Fiscal Policy Under Imperfect Competition with Flexible Prices: An Overview and Survey

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.


Introduction
In a perfectly competitive economy without market imperfections, any competitive equilibrium will be Pareto optimal. Hence there can be no ef ciency 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 stickiness 1 .
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 signi cant 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 to integrate these concepts in macroeconomic models. Nonetheless, their success was limited due to the "subjective-demand-curve" assumption 2 .
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 models 3 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 exible 4 ; (4) public consump-tion has no direct effects on utilities and technologies of private agents 5 ; (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 justi ed 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.

Static Models
In this section we develop a class of static general equilibrium models that nests most of the relevant literature on the topic.

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): which is a continuously twice-differentiable function, with 6 u C > 0, u Z > 0, u CC < 0, u ZZ > 0, and u CZ = u ZC > 0. The sub-utility is constant elasticity of substitution (CES): where c ( j), with j 2 [0; n], represents the consumption of variety j, σ > 1 stands for the (absolute value of the) elasticity of substitution between goods, and λ 2 [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 de ned as what is left over from the unit endowment after working (L): The budget constraint is given by where w represents the nominal wage, Π pro ts, T is tax, and p ( j) is the price of good j. Taxes are a linear function of primary income: where t 2 [0; 1) and T 0 < (1 t) : (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: 6 For sake of simplicity we use the following notation for partial derivatives: www.economics-ejournal.org 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: where P represents the relevant price (or cost-of-living) index for the household given by P = 1 n 1 λ : and the optimal (minimal) expenditure function is given by P:C. Notice the demand for good j is 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 1 λ .
From the second step we obtain: where ω N w: (1 t) =P represents the real net wage, π N (Π: (1 t) T 0 ) =P π: (1 t) τ 0 stands for net pro ts, equation (8) is the private consumption function where C ω N > 0 and C π N > 0, and equation (9) represents the labour-supply 7 This 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 function where L ω N R 0 and L π N < 0. 8 Household consumption intentions are an increasing function of the real net wage (C ω N > 0) and also of the real non-wage income (C π N > 0), both taken as given by households. The net real non-wage income has a negative impact on labour supply (L π N < 0), but the effect of the real net wage (L ω N ) cannot be determined ex ante, as it depends on both the substitution effect (> 0) and on the income effect (< 0).

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 j 2 [0; n], is given by an equation identical to (6). The relevant price index is still given by P and public consumption expenditure is P:G.
The government budget constraint is given by This equation nests two cases, each corresponding to a type of nancing 9 : I. The case when government intends to keep the control over the marginal tax rate (t 0), so that the (net) lump-sum tax becomes the endogenous variable: T 0 = P:G t: (w:L + Π) ; (10.I) II. The case when government decides not to raise a lump-sum tax (T 0 = 0), so that the marginal tax rate becomes: 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 (T 0 ) and the marginal tax rate (t), when these variables are exogenous.

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 j and has h rms 10 . 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.
where D C + G represents aggregate demand. Market clearing in the market for good j requires demand to equal supply: where y i ( j) represents the output of rm i in industry ℑ ( j).

