Fiscal policy under imperfect competition with flexible prices: An overview and survey
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Costa, Luís F.; Dixon, Huw David Article Fiscal policy under imperfect competition with flexible prices: An overview and survey Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Costa, Luís F.; Dixon, Huw David (2011) : Fiscal policy under imperfect competition with flexible prices: An overview and survey, Economics: The Open-Access, OpenAssessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 5, Iss. 2011-3, pp. 1-57, https://doi.org/10.5018/economics-ejournal.ja.2011-3 This Version is available at: https://hdl.handle.net/10419/44435 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en
Vol. 5, 2011-3 |February 1, 2011 | http://dx.doi.org/10.5018/economics-ejournal.ja.2011-3 Fiscal Policy under Imperfect Competition with Flexible Prices: An Overview and Survey Luís F. Costa ISEG (School of Economics and Management)/Technical University of Lisbon and UECE (Research Unit on Complexity and Economics) Huw David Dixon Cardiff Business School/University of Cardiff Abstract This paper surveys the link between imperfect competition and the effects of fiscal policy on output, employment and welfare. We examine static and dynamic models, with and without entry under a variety of assumptions using a common analytical framework. We find that in general there is a robust relationship between the fiscal multiplier and welfare, the tantalizing possibility of Pareto improving fiscal policy is much more elusive. In general, the mechanisms are supply side, and so welfare improving policy, whilst possible, is not a general result. Published as Survey and Overview JEL E62 Keywords Fiscal policy; imperfect competition. Correspondence Huw David Dixon, Cardiff Business School/University of Cardiff, Aberconway Building, Column Drive; Cardiff, CF10 3EU; United Kingdom, e-mail: [email protected]. Citation Luís F. Costa and Huw David Dixon (2011). Fiscal Policy under Imperfect Competition with Flexible Prices: An Overview and Survey. Economics: The Open-Access, Open-Assessment E-Journal, Vol. 5, 2011-3. doi:10.5018/economics-ejournal.ja.2011-3. http://dx.doi.org/10.5018/economics-ejournal.ja.2011-3 © Author(s) 2011. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany
conomics: The Open-Access, Open-Assessment E-Journal 1 Introduction In a perfectly competitive economy without market imperfections, any competitive equilibrium will be Pareto optimal. Hence there can be no efciency motive for macroeconomic policy. However, the presence of imperfect competition in the form of market power leads to an equilibrium which will in general be non-Pareto optimal, with levels of output and employment below competitive equilibrium. This leads to the tantalizing possibility that scal policy can be used to shift the economy to a new equilibrium which will Pareto dominate the initial equilibrium. In this paper we survey and explain the literature on imperfect competition and macroeconomics in the context of scal policy in a "real" model without money. This was one of the key pillars of New Keynesian macroeconomics in the 1980s and 1990s, alongside the nominal models with price and wage stickiness1. The main contribution of New Keynesian economics was to set imperfect competition at the heart of Keynesian economics and its current incarnation as the "New Keynesian/Neoclassical Synthesis". This marked a major departure from the approach of Keynes himself, especially Keynes (1936), who used a perfectly competitive market structure to give microfoundations to the supply side of the economy. Perhaps the two main reasons were (i) that the theory of imperfect competition was relatively underdeveloped at that time and (ii) Keynes's conviction that he was generalizing the existing theory with perfect competition and market clearing being a special case (hence the title of his work). Still in the 1930's, imperfect competition and macroeconomics would be mixed in Kalecki (1938) and in the Dunlop (1938) critique to the real-wage counter-cyclicity implicit in the General Theory. However, despite this promising start, four decades would pass before we can nd a signicant piece of work using imperfectly competitive microfoundations in macroeconomics. During the 1960's and the beginning of the 1970's some of the concepts and techniques that would allow the integration of imperfect competition in general-equilibrium models were developed, in particular Negishi (1961). In the second half of the 1970's we nd the rst attempts 1See Dixon (2008) which sets this strand of literature in the context of the wider New Keynesian approach. www.economics-ejournal.org 1
conomics: The Open-Access, Open-Assessment E-Journal to integrate these concepts in macroeconomic models. Nonetheless, their success was limited due to the "subjective-demand-curve" assumption2. The theory of effective demand with monopolistic price-setting in general equilibrium was developed by Bénassy (1976), Bénassy (1978). However, Hart (1982), was the rst model to operationalise the concept of the "'objective' demand curve" in a simple general-equilibrium model with imperfect competition (Cournot oligopoly for each good and monopoly unions), producing some "Keynesian" outcomes, namely equilibrium with under-employment (though not involuntary unemployment) and a multiplier mechanism for autonomous demand (a non-produced good in this case) that resembles the traditional Keynesian multiplier. Oliver Hart's work gives rise to a new generation of New Keynesian models3 characterised by the use of imperfect competition in general-equilibrium macroeconomic models. A few notable examples are Akerlof and Yellen (1985), Bénassy (1987), Blanchard and Kiyotaki (1987), Hall (1986), Mankiw (1985), Snower (1983), and Weitzman (1982). These and other papers were analysed in surveys of the literature written at the time: Dixon and Rankin (1994) or Silvestre (1993). Despite the fact that we can nd references to scal policy effectiveness under imperfect competition in all the above-mentioned papers, the systematic and focussed treatment of the problem, can only be found in the second half of the 1980's. In this survey, we analyse the effectiveness of scal policy in generalequilibrium models with the following features, along with the standard assumptions of fully rational agents, no uncertainty, and a closed economy: (1) there is imperfect competition in goods markets; (2) labour markets are perfectly competitive; (3) prices of goods and factors are perfectly exible4; (4) public consump2A subjective demand curve is simply one that is "perceived" by the rm. It can be subject to constraint that it passes through the actual price-quantity pair that occurs in equilibrium. However, this led to endemic multiplicity of equilibria. For a short survey of the literature see Dixon and Rankin (1995). 3The rst generation refers to contributions such as Fischer (1977) and Taylor (1979), especially interested in priceand wage-setting rules for relatively long periods (short-run ad hoc nominal rigidity). 4Os course the issue of scal policy in models with sticky prices has been the subject of much recent research, e.g. Correia et al. (2008), Linneman and Schabert (2003), Schmitt-Grohé and Uribe (2004). www.economics-ejournal.org 2
