscal authorities decide to increase the fiscal pressure again.

From this point of view, it must be noticed the direct taxation is far more 'harmless' to the real economy than the indirect taxation is, given the current fiscal behaviour of raising more often the level of VAT or excises than that of direct taxes.

6. REFERENCES

Goolsbee, A. (1997). Taxes, Organization Form and the Deadweight Loss of the Corporate Income Tax, Journal of Public Economics, Vol. 69, (1997) p. 144, ISSN 0047-2727

Lipsey, R. G.& Chrystal, K. A. (1999). Economia Pozitivd, Editura Economica, ISBN 973-590-088-2, Bucuresti (Romania)

Maddala, G.S.& Miller, E. (1989). Microeconomics: Theory and Applications, The McGraw-Hill Companies, Inc., ISBN 0-07-039415-6, U.S.A.

Mishkin, F.S. (2004). The Economics of Money, Banking and Financial Markets (7th edition--The Addison-Wesley series in economics), Pearson Addison-Wesley, ISBN 0-321-12235-6, U.S.A.

Predescu, A., Ilie, V., Predescu, A.; Toader, S. & Ionescu, G.H. (2010). Measuring the Effect of Fiscal Policy and Economic Growth through the Real Wage, Metalurgica International, Vol. XV, No. 1 (January 2010) 29-32, ISSN 1582-2214

Romer, D. (1996). Advanced Macroeconomics, The McGraw-Hill Companies, Inc., ISBN 0-07-053667-8, U.S.A.

Schiller, B.R. (2003). The Economy Today (9th edition), The McGraw-Hill Companies, Inc., INTERNATIONAL EDITION ISBN 0-07-115114-1, New York