Firms
Firm i in industry ℑ ( j), has the following strategic behaviour 11 : it competes with other rms in its industry (q 6 = i) using quantities produced as a strategic variable which determines the industry price -intra-industrial Cournot competition; it treats the aggregate price-level as given.
This is called Cournotian Monopolistic Competition 12 (CMC) and has the limiting case of perfect competition (when the number of rms per industry is very large (h ! ∞) or if varieties are close substitutes (σ ! ∞), and Dixit and Stiglitz (1977) monopolistic competition when all industries have a single producer (h = 1).
Firm i maximises its pro ts (Π i ( j)): where TC i ( j) represents total cost for this rm and p ( j) is seen as a function of y i ( j), as we will see below. The production technology of this good is where N i ( j) represents the labour quantity hired by rm i, A > 0 is the (constant) marginal productivity of labour which for simplicity we normalise to A = 1, and Φ 0 is overhead or administrative labour 13 . Production exhibits increasing returns to scale if Φ > 0 and constant returns to scale if Φ = 0. 14 The labour market is perfectly competitive with an economy-wide market wage w, so that total costs of rm i are The rm acts in a Cournot manner given industry demand in equations (11) and (12), treating the outputs of other rms in the industry (q 6 = i) and macroeconomic variables fP; Dg as given, with "inverse" demand From solving the pro t maximisation problem given by equations (13) to (16), we obtain the optimal price-setting rule for rms in industry ℑ ( j) that corresponds to equalising the marginal revenue to the marginal cost (MC): where S i ( j) y i ( j) =d ( j) is the market share of rm i. Since all rms are identical, we have S i ( j) = 1=h in all industries, so the optimal price-setting rule for all goods j, given by (17) becomes for all p ( j) = p: where µ (p MC) =p = 1= (σ :h) 2 [0; 1) is the Lerner index that represents market power of each rm in each industry. Note this index gives us the reciprocal of the (absolute value of the) price-elasticity of demand faced by each producer in a symmetric equilibrium. In the perfect competition case (h ! ∞ or σ ! ∞) 15 we have µ = 0, i.e. p = MC. In an extreme case of monopoly (h = 1 and σ = 1), we would have µ = 1, where the rm posts an in nitely high price relative to the marginal cost. The higher the value of µ, the higher the representative rm's market power.

Macroeconomic Constraints
For labour-market equilibrium 16 , the (ex-post) equality of labour supplied and demanded is where . Notice that N gives us total labour demand (both productive and "administrative"). Taking into account equilibrium symmetry, labour demand is given by n:h: (y + Φ), where y stands for the equilibrium output of each rm. Real aggregate output is given by 17 In a symmetric equilibrium Y = n:h:p:y=P. Note that, taking into account equation (7) and equilibrium symmetry, we obtain P = n λ =(1 σ ) :p. By substituting it in equation (16), we nally obtain the fundamental identity of national accounting Y = D. 18 We have also the value of non-wage income given by the sum of the pro ts of all rms in the economy: where . We choose the CES basket to be the numéraire, P = 1, so that from (7), we can obtain the price posted in each industry: Note this price diverges from the general level when there is some taste for variety (λ > 0) 19 . Using equation (17.a), we can obtain the equilibrium (real) wage rate that is represented by the following expression, given the mark-up level: Here, besides the love-for-variety effect, we can observe that a larger market power implies a smaller wage, as it contracts labour demand. The corresponding aggregate labour demand can be written as a function of aggregate output, the mass of industries, and the number of rms per industry: where the rst term on the right-hand side corresponds to the directly productive labour input and the second one represents "administrative" labour (the overhead xed cost for the economy). Aggregate pro ts can also be re-written as i.e. it is an increasing function of both the aggregate output and the mark-up level, and a decreasing function of both the mass of industries and the number of rms per industry.

A General Formulation for the Equilibrium
In order to deal with the various models that are nested in this general framework, we will write down the equilibrium values for the wage rate, employment, and non-wage income as functions of the government-consumption level 20 . We will not have to explicitly de ne these functions given the fact that we are only interested on the effects of scal policy: where asterisks identify the macroeconomic-equilibrium values for these variables. Given both scal-policy behaviour types considered in equations (10.I and II), have still to consider that: Using the fundamental identity of national accounting, the aggregate-demand de nition, the consumption function, and the government budget constraint given above, we can write an equation that gives us the equilibrium value for aggregate output Y = D: Output equals consumption, which depends on after-tax wages and pro ts, plus G. From this equation we can easily see that the equilibrium value of output is a function of G : Y = Y (G). Once we have found the value of Y , we can obtain all the additional equilibrium values that depend on it, namely C and U , the latter representing the equilibrium value for households' utility (welfare).