conomics: The Open-Access, Open-Assessment E-Journal tion has no direct effects on utilities and technologies of private agents5; (5) there is no agent heterogeneity. These assumptions allow us to study the effect of imperfect competition in goods markets on scal policy, isolating it from other factors. Therefore, we can present a set of theoretical models using the same framework in order to study the effects of changing a particular basic assumption. We will concentrate on the effects of scal policy in two main objectives: aggregate output and representativehousehold welfare. The choice for these two objectives, especially the rst one, is the usual one in the literature, but it is justied by the assumptions considered, as we will see throughout the survey. Section 2 is dedicated to simple static models and section 3 covers the dynamic models. Section 4 concludes. 2 Static Models In this section we develop a class of static general equilibrium models that nests most of the relevant literature on the topic. 2.1 The Microeconomic Foundations 2.1.1 Households There is a large number of identical households that maximise a utility function depending on the consumption of a basket of goods (C) and leisure (Z): max C;ZU=u(C;Z), (1) 5Additionally we assume a benevolent government, so we can abstract from political-economy issues. www.economics-ejournal.org 3
conomics: The Open-Access, Open-Assessment E-Journal which is a continuously twice-differentiable function, with6uC>0, uZ>0, uCC < 0, uZZ >0, and uCZ =uZC >0. The sub-utility is constant elasticity of substitution (CES): C=n1λ 1σ:Zn 0 c(j)σ1 σ:djσ σ1 , (2) where c(j), with j2[0;n], represents the consumption of variety j,σ>1 stands for the (absolute value of the) elasticity of substitution between goods, and λ2 [0;1]controls the consumers' level of love for variety: if λ=0, then there is no love for variety, when λ=1 we have the Dixit and Stiglitz (1977) case. Leisure is dened as what is left over from the unit endowment after working (L): Z=1L. (3) The budget constraint is given by w:L+ΠT=Zn 0 c(j):p(j):dj, (4) where wrepresents the nominal wage, Πprots, Tis tax, and p(j)is the price of good j. Taxes are a linear function of primary income: T=T0+t:(w:L+Π), (5) where t2[0;1)and T0<(1t):(w:L+Π). Since the CES function is homothetic, the representative household problem given by equations (1) to (5) can be solved in two steps: 6For sake of simplicity we use the following notation for partial derivatives: fx=∂f ∂x(x;y)fxy =∂2f ∂x∂y(x;y). www.economics-ejournal.org 4
conomics: The Open-Access, Open-Assessment E-Journal 1) minimising total expenditure, given the optimal choice for the quantity of private-consumption baskets (C)7; 2) maximising utility, given the optimal expenditure function. From the rst step we obtain the following demand function for each good: c(j) = p(j) Pσ :C n1λ, (6) where Prepresents the relevant price (or cost-of-living) index for the household given by P=1 n1λ:Zn 0 p(j)1σ:dj1 1σ , (7) and the optimal (minimal) expenditure function is given by P:C. Notice the demand for good jis decreasing with a constant price elasticity given by (in absolute value) σ, on the relative price of this good compared to the average (p(j)=P), it is increasing on aggregate consumption intentions (C), and it is not increasing on the mass of available goods (n), with an elasticity given by 1λ. From the second step we obtain: C=C(ωN;πN), (8) L=L(ωN;πN), (9) where ωNw:(1t)=Prepresents the real net wage, πN(Π:(1t)T0)=P π:(1t)τ0stands for net prots, equation (8) is the private consumption function where CωN>0 and CπN>0, and equation (9) represents the labour-supply 7This problem could be solved with a general sub-utility function C=C(n;[c(j)]n 0), as long as it still represents homothetic preferences over goods. However, for sake of simplicity we will keep CES preferences here, as they clearly dominate the literature. www.economics-ejournal.org 5
conomics: The Open-Access, Open-Assessment E-Journal function where LωNR0 and LπN<0.8Household consumption intentions are an increasing function of the real net wage (CωN>0) and also of the real non-wage income (CπN>0), both taken as given by households. The net real non-wage income has a negative impact on labour supply (LπN<0), but the effect of the real net wage (LωN) cannot be determined ex ante, as it depends on both the substitution effect (>0) and on the income effect (<0). 2.1.2 Government We rst assume that the government controls real public expenditure (G). To avoid composition effects, we assume the government-consumption basket has exactly the same CES composition the households' in (2). To minimise total expenditure in all goods for a given level of G, the demand function of each variety for public consumption, g(j)with j2[0;n], is given by an equation identical to (6). The relevant price index is still given by Pand public consumption expenditure is P:G. The government budget constraint is given by P:G=T0+t:(w:L+Π). (10) This equation nests two cases, each corresponding to a type of nancing9: I. The case when government intends to keep the control over the marginal tax rate (t0), so that the (net) lump-sum tax becomes the endogenous variable: T0=P:Gt:(w:L+Π); (10.I) II. The case when government decides not to raise a lump-sum tax (T0= 0), so that the marginal tax rate becomes: t=P:G w:L+Π. (10.II) 8For more detailed explanations and derivations see the appendices in Costa and Dixon (2009). In this case, please refer to section 5.1. 9In Costa and Dixon (2009) we also consider "unproductive labour" expenditure, as in Mankiw (1985). This gives rise to a third type of nancing. www.economics-ejournal.org 6
