BALANCED BUDGET MULTIPLIER WITH INDIRECT TAXES ..., Lecture notes of Economics

Download BALANCED BUDGET MULTIPLIER WITH INDIRECT TAXES ... and more Lecture notes Economics in PDF only on Docsity! BALANCED BUDGET MULTIPLIER WITH INDIRECT TAXES UNDER IMPERFECT COMPETITION Ramén J. Torregrosa Montaner* Universidad de Salamanca Resumen: Se presentan dos contraejemplos a las propiedades keynesianas atri- Abstract: buidas a la competencia imperfecta en modelos de equilibrio general. En particular, bajo los dos tipos habituales de impuestos indirectos, se obtiene una relacién no positiva y no creciente entre las magnitudes del multiplicador con presupuesto equilibrado y del bienestar con respecto al poder de mercado This paper presents two counter-examples to the Keynesian features attributed to imperfect competition in general equilibrium models. In particular, by considering indirect tax rates, a non possitive and mono- tonically non-increasing relationship between the magnitude of both the balanced budget and welfare multipliers and market-power is ob- tained. JEL Classifications: E12, E62, L1é Fecha de recepcién: 01 TV 2002 Fecha de aceptacidn. 27 VIIT 2002 1 am grateful to C. Pita for her helpful comments and suggestions. I am also indebted to the Instituto Valenciano de Investigaciones Econémicas (IVIE). The usual caveat applies.rtorregr@usal.es 4 ESTUDIOS ECONGMICOS 1. Introduction General equilibrium models with imperfect competition have been used as an explanation of some Keynesian features with fully flexi- ble prices. In this line, papers such as Hart (1982), Blanchard and Kiyotaki (1987), Dixon (1987) and, Mankiw (1988), among. others, explore the effect of different market power settings on the macroeco- nomic multipliers, reaching a positive and monotonically increasing relationship between the balanced budget multiplier and the degree of market power. A common setup of these models is that the govern- ment can resort to profits or lump-sum taxation to balance its budget. In this framework imperfect competition works as the only source of inefficiency which generates a space for public intervention. This in- sight is supported on the basis that fiscal policy does not distort rela- tive prices in the margin. This statement calls into question whether these Keynesian features of the multiplier remain unchanged under distortionary tax schemes. Within this trend, Molana and Moutos (1992), and Heijdra, Ligthart and Ploeg (1998) find non-positive mul- tipliers for labor income tax rates, whereas Torregrosa (1998), for the same tax rates, proves that this multiplier can be monotonically de- creasing with respect to market power. Considering this point of departure, this paper deals with the re- lationship between the balanced budget multiplier and market power, for indirect, (ad-valorem and excise) tax rate schemes, providing an- other counter-example to the Dixon-Mankiwé monotonicity result. The paper is structured as follows. In section 2, the model is pre- sented and both the output and the welfare multipliers are calculated in their general form. Sections 3 and 4 develop these multipliers for both the ad-valorem and excise tax rates respectively. Finally, section 5, summarizes with the final comments. 2. The Model and Multipliers Let us consider an economy formed by two commodities: leisure (con- sidered as the numbraire) and a composed commodity produced from labor; n +2 independent agents: the representative consumer, the government and n non-competitive firms. The former two agents constitute the demand-side of the economy and the latter the supply- side, according to the following assumptions: (2) Household preferences are represented by a separable utility function. On the one hand, a Cobb-Douglas sub-utility function over BALANCED BUDGET MULTIPLIER = 7 —slt-—-H. (14) The increase in output due to a raise in government purchases is affected, first, by an income effect through the change in profits and, second, by a price effect that results from an increase in the tax rate needed to finance the higher government purchases. Notice that equation (14) captures the main difference with the lump-sum taxa- tion models quoted in section 1. In fact the first two terms of equation (14) are just the Dixon-Mankiw’s multiplier. The last term adds the distortion due to indirect tax rates, whose effect is the opposite. Finally, it is interesting to study the effect on welfare of this boost to the economy. Substituting equations (3) and (4) in equation (1) the indirect utility function is obtained VQ. 7,9) = (0 + )p"* + 8(9), where y = a*(1—a)!~*. Differentiating with respect to g and taking into account equation (3) we obtain Wa fat ee o 5 ig 7? (4 cB) ae, (15) which represents the impact of the balanced budget expansionary policy on welfare. As can be observed, the positive effect on welfare due to larger government purchases is diminished by the change in consumption. This change is motivated by a price increase and a decrease in profits both generated by the change in the tax rate. It is necessary to remark that this effect on welfare is the opposite to that predicted by Keynes. This is because, according to Keynes, the balanced budget expansionary policy should not cause changes in welfare. The next sections are devoted to computing these effects for both the ad-valorem and the excise tax rates. 