Fiscal Policy Effectiveness
From equation (26) we can obtain the value of the output governmentconsumption multiplier, m = dY =dG, using a rst-order Taylor approximation and the implicit-function theorem: :dG in case II; and g = G=Y 2 [0; 1) is the weight of public consumption in aggregate expenditure. We can expect m to be positive in most cases, but the main goal of this section is analysing it in speci c situations, according to the various hypothesis advanced by many authors from the middle 1980's onwards. Furthermore, we are especially interested in the effect of the market power on scal policy effectiveness, i.e. we will analyse the sign of Finally, the analysis of scal policy effectiveness on households welfare can simply be done in the following way: if m > 0, then an expansionary scal policy will imply a leisure loss, as labour is the only input. Thus, welfare will only increase if private consumption positively reacts to an increase in public consumption and so that it more than offsets the previous leisure reduction. In the next sub-section we will survey the main results of this strand of literature.

The Initiators: Dixon and Mankiw
The rst works exclusively dedicated to this topic are Dixon (1987) and Mankiw (1988), which share the following assumptions: 1. A Cobb-Douglas utility function www.economics-ejournal.org 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 i.e. the marginal propensity to consume is constant and identical for all types of income (C ω N = C π N = α). With a constant mark-up and no love for variety, the equilibrium wage rate is also constant and given by 21 w = 1 µ. 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 i.e. a unit increase in G induces an equilibrium output increase of 0 < 1 α < (1 α) = (1 α: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 pro ts 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 (MRS Z;C U Z =U C = (1 α) :C= (α:Z) in this model) to the real net wage (ω N = 1 µ here). The later is just taken from equation (4), given the equilibrium values for the wages, pro ts, and taxes. Thus, the microeconomic equilibrium for the representative household is given by point E 0 where it chooses an amount of leisure equal to Z 0 and 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 = C schedule, the same as the household budget constraint. On the right-hand panel, we can represent the increasing relationship between total income and pro ts 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 + G curve 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 E 0 to A, reducing both consumption and leisure. Nonetheless, the macroeconomic Y = C + G curve does not move, and that means output increases to point A'. Consequently, due to the demand expansion, pro ts 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, pro ts increase and so on until the process ends in a new equilibrium represented by points E 1 (in both panels) and E 1 ' (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 < 1 α < 1 and then to a pro ts increase of µ: (1 α), 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 pro ts 22 . 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: 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 (µ 1 > µ 0 ), i.e. a smaller elasticity of substitution amongst goods. To keep zero pro ts in the initial equilibrium, we also assume a larger xed cost (Φ 1 > Φ 0 ). 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 pro t 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 1 Y 0 ) is larger here than before, with a weaker monopoly 22 Remember that µ < 1.
www.economics-ejournal.org 16 conomics: The Open-Access, Open-Assessment E-Journal 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 pro ts. 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 pro t 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) identi ed 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 one 23 . 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 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.

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 Here, considering there are no (net) lump-sum taxes, we are in case II, i.e. we have dt = (1 m :g ):dG=Y to substitute in equation (27). Thus, we obtain an equilibrium multiplier given by . 24 At rst sight, the numerator, and also the denominator, appears to be either positive or negative. However, since we know that C = (1 g ):Y and using equation that the government budget constraint implies that t = g , it is simple to see that Y = α: (1 µ + Π ). Therefore, m j dt =(1 m :g ):dG=Y = 0, i.e. scal policy is absolutely ineffective in this case II 25 .
In Figure 3 we can observe what happens, starting from an initial equilibrium E 0 with 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 E 1 , private consumption was completely crowded out by government consumption and output, leisure, and pro ts remain unchanged, given the functionals assumed. Since there is no effect on output, consumption decreases hence welfare falls after an increase in government expenditure.
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 pro ts and wages, as they are both taxed at the same rate. Thus, the incentive to work more ceases to exist, unless pro ts decrease. But to have a decrease in pro ts, 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.