conomics: The Open-Access, Open-Assessment E-Journal For sake of simplicity, we will concentrate on the study of the effects of changing public consumption on the economy, ignoring the effects of changing other scal variables as (net) lump-sum taxes (T0) and the marginal tax rate (t), when these variables are exogenous. 2.1.3 Industries The productive sector is composed by a continuum of industries with mass n>0 and each industry is dedicated to producing a differentiated good jand has h rms10. The industry that produces good j, denoted ℑ(j), is the set of rms that produce it. Market demand directed to industry ℑ(j)(d(j)) is given by the sum of private and government demands, i.e. d(j)c(j)+g(j) = p(j) Pσ :D n1λ, (11) where DC+Grepresents aggregate demand. Market clearing in the market for good jrequires demand to equal supply: d(j) = h ∑ i=1 yi(j), (12) where yi(j)represents the output of rm iin industry ℑ(j). 2.1.4 Firms Firm iin industry ℑ(j), has the following strategic behaviour11: 10For simplicity, we assume that his the same across all industries and is greater than or equal to 1. 11Had we not considered a continuum of goods, but a nite number of varieties instead, an individual producer could be sufciently large to consider the effects of its own actions on macroeconomic variables. In this case, we would observe a feedback effect from the macro into the microeconomic level. For a few examples of models that consider the possibility of large rms at the economy level see Costa (2001), D'Aspremont et al. (1989), or Wu and Zhang (2000), amongst other. www.economics-ejournal.org 7
conomics: The Open-Access, Open-Assessment E-Journal 3. Absence of love for variety (λ=0). 4. A xed number of rms per industry (h=1), i.e. a constant mark-up given by µ=1=σ. 5. A xed mass of industries (n). Considering these assumptions, we have a consumption function given by C=α:w+ΠT0 P, (unrecognized8.A) i.e. the marginal propensity to consume is constant and identical for all types of income (C ωN=C πN=α). With a constant mark-up and no love for variety, the equilibrium wage rate is also constant and given by21 w=1µ. Thus, we know this equilibrium wage will not react to scal policy, i.e. w G=0. From equation (20.a) the reaction of non-wage income to scal policy is given by Π G=µ:m. Considering case I (dT 0=dG), we conclude that mjdT 0=dG =1α 1α:µ>0, (unrecognized27.A) i.e. a unit increase in Ginduces an equilibrium output increase of 0 <1α< (1α)=(1α:µ)<1. Figure 1 pictures the multiplier mechanism in the following way. First, consider that in the initial equilibrium government expenditure is zero (G=0) and prots are also zero (Π=0). On the left-hand panel we can depict the microeconomic decision in the leisure-consumption space using two simple graphical tools: the upward-sloping income-expansion path and the downward-sloping budget constraint. The former corresponds to equating the marginal rate of substitution between leisure and consumption (MRSZ;CUZ=UC= (1α):C=(α:Z) in this model) to the real net wage (ω N=1µhere). The later is just taken from equation (4), given the equilibrium values for the wages, prots, and taxes. 21See equation (22). www.economics-ejournal.org 14
conomics: The Open-Access, Open-Assessment E-Journal Figure 1: The Multiplier in the Dixon-Mankiw Model - Case I Thus, the microeconomic equilibrium for the representative household is given by point E0where it chooses an amount of leisure equal to Z 0and an amount of consumption given by C 0. Since there is no government consumption, the macroeconomic equilibrium in this space is represented by a "production possibilities frontier" between output and leisure that is given by the Y=Cschedule, the same as the household budget constraint. On the right-hand panel, we can represent the increasing relationship between total income and prots that corresponds to equation (20.a) Now, let us introduce government consumption given by G>0. The rst effect on the left-hand panel is that the macroeconomic-equilibrium representation is now different from the microeconomic one, i.e. the Y=C+Gcurve stands above households budget constraint. However, the initial demand stimulus is also perceived by households as a tax increase, since dT 0=dG. Thus, the microeconomic budget constraint shifts down by the amount of lump-sum taxes (G). The negative income effect moves the optimal decision of households from E0to A, reducing both consumption and leisure. Nonetheless, the macroeconomic Y=C+Gcurve does not move, and that means output increases to point A'. Consequently, due www.economics-ejournal.org 15
conomics: The Open-Access, Open-Assessment E-Journal to the demand expansion, prots increase, as shown by point A' in the right-hand panel. Thus, the microeconomic budget constraint shifts upwards and households increase both leisure and consumption. But then, the macroeconomic constraint also shifts upwards, prots increase and so on until the process ends in a new equilibrium represented by points E1(in both panels) and E1' (in the left-hand panel). In a nutshell, the "initial" demand stimulus of one unit of government consumption is partially crowded out, leading to a output increase of 0 <1α<1 and then to a prots increase of µ:(1α), before the second "round" starts. Notice the output increase can be easily explained by the labour-supply side: more government expenditure means more taxes and these have a positive effect on labour supply that more than offsets the negative effect of prots22. Thus, households are willing to work longer hours as their disposable income decreases, the same reason that makes them consume less. We observe that scal policy effectiveness on output is an increasing function of the degree of monopoly that exists in the economy: ∂m ∂ µ dT 0=dG =α:1α (1α:µ)2>0. (28.A) In order to explain what happens, let us use Figure 2. This gure is very similar to Figure 1, but it assumes a larger mark-up level (µ1>µ0), i.e. a smaller elasticity of substitution amongst goods. To keep zero prots in the initial equilibrium, we also assume a larger xed cost (Φ1>Φ0). As we can see in the left-hand-side panel, the larger mark-up level induces a smaller equilibrium wage rate, inducing a downward rotation on the income expansion path around the origin and also a downward rotation of the budget constraint about point (1,0). On the right-hand side, a larger mark-up rotates the prot function up, but the larger xed costs shifts it down in a parallel way. Since the mechanism is similar to the one described in Figure 1, we can notice the output increase (Y 1Y 0) is larger here than before, with a weaker monopoly 22Remember that µ<1. www.economics-ejournal.org 16
