Are the Laffer curve and the green paradox mutually exclusive?

• Published date: 01 October 2017
• Date: 01 October 2017
• DOI: http://doi.org/10.1111/jpet.12242
• Author: Stefano Bosi,David Desmarchelier

Received: 31 October 2016 Accepted: 31 January 2017

DOI: 10.1111/jpet.12242

ARTICLE

Are the Laffer curve and the green paradox

mutually exclusive?

Stefano Bosi1David Desmarchelier2

1EPEE,University of Evry

2BETA,UMR CNRS 7522, University of Lorraine

StefanoBosi, EPEE, University of Evry, Evry,

France(stefano.bosi@univ-evry.fr).

DavidDesmarchelier, BETA,UMR CNRS

7522,University of Lorraine, Nancy, France

(david.desmarchelier@gmail.com).

Theauthors acknowledge the financial support of

theLabEx MME-DII (No. ANR11-LBX-0023-01).

In this paper,we study the relationship between the Laffer curve and

the green paradox in the context of a Ramsey model with endoge-

nous labor supply in which pollution increases consumer demand

(through a compensation effect). We find that—in the long run—the

conditions under which a Laffer curve and a green paradox emerge

are mutually exclusive. Indeed, the Laffer curveexists under a weak

compensation effect, while the green paradox requires a strong

effect. Also, we find that, in the short run, limit cycles may arise in

the presence of a Laffer curve, while they never occur under a green

paradox.

1INTRODUCTION

The Laffer curve (LC)is a well-known paradox first noted by Ibn Khaldun in the fourteenth century1but popularized by

Arthur Laffer in the late 1970s (Wanniski,1978). The LC represents the inverted U-shaped dependence of tax revenue

on tax rates.It demonstrates that two different tax rates—low and high—can produce the same revenue for the govern-

ment. LCs have been implemented in a number of theoretical models. Their introduction into the Ramsey framework

dates back to the mid-1990s (see, among others, Ireland, 1994; Nourry, Seegmuller,& Venditti, 2013; Schmitt-Grohé

and Uribe, 1997; Trabandt& Uhlig, 2011). Many tax schemes can generate LCs, but the basic idea is the following: A

higher tax rate on consumption can reduce the relative price of leisure, which decreases the labor supply and the level

of consumption, thereby reducing tax revenue.

In the environmental literature, the green paradox (GP) refers to a situation in which an environmentalpolicy, for

instance a carbon tax introduced to reduce polluting emissions, actually leads to an increase in these emissions (see

Sinn, 2008, among others). This surprising outcome can be understood as follows. Following Jensen, Mohlin, Pittel,

and Sterner (2015), let us consider an owner of fossil fuel who aims at maximizing her profit over time, and a govern-

ment which announces that a carbon tax will soon be introduced. The resource owner rationally expects her costs to

increase and therefore speeds up fossil fuel extraction, thus exacerbating environmental damage in the short term.

As pointed out by Jensen et al. (2015) in their updated survey,the GP emerges under different assumptions as a robust

feature—when agents behavestrategically in resource markets (Gerlagh & Liski, 2011), when resource and capital mar-

ketsinteract (Van der Meijden, Van der Ploeg, & Withagen, 2015), and when future policies are uncertain (Hoel, 2010).

1“It should be known that at the beginning of a dynasty,taxation yields a large revenue from small assessments. At the end of the dynasty, taxation yieldsa

smallrevenue from large assessments” (Ibn Khaldun, 1377, trans. 1989, p. 230).

Journal of Public Economic Theory.2017;19:937–956. wileyonlinelibrary.com/journal/jpet c

2017 Wiley Periodicals,Inc. 937

938 BOSI AND DESMARCHELIER

We introduce a new interpretation of the GP,focusing instead of the steady state of a simple Ramsey model with a

pollution externality but without any extractionactivity, that is, without natural resources. We assume that pollution

comes from consumption and that the government levies a carbon tax on consumption to pay for depollution. In the

case of endogenous labor supply, a higher consumption tax rate may lower demand sufficiently to generatean LC at

the steady state in a Ramsey economy (see Nourry et al., 2013; Schmitt-Grohé & Uribe, 1997; Trabandt& Uhlig, 2011).

Because the economyis located on the decreasing side of the LC, a higher green tax rate lowers tax revenues and depol-

lution investments, thus increasing pollution levels; in other words, a GP arises, because pollution levelsare positively

related to the green tax rate. This GP is new because (1) it does not appear in a resource extractioncontext and (2) it is

a static relationship (in terms of comparative statics) ratherthan a dynamic effect.

This new GP seems to be related to the existence of an LCbut, as far as we are aware, these two effects have so far

beenstudied separately in the literature. Our paper addresses the issue of their interaction. In particular, we investigate

whether they are mutually exclusiveor can coexist. In this respect, we consider a competitive Ramsey economy with

endogenous labor supply,in which a pollution externality from consumption in turns affects consumption behavior. In

addition, we let the government levya proportional tax on consumption to finance depollution expenditures.

It has been known since Heal (1982) that endogenous fluctuations may emerge through a Hopf bifurcation in the

near steady state of a Ramsey economywhen a pollution externality raises the marginal utility of consumption (the so-

called compensation effect identified by Michel & Rotillon, 1995). If pollution affects consumption demand, we expect

such cycles to occur in the near steady state. In this context, we focus not only on the interplay between the LC and

the GP,but also on its effect on the occurrence of endogenous cycles. In particular, a long-run analysis (comparative

statics) allows us to understand whether LC and GP can coexist or are mutually exclusive,while a short-run analysis

(local dynamics) connects the conditions required for GP,LC, and the emergence of limit cycles.

We find that while an LC does existin the steady state, it does not cause the GP; on the contrary, indeed, we show

that an LCis incompatible with a GP. Tograsp this surprising result, consider the GP jointly with a compensation effect

in preferences. A higher green tax rate raisesthe pollution level (GP) that fosters consumption demand (compensation

effect) and increases tax revenue, so there is no LC.

More precisely,we show that a weak compensation effect leads to an LC, while a strong compensation effect leads

to a GP.This result is interesting for policy makers because it suggests that, if the economy experiences an LC, there is

no GP,and consequently increasing green taxes will lower pollution levels.

Another finding is that taxation is welfare-improving in two cases: (1) when the compensation effect is weak (suffi-

cient for an LC) and households overestimatethe quality of the environment, and (2) when the compensation effect is

strong (sufficient for a GP) and households underestimate the quality of the environment.

In the short run, a compensation effect can giverise to a limit cycle near the steady state of a Ramsey economy (Heal,

1982).2We compare the conditions required for limit cycles (through a Hopf bifurcation) with those governingthe LC

and GP.We find that the occurrence of limit cycles implies the existenceof an LC, while these cycles are ruled out under

aGP.

The remainder of this paper is organized as follows. Sections 2–5 introduce the fundamentals of the subsequent

analysis. Section 6 studies the equilibrium, and Sections 7 and 8 analyze the steady state. Equilibrium transition and

bifurcations are considered in Section 9. The special case with constant elasticities is assessed in Section 10. Section

11 concludes. All the technical details (proofs) are grouped in Appendix A.

2FIRMS

The representative firm produces a single output. Its constant returns to scale technology is represented by an aggre-

gate production function

Y(t)=F(K(t),L(t)),

2Bosiand Desmarchelier (Forthcoming) find an opposite result in the case of an environmental Kuznets effect. In this context, limit cycles arise under a distaste

effect,and they do not under a compensation effect.