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 pro ts 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-pro t 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 pro ts into consumption and from consumption to aggregate demand again. Then, the multiplier is given by 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).  Figure 4 shows us what is happening in the free-entry model. There is no need for the right-hand-side panel as pro ts are compressed to zero by entry and exit. Thus, an increase in G shifts 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 α units for each unit of government consumption.
We can also notice that a change in µ moves 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): m j dT 0 =dG = 1 α: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 pro ts distribution affects private consumption. Once this mechanism is shut down, only the income effect in labour supply leads to increased output.

Preferences
The main result of Startz (1989) is extremely appealing, as it eliminates the pro tmultiplier mechanism. Dixon and Lawler (1996) consider what happens when we generalise the assumption on preferences 27 . If we keep the assumptions of the DMS framework,but allow for general preferences, the no-entry multiplier is given by 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 C π N = α.
Considering free entry, we obtain the "long-run" multiplier given by which was constant and equal to 1 α in 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 expansion path is now given by C = Σ (1 µ) :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: and this result is also easily explained by the neutralisation of the pro t effect 28 . Thus, the previous results are similar to the DMS framework and we only have to substitute α by C π N . However, in general, the marginal propensity to consume of pro ts 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 C π N is decreasing (increasing) with µ. 29

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 are free to enter or leave the market, their mass becomes an endogenous variable given by from the free-entry condition Π = 0. Thus, an aggregate-demand increase induces an increase in real wages that will affect scal policy effectiveness as 30 i.e. entry of rms, a consequence of the aggregate demand stimulus, leads to a real-wage increase and consequently to a consumption increase, opening a transmission channel similar to the pro t one in the no-entry model. In this case, the multiplier is given by Notice that, due to λ > 0 we have γ > 0 and consequently a larger multiplier than in the free-entry constant-returns case (1 α).
On the left-hand-side panel of Figure 5 we can observe that scal policy would change the equilibrium from point E 0 to point A. That is the situation depicted in Figure 4, corresponding to a xed-wage environment. However, point A is not an equilibrium in this model, as the real wage is a function of the aggregate output w = Ω (Y ) with Ω 0 ( ) > 0. This fact can easily be observed by combining equations (22)  variety and labour demand in the case of increasing returns to specialisation. In any case, the equilibrium wage rate goes up, as we can observe on the secondary axis of the right-hand-side panel of Figure 5. The wage increase rotates the income expansion path, the household budget constraint, and the macroeconomic constraint up in the left-hand-side panel. The new equilibrium is nally reached in point E 1 with a larger output and a smaller decrease in private consumption. Despite the fact that we are using a consumption function with constant marginal propensities to consume, this multiplier depends upon the monopoly power level in the economy through g and γ = µ:λ = (µ:λ + 1 µ). It is simple to demonstrate that γ is increasing with the mark-up 31 , but it is not so easy to show how does g depends on µ. At rst glance, one could think the weight of public consumption in output should be increasing with the monopoly degree, as it means more inef ciency, thus less output. However, taking into account net pro ts are zero, the macroeconomic production function can be represented as In the equation above we can observe that, for the same employment level, an increase in µ leads to a reduction in the term (1 µ), but it also increases the exponent, as it corresponds to a reduction in σ . This means that the monopoly degree under monopolistic competition reinforces the effect of increasing returns. There is also an indirect effect that acts through n, since an increase in µ stimulates entry.
Therefore, we can easily determine what is the effect on the multiplier when we start from a zero-government-consumption steady state In this particular case, the larger is the market power, the larger is the entry effect on the real wage, increasing the effectiveness of the initial scal stimulus. An identical outcome can be obtained for situations where g does not react dramatically to changes in the mark-up. Using numerical simulations with plausible values for the parameters, we also obtain a multiplier that is an increasing function of µ. Now comparing the "short-" and "long-run" multipliers, we observe that Considering that γ and g depend upon the values of other parameters in the model, it is not possible to say a priori if this value is larger of smaller than one. Thus, we know that for µ < γ:[1 (1 α):g ] α the free-entry ("long-run") multiplier is larger than the multiplier with a xed mass of rms, given the positive externality caused by the entry of new rms. The opposite result is obtained when the markup is high.