conomics: The Open-Access, Open-Assessment E-Journal Figure 2: The Multiplier and the Mark-up in the Dixon-Mankiw Model - Case I power. So why does this happen? The answer lies on the combination of three effects: i) there is a negative substitution effect on labour supply due to the lower wage rate; ii) but the income effect of the lower wage rate is positive; and iii) there is a negative effect on labour supply due to larger prots. The net effect on labour supply is clear-cut: people want to increase hours worked by more than in the case depicted in Figure 1. This is due to the reinforced negative effect of taxes when the wage rate is lower. However, the crucial effect is the last one: a higher mark-up induces a larger prot windfall that will lead to a larger consumption by households, reinforcing the second-round effect of the multiplier. Given the similarity of this mechanism to the basic Keynesian model, some authors (e.g. Mankiw) identied it with the traditional Keynesian spirit. However, Dixon (1987) draws our attention to the fact that the economic mechanism that supports this outcome has much more to do with the Walrasian spirit than with the Keynesian one23. In fact, the consumption-leisure choices made by households are basically the same under an expansionary scal policy either we face perfect or imperfect competition. The main difference has to do with the division 23This was a point also made by Bénassy (1995). www.economics-ejournal.org 17
conomics: The Open-Access, Open-Assessment E-Journal of income between wage and non-wage income which is affected by the degree of imperfect competition. The effect of scal policy on welfare is clear: output increases by less than public consumption. Thus, private consumption decreases due to the effect of higher taxes. Therefore, households work harder and their welfare decreases as a consequence of both effects. 2.3.2 Taxation One extension of Dixon (1987) and Mankiw (1988) is to allow a more realistic income tax (T 0=0 and 0 <t<1) to nance government expenditure, as in Molana and Moutos (1991). In what concerns to households, their behavioural functions are now given by C=α:(1t):w+Π P, (8.B) L=1(1α):(1t):w+Π w:(1t). (9.B) Here, considering there are no (net) lump-sum taxes, we are in case II, i.e. we have dt= (1m:g):dG=Yto substitute in equation (27). Thus, we obtain an equilibrium multiplier given by mjdt=(1m:g):dG=Y=Yα:(1µ+Π) ∆B , (27.B) where ∆B=Yα:(1µ+Π) + α:(1g):(1µ+Πµ:Y).24 At rst sight, the numerator, and also the denominator, appears to be either positive or negative. However, since we know that C= (1g):Yand using equation (8.B) in addition, we have C=α:(1t):(1µ+Π). If we also consider 24Since we know that, in equilibrium, we have (1µ)<Πµ:Y=(1µ):n:Φ<0, then we obtain ∆B=Yα:(1µ+Π)+α:(1g):(1µ):(1n:Φ). The constraint n:Φ<1 is a consequence of having 1 LNn:m:Φ0. www.economics-ejournal.org 18
conomics: The Open-Access, Open-Assessment E-Journal Figure 3: The Multiplier with Proportional Taxes - Case II that the government budget constraint implies that t=g, it is simple to see that Y=α:(1µ+Π). Therefore, mjdt=(1m:g):dG=Y=0, i.e. scal policy is absolutely ineffective in this case II25. In Figure 3 we can observe what happens, starting from an initial equilibrium E0with G=0, t=0, and Π=0. On the left-hand-side panel we now have a secondary axis to represent the tax rate, a decreasing function of output given G>0. Thus, when positive government consumption is introduced, the tax rate increases from zero to t 1>0. This implies a downward rotation of both the income expansion path and the budget constraint. In the new equilibrium E1, private consumption was completely crowded out by government consumption and output, leisure, and prots remain unchanged, given the functionals assumed. Since there is no effect on output, consumption decreases hence welfare falls after an increase in government expenditure. 25With the information obtained for the numerator, we know now that ∆B= α:(1g):(1µ):(1n:Φ)>0. www.economics-ejournal.org 19
conomics: The Open-Access, Open-Assessment E-Journal So, why is there such a dramatic loss of effectiveness? Contrary to case II, here an increase in public consumption only presents a potential substitution effect on labour supply, as it implies a tax-rate increase. However, this tax-rate increase has identical consequences on prots and wages, as they are both taxed at the same rate. Thus, the incentive to work more ceases to exist, unless prots decrease. But to have a decrease in prots, we would need an output fall and that is not compatible with an increase in employment in this case. Molana and Moutos (1991) also demonstrate that, when taxes are levied only on wage income, we may even obtain a negative multiplier. 2.3.3 Entry Dixon (1987) and Mankiw (1988) models assume the economy is in a "shortrun" situation, i.e. rms are not allowed to enter or leave the productive sector. However, in the Marshallian "long run," entry and exit will occur until prots are zero. Startz (1989) presents a "long-run" model using the basic assumptions in both Dixon (1987) and Mankiw (1988)26. This framework has been called the Dixon-Mankiw-Startz (DMS) model. Since there is no uncertainty, dynamics, or cost of creating a new rm (or shutting down and existing one), the zero-prot condition is Π=0. Therefore, non-wage income ceases to respond to scal-policy impulses, as Π G=0. This feature cuts the transmission mechanism through prots into consumption and from consumption to aggregate demand again. Then, the multiplier is given by mjdT 0=dG Π G=0 =1α>0. (27.C) This multiplier is still positive, in the (0;1)interval, but it does not depend on the degree of monopoly power: scal policy effectiveness would be identical in the Walrasian case (µ=0) and in all imperfectly competitive cases (0 <µ<1). 26In fact, Startz (1989) uses a Stone-Geary utility function instead of a Cobb-Douglas. However, the latter can be seen as a particular case of the former and the crucial property for the results obtained (i.e. constant marginal utility shares) is kept with a much simpler Cobb-Douglas function. www.economics-ejournal.org 20
conomics: The Open-Access, Open-Assessment E-Journal Figure 4: The Free-entry Multiplier of Startz Figure 4 shows us what is happening in the free-entry model. There is no need for the right-hand-side panel as prots are compressed to zero by entry and exit. Thus, an increase in Gshifts the microeconomic budget constraint down and the income effect of higher taxes induce an increase in labour supply and a decrease in consumption. Therefore, aggregate output increases, but there is a partial crowding out of private consumption of αunits for each unit of government consumption. We can also notice that a change in µmoves the income expansion path and the budget constraint, but it does not alter the result in terms of scal policy effectiveness as they both rotate in the same proportion like in the at-rate-tax case. Furthermore, we can observe the free-entry (or "long-run") multiplier, given by equation (27.C), is smaller than the no-entry ("short-run") multiplier given by equation (27.A): www.economics-ejournal.org 21
