Review of Economics

Review of Economics 2016; 67(3): 255–262

Gerasimos T. Soldatos*

The Laffer Curve, Efficiency, and Tax Policy: A Note DOI 10.1515/roe-2016-0006

Abstract: This short article underlines the efficiency considerations reflected by a Laffer curve. In a static context in which inflation is assumed away, the Laffer curve describes what would the response of tax revenue to tax rate change be under increasing inflation if there were allocative efficiency, i. e. given perfect competition and full-employment output. The link between market structure and state of economic activity thus emerges as a critical determinant of the shape of Laffer curve. Under imperfect competition, the entire Laffer curve would reflect how the business “leadership” having emanated from the prevailing market structure, uses taxation as a means of higher profit earning capacity. Keywords: Laffer curve, efficiency, macroeconomic performance, tax policy JEL Classification: D40, E31, E32, H21, H32

1 Introduction The literature on the Laffer curve, as reviewed lately by KAZMAN (2014), points to many factors influencing the shape of this curve. One of them should be the conditions of efficiency under which the Laffer curve is studied. Yet, this is a factor overlooked by the literature. This short article underscores the issue of efficiency, because allocative efficiency is related to perfect competition, and once it is found to be related to Laffer curve too, so should the market structure in general be associated with this curve. This is important since the real world in which the presence of Laffer curve is documented, is one of the X-inefficiency of market concentration, meaning that direct taxation affects and is affected by market power. Consider, for instance, the case of corporate income tax, for which LIU and ALTSHULER (2013, 215) find that: “labor bears a significant portion of [its] burden… [and] that the elasticity of wages with respect to the corporate marginal effective tax rate increases with industry concentration”. Presumably, this burden

*Corresponding author: Gerasimos T. Soldatos, American University of Athens, 15232 Athens, Greece, E-mail: [email protected]

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Gerasimos T. Soldatos

strengthens the reduction of leisure and consumption induced by the tax on salaries and wages. And, it makes the income inequality caused by monopoly power (COMANOR and SMILEY, 1975) even greater. This, in turn, increased income inequality implies according to BENASSI, CELLINI, and CHIRCO (2002) weakening demand and increasing concentration even further. That is, we have a chain of reactions to the tax that would have been predicted by New Keynesian scenarios à la COSTA and DIXON (2011), according to which the greater market concentration is, the lower the real wage and hence leisure and consumption are, (and the higher the fiscal multiplier becomes though it remains less than one). To have tax authorities reflecting upon matters like these before acting based on information from some Laffer curve, there has to be a connection of this curve with the X-inefficiency of market concentration. This link is what this note attempts to trace in the next section based on a Cobb-Douglas production technology. DENICOLO (1988) has shown that such a production function results in an upward sloping Laffer curve all the way up to t = 1, where t is the tax rate. But, this is not the point here, the Cobb-Douglas case is analytically simple, and so good enough to make our efficiency point. The precise way the Laffer curve is linked then to imperfect competition, is examined by evaluating in the concluding Section 3 the empirical evidence about this curve in the light of the efficiency result.

2 Formal considerations Let Y stand for the tax base produced according to the Cobb-Douglas technology, Y = La K b

(1)

T = tY

(2)

T = tLa K b

(3)

so that tax revenue,

is,

where L is labor, K is capital, and constants a and b are the corresponding output-income elasticities. Therefore, the total differential of ð2Þ, ΔT = YΔt + tΔY in conjunction with the total differential of ð1Þ,


(4)

The Laffer Curve, Efficiency, and Tax Policy

ΔY = a

257

ΔL ΔK Y +b Y L K

yield, ΔL ΔK Y + bt Y) L K ΔT t ΔL t ΔK =Y 1+a +b Δt Δt L Δt K ΔT = YΔt + at

(5)

which is the slope of the Laffer curve in the t − T space. Next, if the incomes of L and K are w and r, respectively, implying a production cost, C = wL + rK (6) its minimization with respect to L and K given ð1Þ, gives that: 1

L = Ya+b

ar a +b b

1

K = Ya+b

(7)

bw bw ar

a +a b (8)

which when inserted in ð6Þ give the cost function, 1

a

b

C ðY, w, rÞ = θY a + b wa + b ra + b with

(9)

"

# aa +b b ba +a b + θ= b a

Totally differentiating ð7Þ and ð8Þ, one obtains that: ΔL 1 ΔY Δr Δw = +b −b L ða + bÞ Y r w ΔK 1 ΔY Δw Δr = +a −a K ða + bÞ Y w r which when inserted in ð5Þ, give after some operations that: ΔT t ΔY =Y 1+ Δt Δt Y

(5′)