Endogenous Mark-ups
The assumption that entry of rms is done through the creation of new monopolies associated to new products hides an additional assumption that product innovation is cheaper than copying an existing good or creating a close substitute. When facing signi cant costs associated with creating a differentiated product, the incentive to create a new industry may be smaller than the incentive to enter an existing industry. Thus, h may be the endogenous variable in our free-entry model instead of n. 32 Up to this point, we considered that µ was a constant, as we assumed that both h was xed (and equal to one, a basic assumption in monopolistically competitive models) and also that σ was xed due to CES preferences 33 . When we alter the endogenous variable in the entry process, we also endogenise µ = 1= (σ :h). This value can be obtained through the zero-pro t condition, assuming once again there is no love for variety (λ = 0): where φ = n:Φ=Y is an increasing returns to scale indicator for the production function and it represents the weight of total xed costs in aggregate output. We can notice its equilibrium value is a decreasing function of the equilibrium output. Note that, in this case, the market power has a negative correlation with aggregate output, which is consistent with counter-cyclical mark-ups as documented in the empirical literature 34 . Despite the fact this hypothesis is considered in Dixon and Lawler (1996), the treatment of scal-policy effectiveness in an endogenous-mark-up framework is done in Costa (2004). However, there are other endogenous-mark-ups models, 32 For a more detailed analysis of the underlying process and its fundamentals see Costa and Dixon (2007). 33 Throughout the text we loosely use the expression "endogenous mark-ups," as widely used in the literature, to signify "varying mark-ups," as µ is always endogenous even when it is equal to 1=σ . We thank an anonymous referee for highlighting this point. 34 E.g. see Martins et al. (1996) or Martins and Scarpetta (2002).
www.economics-ejournal.org 27 though not speci cally dedicated to scal-policy effectiveness, that are surveyed in Rotemberg and Woodford (1999).
In the case treated here, it is the real wage that reacts to scal policy, as we have w = 1 µ . Nonetheless, considering the reduced-form macroeconomic production function with free entry Y = (1 µ) :L, the endogenous mark-up may work as a productivity shock, but it originates in the aggregate-demand side in the case of scal policy 35 .
Thus, an increase in public consumption translates into a mark-up reduction, i.e. a real-wage increase w G = (µ ) 2 :m = (n:Φ) > 0. Therefore, the increase in intra-industrial competition induced by an expansionary scal policy leads to a second stimulus in private consumption, via real wages, reinforcing the multiplier mechanism and acting as a positive externality: The graphical representation of this mechanism is also given by Figure 5, where w = Ω (Y ) is obtained from equation (30). Despite the difference in the economic mechanism, the real-wage transmission mechanism is similar to the previous model.
Considering that µ is now an endogenous variable, it makes no sense to calculate the derivative of this multiplier in order to the mark-up. However, any change in the parameter values or exogenous variables that leads to a higher mark-up (e.g. a smaller public consumption or a higher xed cost) induces an increase in scal policy effectiveness.
Finally, considering the no-entry mechanism is the same as in the previous case, we have . 35 There is a recent interest in this subject in the business-cycle literature. For an example, see Barro and Tenreyro (2006), inter alia.