conomics: The Open-Access, Open-Assessment E-Journal Γ A(C) mjdT 0=dG Π G=0 mjdT 0=dG =1α:µ<1. As we saw when comparing both models with the same lump-sum tax nancing public expenditure, the main difference between these two types of model is the way prots distribution affects private consumption. Once this mechanism is shut down, only the income effect in labour supply leads to increased output. 2.3.4 Preferences The main result of Startz (1989) is extremely appealing, as it eliminates the protmultiplier mechanism. Dixon and Lawler (1996) consider what happens when we generalise the assumption on preferences27. If we keep the assumptions of the DMS framework,but allow for general preferences, the no-entry multiplier is given by mjdT 0=dG =1CπN 1CπN:µ>0, (27.D1) which is positive and less than one if we assume the marginal propensity to consume of net non-wage income is restricted to the (0;1)interval, as in the particular case of the DMS framework where CπN=α. Considering free entry, we obtain the "long-run" multiplier given by mjdT 0=dG Π G=0 =1CπN>0, (27.D2) which was constant and equal to 1αin the particular case of Startz (1989). Assuming u()still represents homothetic preferences, the graphical representations are similar to Figures 1 and 4 and the only difference is that the income 27In fact, that article also demonstrates Startz's result also depends upon the production technology. However, we will not analyse that side of the story here. www.economics-ejournal.org 22
conomics: The Open-Access, Open-Assessment E-Journal expansion path is now given by C=Σ(1µ):Z, where Σ()is a general increasing function. If we assume preferences are not homothetic, the income expansion path becomes non-linear, but the outcomes are identical. Furthermore, it is easy to observe the no-entry multiplier is larger than the free-entry one: Γ D mjdT 0=dG Π G=0 mjdT 0=dG =1CπN:µ<1, and this result is also easily explained by the neutralisation of the prot effect28. Thus, the previous results are similar to the DMS framework and we only have to substitute αby CπN. However, in general, the marginal propensity to consume of prots depends upon the mark-up. Therefore, the "long-run" scal multiplier is the larger (smaller) the larger is the market power in the economy, when CπNis decreasing (increasing) with µ.29 2.3.5 Increasing Returns to Variety Let us now return to the functionals assumed in the DMS model. However, we assume there is some taste for variety, i.e. λ>0. In this case, equation (22) tells us that, for a given mark-up level, the real wage is an increasing function of the mass of goods existing in the economy. This love-for-variety assumption is explored in Heijdra and van der Ploeg (1996). Devereux et al. (1996) present a (dynamic) model where there is a lovefor-variety technology, known as increasing returns to specialisation, with intermediate inputs in the production function. When the mass of rms and goods (n) is xed, i.e. when there is no entry or exit, the scal multiplier is still given by equation (27.A). However, if rms 28Dixon and Lawler (1996) also demonstrate this is not always the case when production technology does not exhibit constant marginal returns. 29Costa and Dixon (2009) provide a useful example using the CES preferences in Heijdra and van der Ploeg (1996). www.economics-ejournal.org 23
conomics: The Open-Access, Open-Assessment E-Journal 2.3.7 Extensions and Generalisations Many additional works try to analyse the relationship between market power and scal policy effectiveness, but we cannot go through all of them here. However, some of the most interesting results can be briey described in this section. Molana and Montagna (2000) introduce heterogeneity in the marginal product of labour in a DMS-style framework, also keeping love for variety. There, the zero-prot condition only applies to the "marginal rm (industry)," the reason why its more efcient competitors present positive prots. In their model, the absence of taste for variety leads to the entry of less efcient rms, so it reduces the average efciency of the economy and also scal policy effectiveness. Love for variety tends to oppose this effect. Torregrosa (1998) supplies a demonstration for the conjecture in Molana and Moutos (1991) stating that a negative multiplier can be obtained when there exist only proportional taxes on labour income. Reinhorn (1998) studies optimal scal policy in a framework where public consumption directly affects consumers utility. Finally, Censolo and Colombo (2008) study the way scal policy effectiveness is inuenced by differences between the composition of private and public expenditures, when different market structures (perfect and monopolistic competition) exist simultaneously in the same economy. 3 Intertemporal Models In the following section, we will develop a dynamic general equilibrium model which corresponds most closely to the static models considered in the previous section. 3.1 Intertemporal Household In particular, the instantaneous household utility follows as before: equations (1) and (2) with λ=0:The innitely-lived household has a discount rate of ρ>0 www.economics-ejournal.org 30
conomics: The Open-Access, Open-Assessment E-Journal and, instead of (1), it maximises lifetime utility: max C;ZU=Z∞ 0 u((C(τ);Z(τ)):eρ:τ:dτ. (31) In the dynamic model the household owns capital K(τ)at moment τwhich it rents out to rms at price R(τ): hence its total income at time τis as before, labour income w(τ):L(τ)and equity prots Π(τ), plus the income from capital R(τ):K(τ).37 Notice that, with an innitely-living household, Ricardian equivalence holds. Thus, since we are not interested in studying how public debt evolves overtime, nothing is lost if we assume government follows a balanced-budget rule at each moment τ. Also, for simplicity, in this section we will assume that the government nances expenditure by a lump-sum tax P(τ):G(τ) = T0(τ), i.e. we have t(τ) = 0. We still consider the preferences for varieties given by equation (2) and the resource constraint in equation (3). Therefore, the intertemporal budget constraint can be simply expressed in terms of aggregate variables. The household can choose to allocate its income between consumption or accumulating capital, given the tax to be paid. The accumulation of capital is thus: K(τ) = w(τ):L(τ)+R(τ):K(τ)+Π(τ) P(τ)C(τ)G(τ). (32) For simplicity we ignore time indices (τ)from this point onwards. Also, we continue to choose the composite good as numéraire, so P(τ) = 1. 3.2 Firm and Production For simplicity, we assume that there is one rm per industry: h=1 (monopolistic competition)38. Each instant τ, the representative rm j2[0;n]employs labour 37We ignore depreciation of capital in order to keep the presentation simple. Considering a positive depreciation rate, δ>0, does not change the quality of results. 38Therefore, we do not need the subscript ito identify a rm, as we can use the good jit produces for the same purpose. www.economics-ejournal.org 31