3. Balanced Budget Expansionary Policy Under Ad-valorem Tax Rates In this case Ry = tp(Q)a, with 0 < t < 1. Thus, according to equation (9), the equilibrium price is i "= 7-0-9) “) 8 ESTUDIOS ECONOMICOS Due to equations (5) and (8), equilibrium government purchases are given by g=tQ, (17) and aggregate profits by Be ~ Top @. (as) In order to compute the balanced budget multiplier defined in equation (14), the variations on profits and price of the balanced budget expansionary policy must be calculated. First, from equation (18), — pH dg” dn w_aQ ag (19) Second, to obtain the effect on price, let us start computing the effect of such an expansion on the tax rate consistent with the gov- ernment’s budget constraint given by equation (17), which is a olf, 4Q a #-5(1 2). (20) Thus differentiating equation (16) with respect to g, and taking into account equation (20), dp L =) FoF a fi). Q1 dg (1-#)Q ( dg (1) Substituting equations (19) and (21) in equation (14), the output balanced budget multiplier equals zero, i-e., aQ _ dg 0. This means that a balanced budget expansionary policy has.no effects on output (employment). The explanation of this total crowding out effect, under ad-valorern tax rates, is that this boost to the economy increases both government’s demand and prices, in such an amount that the decrease in consumption equals the increase in the govern- ment’s demand. Hence, firms do not change either their output level or profits (substituting the result in equation (19), 42 = 0). The BALANCED BUDGET MULTIPLIER 9 effect on price is calculated differentiating equation (21) with respect to g, which is dp dg =HQ This allows us to compute the effects of the balanced budget expan- sionary policy on the welfare. Then, substituting the multipliers in equation (15), taking into account equation (13) and (17) and oper- ating, the following equality holds >a. av _ ow l-@ ay eo. (22) As can be seen, a balanced budget expansionary policy under ad-valorem tax rate affects welfare in two ways: a positive effect de- rived from the increase in government purchases, and a negative effect arising from the increase in price due to the increase in the tax rate. Finally, the direction in which the effect of the balanced budget ex- pansionary policy on the welfare changes with respect to the degree of market power can be computed differentiating equation (22) with respect to ys ~a dP 8 = yf] at (1 = a)p om Since, according to equation (16), dp dp a the effect of the balanced budget expansionary policy on welfare is monotonically decreasing with respect to the degree of market power. 4, Balanced Budget Expansionary Policy Under Excise Tax Rates In this case Ry = tq; with 0 < ¢ < 1,1 Thus, according to equation (9), the equilibrium price is 1 Despite the fact that ¢ can be greater than one, it is assumed that t < 1 This is because the model is expressed in units of leisure, Thus, 6 > 1 would mean an excise tax rate higher than the current wage. This condition is also compatible with the fact that household expenditure is higher than public expenditure. Indeed, 12 ESTUDIOS ECONO6MiCOs Conclusions In this paper, both the monotonicity of the output multiplier and the effects on welfare of a balanced budget expansionary policy have been analyzed under the two main indirect taxes. The main contributions of this paper are: First, for the ad-valorem tax rate scheme, the output multiplier equals zero, which means that changes in public purchases have no effect on output, reaching a total crowding out effect independent of the degree of market power. The explanation of this crowding out effect is that the government’s expansionary policy increases the price (through taxes) in such way that consumption falls in the same proportion as the increase in government purchases. With respect to the effect on welfare, this is monotonically decreasing with market power, which is opposite to that predicted by Keynes. Secondly, in the case of an excise tax rate, the results are related to the market power in the opposite way to the conclusion reached by Dixon (1987) and Mankiw (1988) for non-distortionary taxation. The output balanced budget multiplier is negative and monotonically decreasing with respect to market power. The reason for this is that an increase in the excise tax rate distorts relative prices reducing out- put in greater proportion than the increase in public expenditure. This negative effect also increases as the degree of market power in- creases. Regarding welfare the effect of a government expansionary policy is monotonically decreasing with respect to market power as in the former case. In conclusion, Keynesian features attributed to the general equi- librium models with fully flexible prices and imperfect competition depend almost entirely on the tax scheme considered. It is true that market power causes inefficiency but it is also true that some taxes might do so, too. In this sense, the government could be using an inefficient tool to amend a market failure. References Blanchard, ©. and N. Kiyotaki (1987). “Monopolistic Competition and the Ef. fects of Aggregated Demand”, American Economic Review, 77, pp. 847-666. Dixon H. (1987). 4 Simple Model of Imperfect Competition with Watrasian Features, Oxford Fconomic Papers, 39, pp. 143-160. Hart, O. (1982). "A Model of Imperfect Competition with Keynesian Features”, The Quarterly Journal of Economics, 97, pp. 109138. BALANCED BUDGET MULTIPLIER = 13 Heijdra, B. J., J. E. Ligthart,and F. van der Ploeg (1998), Fiscal Policy, Dis- tortionary Taxation, and Direct Crowding out Under Monopolistic Compe- tition, Oxford Economic Papers, 50, pp. 79-88. Mankiw, N. G. (1988). “Imperfect Competition and the Keynesian Cross”, Eco- nomics Letters, 26, pp. 7-13. Molana, H. and T, Moutos (1992). A Note on Tazation, Imperfect Competition and the Balanced Budget Multiplier, Oxford Economics Papers, 44, pp. 68 7A, Torregrosa, R. J. (1998). “On the Monotonicity of Balanced Budget Multiplier Under Imperfect Competition”, Economics Letters, 59, pp. 331-335.