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Thus, near the initial equilibrium where µ = µ , the "long-run" multiplier is larger than the "short-run" one, as long as the monopoly power indicator is suf ciently large, i.e. as long as µ > α:n:Φ.
D' Aspremont et al. (1995) provide an earlier analysis of scal policy in a Cournotian framework for an overlapping-generations economy with a single produced good. Molana and Zhang (2001) study the steady-state effects in an intertemporal model similar to Costa (2004), where they assume that µ = µ (n) with µ 0 (n) < 0. In a way similar to Galí (1995), these authors assume that there is imperfect competition in intermediate goods markets used to produce nal goods and where a larger mass of varieties increases the elasticity of substitution amongst them. Despite the different endogenous mark-up generation mechanism, the qualitative results are similar 36 .
In both the endogenous mark-up and the taste for variety (or increasing returns to specialisation) cases, scal policy (or aggregate demand management policy in general) has a positive effect on the ef ciency level in the economy. This allows the balanced-budget multiplier to be greater than one and simultaneously, for a given employment level, the output to be larger. Consequently, taking into account the multiplier effect of public over private consumption is given by m 1, it is possible to obtain a positive nal effect on households consumption. For the same reason, leisure will not decrease so much as in the previous cases.
Therefore, it is possible that scal policy, without any direct externalities, has a positive effect on households welfare as long as: i) the effect of the ef ciency gain is large enough to guarantee that m > 1 and ii) the increase in private consumption is suf ciently important to offset the reduction in leisure.

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 brie y 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-pro t condition only applies to the "marginal rm (industry)," the reason why its more ef cient competitors present positive pro ts. In their model, the absence of taste for variety leads to the entry of less ef cient rms, so it reduces the average ef ciency 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 in uenced by differences between the composition of private and public expenditures, when different market structures (perfect and monopolistic competition) exist simultaneously in the same economy.

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.

Intertemporal Household
In particular, the instantaneous household utility follows as before: equations (1) and (2) with λ = 0: The in nitely-lived household has a discount rate of ρ > 0 and, instead of (1), it maximises lifetime utility: In the dynamic model the household owns capital K (τ) at moment τ which it rents out to rms at price R (τ): hence its total income at time τ is as before, labour income w (τ) :L (τ) and equity pro ts Π (τ), plus the income from capital R (τ) :K (τ). 37 Notice that, with an in nitely-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) = T 0 (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: 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.

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 j 2 [0; n] employs labour and capital to produce output: where we assume that F K > 0, F N > 0, F KK < 0, F NN < 0, F KN > 0, also that function F ( ) is homogeneous to degree 1 (HoD1), i.e. the technology would present constant returns to scale (CRtS) if Φ was 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 pro t maximization imply (in a symmetric industry equilibrium): with the mark-up µ = σ 1 . 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 Since function F ( ) HoD1 in (K; N), by Euler's Theorem 39 we have Furthermore, in a symmetric equilibrium where p ( j) = P = 1, the pro ts of each rm are simply 40 : so that aggregating across all rms with equilibrium in the capital market, i.e. K = Again, equilibrium in the labour market implies that N = L. 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 pro t of µ, since only a proportion (1 µ) is used to pay for labour and capital. There is also the overhead xed cost, which may make the pro t per rm negative or positive, depending upon the level of output.

The Household's Intertemporal Optimization
The household chooses (C(τ); L(τ)) to maximize lifetime utility (31) subject to the accumulation equation (32) Using (34) we can express (w; R) in terms of the marginal products. Hence, we derive two basic optimality conditions: Intra-temporal optimality Once again 41 , M (C; Z) ;the marginal rate of substitution between consumption and leisure equals the net real wage rate Inter-temporal optimality The Euler condition. Assuming that u CZ = 0, i.e. assuming the felicity function is additively separable, this can be written as where θ u C =(C:u CC ) is the elasticity of intertemporal substitution in consumption.

Steady State
In the steady state, we have the condition that C = 0: Hence the Euler condition implies that where asterisks stand for steady-state values. In the Walrasian case (µ = 0) this is just the modi ed 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:F K L ; 1 = L: f (k), where k K=L. Hence the steady-state Euler condition is where f 0 (k) = F K K L ; 1 > 0 and f 00 (k) = F KK K L ; 1 < 0. With this particular market structure we can write the solution to this as k = k (µ) with k 0 (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 With this we have the income expansion path (IEP) for consumption and leisure, de ned by the intertemporal optimality condition and the steady-state wage www.economics-ejournal.org 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 by 42 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 n is xed. The household receives pro t 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, pro ts 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 gure 43 . Here we can see the equilibrium level of C and L = 1 Z . The optimal capital stock is then simply K = L :k (µ). 42 This can be derived from the budget constraint: 43 Uniqueness is not guaranteed when we have a signi cant taste for variety, i.e. λ is large, when the mark-up is endogenous, i.e. µ = µ (k ), or when there are increasing returns to scale at the aggregate level.