conomics: The Open-Access, Open-Assessment E-Journal and capital to produce output: y(j) = maxfF(K(j);N(j))Φ;0g. (33) where we assume that FK>0, FN>0, FKK <0, FNN <0, FKN >0, also that function F()is homogeneous to degree 1 (HoD1), i.e. the technology would present constant returns to scale (CRtS) if Φwas equal to zero, and the Inada conditions hold. The rm faces the demand curve (16) with h=1. Given the real wage and rental on capital, the rst-order conditions for prot maximization imply (in a symmetric industry equilibrium): (1µ):FK(j) = R;(1µ):FN(j) = w.(34) with the mark-up µ=σ1. Since the marginal products of labour and capital are the same across all rms (this is ensured by competitive factor markets), we can rewrite the household's accumulation equation using (34) as K= (1µ):(FN:N+FK:K)+ΠCG. Since function F()HoD1 in (K;N), by Euler's Theorem39 we have K= (1µ):F(K;N)+ΠC+G. Furthermore, in a symmetric equilibrium where p(j) = P=1, the prots of each rm are simply40: Π(j) = p(j):y(j)TC(j) = µ:F(K(j);N(j))Φ, so that aggregating across all rms with equilibrium in the capital market, i.e. K=Rn 0K(j):dj, we have Π=µ:F(K;N)n:Φ. (35) Again, equilibrium in the labour market implies that N=L. 39When F()is HoD1, F(K;N) = FK:K+FN:N. 40This follows from the homgeneity of F(), and the relation between the marginal products, the mark-up, and the factor payments. www.economics-ejournal.org 32
conomics: The Open-Access, Open-Assessment E-Journal Under imperfect competition, a wedge is driven between the marginal product of each factor and the factor return: this leads to each additional unit of output yielding a marginal prot of µ, since only a proportion (1µ)is used to pay for labour and capital. There is also the overhead xed cost, which may make the prot per rm negative or positive, depending upon the level of output. 3.3 The Household's Intertemporal Optimization The household chooses (C(τ);L(τ)) to maximize lifetime utility (31) subject to the accumulation equation (32), in effect a dynamic budget constraint. The current-value Hamiltonian for this intertemporal optimisation problem is H=u(C;1L)+ ξ:(w:L+R:K+ΠCG), and the rst-order conditions for this are HCuCξ=0; HL uZ+ξ:w=0; HKξ:R= ξ+ρ:ξ; lim τ!∞eρ:τ:ξ(τ):K(τ)=0. Using (34) we can express (w;R)in terms of the marginal products. Hence, we derive two basic optimality conditions: Intra-temporal optimality Once again41,M(C;Z);the marginal rate of substitution between consumption and leisure equals the net real wage rate M(C;Z)uZ uC = (1µ):FN. Inter-temporal optimality The Euler condition. Assuming that uCZ =0, i.e. assuming the felicity function is additively separable, this can be written as 41See Costa and Dixon (2009), section 5.1. www.economics-ejournal.org 33
conomics: The Open-Access, Open-Assessment E-Journal C C=θ:[(1µ):FKρ], where θ uC=(C:uCC)is the elasticity of intertemporal substitution in consumption. 3.4 Steady State In the steady state, we have the condition that C=0:Hence the Euler condition implies that (1µ):F K=ρ, where asterisks stand for steady-state values. In the Walrasian case (µ=0)this is just the modied golden rule. What imperfect competition does is to discourage investment, since the returns on investment are depressed (there is a wedge between the marginal product and the rental on capital). Now, under the assumption that function F()is HoD1, we can write it in factor intensive form F(K;L) = L:FK L;1=L:f(k), where kK=L. Hence the steady-state Euler condition is f0(k) = ρ 1µ, (36) where f0(k) = FKK L;1>0 and f00 (k) = FKK K L;1<0. With this particular market structure we can write the solution to this as k= k(µ)with k0 (µ)<0. With F()HoD1, the steady-state Euler condition is very powerful: not only is the marginal product of capital determined, but so is the steady-state wage rate w(µ) = f(k(µ)) ρ:k(µ) 1µ. (37) With this we have the income expansion path (IEP) for consumption and leisure, dened by the intertemporal optimality condition and the steady-state wage u Z u C = (1µ):F N=w(µ). (38) www.economics-ejournal.org 34
conomics: The Open-Access, Open-Assessment E-Journal As in the static model, the IEP will be upward sloping in (Z;C), since both consumption and leisure are normal, it will be a straight line if preferences are quasihomothetic and it will be a linear ray through the origin if preferences are homothetic. There is a steady-state relationship between income and consumption given by42 C=L:f(k(µ))n:ΦG. (39) We will call this the Euler frontier (EF). Note that the EF is not the household's budget constraint (BC). Let us take the case where nis xed. The household receives prot income Π, which it sees as a lump-sum payment and also the rental income on capital. The household thus only sees the variation in labour income as it considers varying L: the slope of the actual budget constrain is thus w(µ). The actual budget constraint is given by the grey dotted line in Figure 6: if the household is at point E, it is atter than the EF. Also, at the intercept there is all of the non-labour income (rental on capital, prots less tax). The unique steady-state equilibrium is the found at the intersection of the IEP and EF at point E, as depicted in the same gure43. Here we can see the equilibrium level of Cand L=1Z. The optimal capital stock is then simply K=L:k(µ). 42This can be derived from the budget constraint: C=w(µ):L+R:K+ΠG= =w(µ):L+ρ 1µL:k(µ)+ µ:L:f(k)n:ΦG= =L:f(k(µ))n:ΦG. 43Uniqueness is not guaranteed when we have a signicant taste for variety, i.e. λis large, when the mark-up is endogenous, i.e. µ=µ(k), or when there are increasing returns to scale at the aggregate level. www.economics-ejournal.org 35