This is the slope of the Laffer curve under productive efficiency. Letting P be the price level, and assuming perfect competition, an alternative expression of this slope based on allocative efficiency may obtain by noting


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that from the profit maximization condition, P = ∂C=∂Y, one may derive the change in Y in response to a change in P by solving in line with MOSS (2015) ∂C Δ ∂Y ΔP = ðΔL + ΔK Þ ΔY Consequently,

∂C ΔL + ΔK ΔY = Δ ∂Y ΔP

(10)

which when inserted in ð4Þ gives ∂C ΔL + ΔK ΔT t ∂C ΔL + ΔK ΔT = tΔ + YΔt ) = Δ +Y ∂Y ΔP Δt Δt ∂Y ΔP or taking the marginal cost from ð9Þ, 1 − ða + bÞ ΔT t θ ΔL + ΔK a b a + b a + b a + b =Y + Δ Y w r Δt Δt a+b ΔP The total differential of the marginal cost is: ∂C θ θð1 − a − bÞ 1−a−b a b Δ =Δ ΔY Y a + b wa + b r a + b = 2ða + bÞ − 1 ∂Y a+b ða + bÞ2 Y a + b θa θb + Δw + a Δr b 2 a + b ða + bÞ2 ra + b ða + bÞ w

(11)

(12)

But, since for the Cobb-Douglas function: b

Δw bwa + b θa θb =− , Δw + a a Δr = 0 b Δr ar a + b ða + bÞ2 r a + b ða + bÞ2 wa + b it follows for ð11Þ that: ∂C θð1 − a − bÞ ∂C θð1 − a − bÞ 1 − ða + bÞ ΔY = = Δ ΔY ) Δ Y a+b 2 2ða + bÞ − 1 ∂Y ∂Y Y ða + bÞ2 ða + bÞ Y a + b Hence ð10Þ becomes: " # ΔT t θð1 − a − bÞ 1 − ða + bÞ ΔY ΔL + ΔK =Y + Y a+b Δt Δt ða + bÞ2 Y ΔP It will be equal to ð5′Þ if "

# 2ða + bÞ − 1 θð1 − a − bÞ ΔL + ΔK = Y a+b 2 ΔP ða + bÞ


(10′)

(13)


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The right-hand side of ð12Þ is positive, and so should the left-hand side be. This is true only when 1 − a − b > 0, i.e. under decreasing returns to scale, because according to empirical evidence, there is a threshold inflation below which both, ΔL=ΔP and ΔK=ΔP, are positive, and above which, both are negative (KHAN and TARIQ RANA, 2014). But, note that under constant returns, the left-hand side of ð12Þ becomes zero and the right-hand side equal to Y > 0. This discrepancy increases with increasing returns, because the left-hand side of ð12Þ becomes negative and the exponent of Y in the right-hand side becomes greater than 1, 2ða + bÞ − 1

implying a Y a + b > Y. To interpret these results, note that they suggest schematically that, to every ray ’ towards a Laffer curve in the t − T space representing ð5′Þ, corresponds a ray ψ of equal length above ’ in the t − T − ða + bÞ space, representing ð10′Þ, the length being the distance between the origin of the axes and the point of the curve ’ meets it. Schematically, because the expressions become indeterminate when a + b = 0 or when ΔP = 0. The fact remains that every point on a Laffer curve is associated with different ða + bÞ, which sum increases as t increases. In other words, what our results appear to suggest is that a Laffer curve in the t − T space reflects productive only efficiency, and every point on it relates to different allocative efficiency. Nevetheless, since neither the production nor the cost function are assumed to be altered by taxation, and since the allocatively efficient input mix should thereby be the one at a + b = 1, differences in allocative efficiency signifies differences in non-normal-profit profitability originating in the change of the general price level. If ΔP = 0, if price changes were disregarded from our calculations, the optimal input mix would be that under a + b = 1: it is that ΔP ≠ 0, which complicates the picture as described in the last paragraph. The “third” axis that measures ða + bÞ, registers really the inflation rate, being null at the origin of the three axes; it is there where ða + bÞ = 1. So, every point on a Laffer curve is associated with different inflation rate, which rate increases as t increases. And, if this curve is bell-shaped as implied by Rolles’ theorem in mathematics, the curve peaks at the threshold rate that reverses the signs of ΔL=ΔP and ΔK=ΔP, because ΔP on the third axis is always rising and hence, only this sign reversal can explain the decline of tax revenue after this threshold point. This is the point beyond which supra-normal profit starts declining, taking its toll on factor incomes and influencing labor and investment motives. The Laffer curve describes what would the response of T to a change in t be under increasing inflation if there were productive and allocative efficiency, i. e. given full-employment output. This big “if” says that when tax policy is considering real, deflated quantities, and plans based on them, it presumes implicitly an environment of Walrasian-Lindahl general equilibrium, in which case policy should not change.