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 de ne labour supply as an implicit function of (C; K) : L = L(C; K; µ); with L C < 0 < L K and L µ < 0. 44 The dynamics are represented by the two isoclines: The consumption isocline is downward sloping in (K;C): it is de ned 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 (1 µ) :F K < ρ; to the left it is increasing. The capital isocline has the standard upward-sloping shape 45 : it need not be globally concave due to the effect of K on the labour supply. The phase diagram thus has a unique saddle-path solution as depicted in Figure 7.

The Effect of Imperfect Competition on the Long-run Equilibrium
In this section we illustrate the effect of a change in µ on the steady-state equilibrium from both (1 L;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: The EF curve rotates anti-clockwise. Since we have The real wage falls, so that the IEP moves to the right. Since from (37) These two effects are depicted in Figure 8, where the equilibrium moves from E 0 to E 1 when we compare a low-mark-up steady-state (µ = µ 0 ) with a largemark-up one (µ = µ 1 > µ 0 ).
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 L when µ is 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 speci c example.
Turning to capital-consumption space and the phase diagram, the way to understand the effect of µ is 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 F K falls as L decreases) and (ii) the capital isocline shifts downwards, as there is less output given (K;C). The shift from equilibrium E 0 to E 1 in 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 µ on labour supply is ambiguous. Here capital decreases, which is compatible with the reduction in employment observed in Figure 8.

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 If there is instantaneous free entry which drives pro ts to zero, from (35), for given (K; L) ; pro ts are zero when www.economics-ejournal.org 39 conomics: The Open-Access, Open-Assessment E-Journal Let us turn to leisure-income space. Free entry does not affect the IEP, which just depends on the real wage w (µ) which is not in uenced by entry. However, entry does affects the Euler frontier (39) since the level of aggregate overheads n :Φ varies according to (43). In factor-intensive notation, we have the "Free Entry Euler Frontier" (FEEF) that simpli es to The FEEF is steeper than the EF: a higher labour supply means that the mass of rms is larger which increases the socially wasteful overhead n :Φ thus reducing consumption by more than if n is xed. The two lines meet at the labour supply where the free-entry mass of rms happens to be equal to the exogenously given www.economics-ejournal.org 40 conomics: The Open-Access, Open-Assessment E-Journal Figure 10: Steady-State Equilibrium with Free Entry (I) mass of rms 46 : for labour supplies below this the FEEF lies above the EF (since there are less rms); for labour supplies above this the FEEF lies below the EF. This is depicted in Figure 10, where EF and FEEF intersect at point E.
If we turn to (K;C) space, free entry does not in uence the consumption isocline (since overheads do not in uence the marginal product of capital). The capital isocline becomes The capital isocline is affected: the xed-n isocline is steeper and intersects the free-entry isocline at the capital stock where the mass of rms under free entry 46 From (43), for given n, the critical level of labour supply is www.economics-ejournal.org 41 conomics: The Open-Access, Open-Assessment E-Journal Figure 11: Steady-State Equilibrium with Free Entry (II) equals the xed n (which is K ). For capital stocks below that, the free-entry isocline implies less overheads and lies above the xed-n isocline, and for capital above that level, it lies below the xed-n case. We depict this in Figure 11.
Also, we can easily see entry does not affect the dynamics of the steadystate equilibrium 47 . Notice the xed-mark-up monopolistically competitive model with free entry is formally equivalent to a Ramsey model with more inef cient production function given by (1 µ) :F.