conomics: The Open-Access, Open-Assessment E-Journal Figure 6: The Steady-State Equilibrium 3.4.1 Dynamics Whilst the steady state is best understood in terms of leisure-consumption space, the dynamics is best understood in the classic Ramsey projection (K;C). As a rst step, we need to note that the intratemporal relationship means that we can dene labour supply as an implicit function of (C;K):L=L(C;K;µ);with LC<0<LK and Lµ<0.44 The dynamics are represented by the two isoclines: C=0 : (1µ):FK(K;L(C;K;µ))ρ=0; (40) K=0 : F(K;L(C;K;µ))n:ΦGC=0. (41) The consumption isocline is downward sloping in (K;C): it is dened by the equality of the marginal revenue product of capital being equal to the discount rate. To the right of the consumption isocline, consumption is falling, since 44See Costa and Dixon (2009), section 5.5. www.economics-ejournal.org 36
conomics: The Open-Access, Open-Assessment E-Journal Figure 7: The Saddle-Point Stable Equilibrium (1µ):FK<ρ; to the left it is increasing. The capital isocline has the standard upward-sloping shape45: it need not be globally concave due to the effect of Kon the labour supply. The phase diagram thus has a unique saddle-path solution as depicted in Figure 7. 3.5 The Effect of Imperfect Competition on the Long-run Equilibrium In this section we illustrate the effect of a change in µon the steady-state equilibrium from both (1L;C)space and (K;C)space. First, let us analyse the consequences of imperfect competition in leisure-consumption space. We have two effects of an increase in the degree of imperfect competition: 45See Costa and Dixon (2009), section 5.7. Notice that with δ>0 the capital isocline would present the usual hump shape: increasing before the modied golden-rule capital stock and decreasing afterwards. www.economics-ejournal.org 37
conomics: The Open-Access, Open-Assessment E-Journal The EF curve rotates anti-clockwise. Since we have f0(k) = ρ 1µ; dk dµ=f0(k) (1µ):f00 (k)=ρ (1µ)2:f00 (k)<0. The real wage falls, so that the IEP moves to the right. Since from (37) w(µ) = f[k(µ)]ρ:k(µ) 1µ; dw dµ=ρ:k(µ) (1µ)2<0. These two effects are depicted in Figure 8, where the equilibrium moves from E0to E1when we compare a low-mark-up steady-state (µ=µ0) with a largemark-up one (µ=µ1>µ0). Clearly, the shift in the IEP represents a pure substitution effect. As the wage falls, the household substitutes leisure for consumption. The EF rotation, however, marks a counterbalancing income effect: income is lower for any Lwhen µis higher. This operates to increase labour supply and decrease consumption. So, both income and substitution effects operate to reduce consumption: they operate in opposite ways on the labour supply. In Figure 8 leisure increases, which means that the income effect dominates for that specic example. Turning to capital-consumption space and the phase diagram, the way to understand the effect of µis via the effect on L: for given (K;C), an increase in µ increases the wedge between the marginal product of labour and the wage, hence leading to a reduction in the labour supply. Less labour means that both total output and the marginal product of capital fall. Hence we have two effects of an increase in µ: (i) the consumption isocline shifts to the left (since FKfalls as L decreases) and (ii) the capital isocline shifts downwards, as there is less output given (K;C). www.economics-ejournal.org 38
conomics: The Open-Access, Open-Assessment E-Journal Figure 8: Market Power and the Steady-State Equilibrium (I) The shift from equilibrium E0to E1in Figure 8 is represented in (K;C)in Figure 9. Note that whilst steady-state consumption falls, the effect on capital is potentially ambiguous. This is because the effect of µon labour supply is ambiguous. Here capital decreases, which is compatible with the reduction in employment observed in Figure 8. 3.6 Free Entry Until now, we have assumed that the mass of rms/goods is xed across time, so that n(τ) = n. In this case, aggregate output is given by Y(τ) = L(τ):f(k(τ))n:Φ. (42) If there is instantaneous free entry which drives prots to zero, from (35), for given (K;L);prots are zero when n(τ) = µ:F(K(τ);L(τ)) Φ=µ Φ:L(τ):f(k(τ)). (43) www.economics-ejournal.org 39
conomics: The Open-Access, Open-Assessment E-Journal We are especially interested in what happens at time τ=0, when the scal shock occurs. In both cases we observe a decrease in C(0)due to the combination of two effects: (i) the long-run consumption level decreases as described before and (ii) the capital stock is below its long-run optimal level (i.e. K(0)<K)50. However, if we want to compare the no-entry to the free-entry versions of the model, we can notice that ΛC(0) = ΛCβNE :ΛK+Λβ:(K(0)K NE ), (48) where ΛXXNE XFE, with XNE =XjNo entry and XFE =XjFree entry is a measure of distance between the no-entry and the free-entry equilibrium values for variable X. We can see in Figure 13 that ΛC>0, i.e. the long-run drop in consumption is larger under free entry than in the xed-nmodel. We can also observe that ΛK<0, i.e. the long-run increase in the optimal capital stock is larger under free entry. Finally, we know that K(0)K NE <0 for the increase in government expenditure depicted in this example. Thus, we can expect a larger short-run decrease in private consumption in the free entry case (ΛC(0)<0), unless the stable manifold is much steeper in the no-entry case, i.e. Λβ>ΛCβNE :ΛK K NE K(0)>0. Let us use a numerical illustration in order to see what can happen in specic models. First, we assume the felicity function is isoelastic in both consumption and leisure, i.e. u((C(τ);Z(τ)) = C(τ)11 θ1 11 θ +b:Z(τ)11 ψ1 11 ψ , where θ,ψ,b>0. Second, let us assume F()is Cobb-Douglas, i.e. F(K(τ);N(τ)) = A:K(τ)η:N(τ)1η, where 0 <η<1. Now, we choose the following parameter values: η ρ θ ψ σ b G0Φ 1=3 0:04 1 1 10 10=6 0:1643 0:0913 50See the values for the long-run multipliers in Costa and Dixon (2009), section 5.8. www.economics-ejournal.org 46