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If Y = 100, P = 100, and t = 10 % on PY = 10,000, T will be equal to 1,000, while T = 1,021.2 may be collected when Y = 100, P = 111, PY = 11,100, and t = 9.1 %. This tax-cut raises nominal tax revenue, but lowers the real revenue vis a vis t = 10 % by 1,110–1,021.2 = 88.8 monetary units. There is need, indeed, for policy design based on deflated quantities; it is a must, a necessary condition, but not a sufficient one since it assumes away the state of economic activity and the market structure of the economy under which income is generated and distributed. Inflation and by Phillips curve unemployment affect market efficiency and vice versa, and according, for example, to MIRRLEES et al. (2011), tax design should not be disregarding its nexus with efficiency. Yet, tax design is approached by public finance in general as an applied microeconomics and public administration issue, which, of course is a proper approach, but microeconomic and tax agency behavior are intimately related to macroeconomic performance. It is to this link that our results herein point. The next section concludes this article with a discussion of this link.

3 Concluding remarks To get a glimpse of the link between Laffer-curve based tax policy and macroeconomic developments, let us contemplate our results in connection with the discussion of the empirical findings regarding this curve. Let us assume for a moment that price-variation induced profitability signifies deviation from the perfectly competitive case; it originates, that is, in imperfect competition. After all, imperfect competition is one of the assumptions underlying the Phillips curve, (the other is sticky prices; CARLSTROM and FUERST, 2008). Inflation becomes endogenous to market power and hence, in one-to-one correspondence with the sum ða + bÞ, given that a and b are income elasticities. Real output, production is now constantly changing, manipulated along with prices by businessmen so as to be meeting their profit aspirations as t changes. From this point of view, Laffer curve results herein point to a concern of the taxpayer related to profitmaking, and the profession of the taxpayer matters. A worker, for instance, has no such a concern at all, and his Laffer curve should be flat. The non-wage earner is the one who should care about the link between taxes and profits or rents. A monopolist, for example, would be sensitive to Δt to the extent he can avoid it in case of a tax increase, or cannot benefit from a tax cut. In either case, the profit incentive dictates some kind of change in the way business is conducted. Therefore, our results corroborate the well-documented finding that only high income earners respond to tax rate changes through mainly tax avoidance



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and/or switching between different forms of income. But, the same reaction workers can have by allocating more labor time to hidden economy still legal activities, since this involves manipulation of the tax base and a shift of income generation to an alternative source as well. This is a well-documented pattern of behavior too, (BAJADA and SCHNEIDER, 2005). From this point of view, what the increased responsiveness of high income earners to tax changes indicates is considerably increased opportunities to react in the same way a laborer would react. Within the context of this note, this means that as t increases, most of the accompanying increase in ða + bÞ comes from increasing b. In other words, the entire Laffer curve reflects really how high income earners use taxation as a means of even higher income earning capacity. They are mostly the business “leadership” having emanated from the prevailing market structure, they reflect and represent this structure, and influence macroeconomic performance. This actually is in line with the empirical evidence on the Laffer curve (KAZMAN, 2014), which evidence reflects in addition empirical findings like those from JENKINS et al. (2012) and notably by PIKETTY (2015) about the increasing income inequality of our times. The consultation of empirical evidence on Laffer curve by tax agencies towards the design and redesign of the tax system should be taking into account such considerations as well. This is the main message of this article. Practically, it may not be of much help because “the relationship between inequality and taxation is mixed, at best” (KULA and MILLIMET, 2010, 417). What is for sure from endogenous growth theory as documented empirically by e.g. MO (2000, 293), “income inequality has significant negative effect on the rate of GDP growth”, and taxation should be one of the means against this very fact. For example, as remarked in the introductory section, there appears to be in operation a New Keynesian version of the national and international economy. Should tax policy be conducted as prescribed by this school of thought? The answer to this question lies beyond the scope of this paper, but one thing the spirit of the whole discussion makes sure is that taxation should be (i) inspired by the overall macroeconomic policy, (ii) accompanied by anti-monopoly policy. It is the spirit of the quest for efficiency as the driving force behind income and wealth redistribution, which is welfare-enhancing by itself and by sustaining economic growth. According to ŠTIKAROVÁ (2014), there is a significant amount of work supporting this thesis as much as its refutation, which is one more perspective under which our earlier discussion may be appreciated. Acknowledgment: This article has benefited from the comments and suggestions of two anonymous referees. Any remaining errors or omissions are my own.


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