Fiscal Policy, Entry, and Imperfect Competition
We will explore the effects of an increase in government expenditure funded by a lump-sum tax. This will divide into the long-run steady-state effects and the short-run impact effects, as well as the transition towards the steady state. We will assume that in the initial position we start off with zero pro ts, even in the case of a xed mass of rms. That means that the EF and FEEF both pass through the same point in steady state, i.e. point E 0 in Figure 12.
Turning rst to the long-run steady-state effects of an increase in government expenditure. In leisure-consumption space, the IEP is unaffected by the change in G. The EF and FEEF are both shifted down by a vertical distance equal to the increase in government expenditure. The new steady states are E NE for a xed number of rms, and E FE with free entry. As in the static case, the multiplier is "Walrasian" in the sense of being less than one and greater than zero. The drop in consumption is less than the increase in government expenditure 48 . How much less is determined by the slope of the EF and FEEF: a steeper slope results in more crowding out of consumption in steady state. This leads us to three simple conclusions: The multiplier with free-entry is smaller than the multiplier with a xed mass of rms, since FEEF is steeper than EF. This result is found in Coto-Martinez and Dixon (2003) for an open-economy context. Employment increases (leisure decreases) as G increases and the increase in the labour supply is greater when there is free entry.
An increase in imperfect competition makes both the FEEF and the EF atter, leading to less crowding out and to a larger output multiplier in each case.
None of these results requires that the initial steady-state is the same (where the FEEF and EF intersect) if there are homothetic preferences (and hence a linear IEP). If the IEP is non-linear, the result will hold if the initial position is the same. The intuition behind these results is the following: an increase in government spending nanced by a lump-sum tax makes the household worse off, so it cuts back on the good things in life, consumption and leisure. Because the economy is less ef cient (at the margin) with free entry, the required effort to supply the Figure 12: Long-Run Effects of Fiscal Policy extra output to the government is greater than with xed n, so that consumption and leisure decline more under free entry. An increase in imperfect competition means that whether there is a xed mass of rms or free entry, the weight of the tax burden falls more heavily on leisure so that the crowding out of consumption is less.
If we compare the steady states in (1 L;C) space, there is a striking similarity between static and dynamic models. Now, let us turn to the dynamics of the model with imperfect competition. In Coto-Martinez and Dixon (2003) these results are generalised to a small open economy setting.

Fiscal Policy: Short-run Dynamics
In Figure 13, using the (K;C) space, we have the two accumulation equations which we assume intersect at the initial steady-state. In this case, the xed-n capital accumulation schedule is steeper than the free-entry curve, as seen above. The effect of a permanent increase in G is to shift both curves down vertically in 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 where ΛX X NE X FE , with X NE = Xj No entry and X FE = Xj Free 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-n model. 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 > ΛC β NE :ΛK K NE K(0) > 0. Let us use a numerical illustration in order to see what can happen in speci c models. First, we assume the felicity function is isoelastic in both consumption and leisure, i.e.
u ((C (τ) ; Z (τ)) = C (τ) 1 1 F (K(τ); N(τ)) = A:K(τ) η :N(τ) 1 η , where 0 < η < 1. Now, we choose the following parameter values: The value of η was chosen in order to generate a long-run capital share in total income equal to one third. The value for ρ implies a 4 per cent return on capital per period. The values for θ and ψ imply elasticities of intertemporal substitution equal to one for both consumption and leisure. The value of σ gives 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 G 0 is the one that leads to a 20 per cent steady-state share of government consumption in output, and the value for Φ is such that pro ts are zero in the initial equilibrium (E 0 in Figure 13) when n = 1.
For this numerical illustration, a permanent one per cent increase in G leads 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.

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 pro ts). 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 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) andHall (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).

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), 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 multiplier 51 . 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 short-and 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 ef cient 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 later 52 . 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. nich (CESIfo), and York. Financial support by FCT (Fundação para a Ciência e a Tecnologia), Portugal is gratefully acknowledged. This article is part of the Multiannual Funding Project (POCI/U0436/2006). Teaching materials are available on https://aquila.iseg.utl.pt/aquila/homepage/f619/teaching/graduate/ scal-policyunder-imperfect-competition-with-fexible-prices.