conomics: The Open-Access, Open-Assessment E-Journal The value of ηwas chosen in order to generate a long-run capital share in total income equal to one third. The value for ρimplies a 4 per cent return on capital per period. The values for θand ψimply elasticities of intertemporal substitution equal to one for both consumption and leisure. The value of σgives rise to a 11 per cent price-wedge over the marginal cost in the steady state. The value for b was chosen in order to generate L=1=3, the value for G0is the one that leads to a 20 per cent steady-state share of government consumption in output, and the value for Φis such that prots are zero in the initial equilibrium (E0in Figure 13) when n=1. For this numerical illustration, a permanent one per cent increase in Gleads to an immediate 1.3 per cent decrease in consumption in the no-entry case and to a 1.4 reduction in the free-entry case. Thus, in this example, despite the fact that the stable manifold is steeper in the no-entry case (i.e. Λβ>0), the last term on the right-hand-side of equation (48) is smaller than the sum of the positive effects. This example corresponds to Figure 13: in the no-entry case the equilibrium response of households leads to the short-run equilibrium represented by point B, whilst point C represents its free-entry counterpart. We also varied all the parameters in their ranges and obtained similar results, i.e. for these functionals we could not numerically generate a situation where ΛC(0)<0. Of course we cannot guarantee such an event would not occur with different felicity or production functions, but we can expect this result to hold in most of the real policy experiments. 3.9 Extensions and generalisations As we saw, dynamic models allow us to study not only the long-run (steady-state) effects, but also the short-run effects that occur due to the fact that agents may use a part of their resources presently available to obtain better future outcomes, according to a discounted optimisation problem (either utility or prots). Amongst these models, Heijdra (1998) is an inevitable reference where a continuos-time dynamic model with monopolistic competition is presented, including love for variety and Ethier effects (i.e. increasing returns from diversity in the investmentgoods sector). Costa (2007) (the effect of capital depreciation), Devereux et al. (1996) (increasing returns to specialisation), Harms (2002) (persistency of scal www.economics-ejournal.org 47
conomics: The Open-Access, Open-Assessment E-Journal shocks), Heijdra et al. (1998) (distortionary taxation and useful public expenditure), Linneman and Schabert (2003) (price stickiness and scal-monetary policies interaction), Molana (1998) (intertemporal substitution between current leisure and future consumption), or Ravn et al. (2006) (endogenous mark-ups due to deep habits) are also examples if important references in this line of research. We can also observe a recent revival of interest in the effects of scal policy in imperfectly competitive economies with sticky prices where complementarity between private consumption and leisure may generate consumption crowding in - see Bilbiie (2011) - and additionally the zero lower bound for the interest rate provides increased effectiveness - see Christiano et al. (2009) and Hall (2009). On the empirical front, the recent interest on the quantitative effects of scal shocks, especially when mark-ups respond counter-cyclically to them, can be observed in Afonso and Costa (2010), Hall (2009), or Monacelli and Perotti (2009). 4 Concluding Remarks In this paper we studied scal policy effectiveness in static general equilibrium models where there is imperfect competition in goods markets. We observed this effectiveness, both over output and households welfare, and its relation with the degree of monopoly depend upon a large number of factors, namely the ones analysed here: i) the type of taxes used; ii) the possibility of free entry; iii) consumers preferences; iv) the existence of increasing returns on the mass of varieties; and v) the existence of endogenous mark-ups. Overall we nd that the effectiveness of scal policy does indeed depend on the degree of imperfect competition. This is because the mark-up distorts the relative price of consumption and leisure (the latter becomes cheaper). For a broad range of results (with many caveats), we nd that the multiplier is increasing in the degree of imperfect competition. However, the effect on welfare will still tend to be negative: the reason output increases is that households are induced to work harder by being taxed. In order to obtain the "Keynesian" welfare effect, you need to have some extra ingredient: for example increasing returns, love for variety, or an endogenous mark-up. One of the main achievements of these models was to reintroduce the wealth effect on labour supply into the analysis of scal policy. Since Patinkin (1965), www.economics-ejournal.org 48
conomics: The Open-Access, Open-Assessment E-Journal the wealth effect on the labour supply had been suppressed in macroeconomics, resulting in the vertical long-run aggregate-supply curve and zero long-run scal multiplier51. The DMS papers made the wealth effect on the labour supply of an increase in taxation resulting from an increase in government expenditure central to the analysis of scal policy. This was a theme taken up later by Real Business Cycle theorists, e.g. Baxter and King (1993), and later the New Keynesian synthesis, e.g. Woodford (2003). In dynamic models, many of the same issues arise, particularly if we focus on the steady-state results. However, we have an additional dimension of the realtime dynamics and in particular the comparison of shortand long-run effects. In both static and dynamic models, the role of entry is crucial, as was argued by Startz (1989). With a xed mass of varieties, extra output is produced in a marginally efcient way. With free entry, extra output sucks in additional rms and overheads. In many models this leads to a lower multiplier and lower welfare. From the point of view of the history of economic thought it is rather strange that John Maynard Keynes, Joan Robinson the founder of monopolistic competition theory, and Richard Khan, who invented the multiplier, coexisted in the same time and place (Cambridge, England in the 1930s). Despite the space-time and intellectual proximity between them, the link was not made between imperfect competition and macroeconomics until much later52. In this survey, we have traced through general equilibrium macroeconomic models how this "tantalizing possibility" was realised in the ensuing 60 years. As we have seen, the simple fact that the imperfectly competitive equilibrium is not Pareto optimal does not imply that Pareto-improving scal policy is generally possible. However, it does have important and more-or-less Keynesian features as regards the multiplier. Acknowledgement: We are grateful to Isabel Correia, Phillip Lawler, and to two anonymous referees and the editor (Roberto Perotti) for helpful comments and suggestions on previous versions. We are also grateful to our Ph.D. and M.Sc. students at Cardiff, Finnish Doctoral Programme, ISEG/TULisbon, Mu51For an historical perspective see Dixon (1995) - also available on http://www.huwdixon.org/SurngEconomics/chapter3.pdf . 52See Marris (1991) for more details, especially pp. 181-187. www.economics-ejournal.org 49
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