In this note we show that the claim from Chen et al (2005) that their model generates an endogenous markup is incorrect. This is not only a nomenclature issue: using the �fixed markup which we show to be the only one consistent with the structure of the model implies the main conclusions in that paper do not hold. In particular, government expenditure in infrastructure cannot affect the business cycle in this model by deliberately changing the market structure of the economy.Endogenous markup

Costa, Luís

Palma, Nuno

English

Research Papers in Economics

Comment on "Productive Public
Expenditure with Endogenous Price
Markup"￿
Lu￿s Costay Nuno Palmaz
June 2007
Abstract
In this note we show that the claim from Chen et al (2005) that their
model generates an endogenous markup is incorrect. This is not only a
nomenclature issue: using the ￿xed markup which we show to be the only
one consistent with the structure of the model implies the main conclu-
sions in that paper do not hold. In particular, government expenditure
in infrastructure cannot a⁄ect the business cycle in this model by delib-
erately changing the market structure of the economy.
JEL Classi￿cation: E10, E62, H54.
Keyword: Endogenous markup.
￿Without implication, the authors would like to thank Huw Dixon for his comments on an
earlier version. UECE (Research Unit on Complexity and Economics) is ￿nancially supported
by FCT (Funda￿ªo para a CiŒncia e a Tecnologia), Portugal. This comment is part of the
multi-annual Funding Project (POCTI/0436/2003).
yCorresponding author. ISEG (School of Economics and Management), Technical Univer-
sity of Lisbon (TULisbon), Rua do Quelhas 6, 1200-781 Lisboa, Portugal; and UECE (Re-
search Unit on Complexity and Economics), Rua Miguel Lupi 20, 1249-078 Lisboa, Portugal;
e-mail: lukosta@iseg.utl.pt
zLondon School of Economics and Political Science, Houghton Street, London WC2A 2AE,
United Kingdom, e-mail: n.p.palma@lse.ac.uk
11 Introduction
In a recent article in Oxford Economic Papers, Chen et al. (2005) analyze
the role of government expenditure in an imperfectly competitive static model,
following the Dixon (1987), Mankiw (1988), and Startz (1989) approach, but
introducing a government-expenditure externality through the production func-
tion. The authors claim this gives rise to an endogenous " (...) ￿ markup,￿
which is used to measure the degree of monopoly"1. In this comment we show
the above mentioned model does not contain an endogenous markup, but a ￿xed
one, and the authors￿claim is based upon an incorrect interpretation of what
the marginal cost for the typical ￿rm in the model.
Section 2 presents the markup de￿nitions used in the literature and discusses
the importance of this variable. Section 3 considers the microfoundations of the
original paper and compares their markup measure with the standard ones.
Section 4 concludes.
2 Markup De￿nitions and Usage
When ￿rms have the power to set prices facing downward-sloping demand
curves, monopoly (market) power can be measured by the wedge between the
marginal cost of production (MC) and the price paid by the buyer (p), wedge
that the seller can keep to him/herself.
In order to quantify it, there are two main measures of market power used
in the literature:
- the Lerner index, more popular in the IO literature, that is de￿ned as
￿ =
p ￿ MC
p
, ￿ [0;1] (1)
- the price-cost wedge, used more often in the Macroeconomics literature,
that is de￿ned as
z =
p
MC
, ￿ [1;+1] (2)
Both measures are connected by the monotonic relationship ￿ = 1 ￿ 1=z;
and a larger value for either ￿ or z implies a higher degree of monopoly power.
The claim that one particular macro-model produces changes in the values
of market power is crucial, as noticed by Barro and Tenreyro (2006):
From the standpoint of generating ￿ uctuations in aggregate eco-
nomic activity, movements in markups ￿re￿ ecting shifts in the ex-
tent of competition ￿work similarly to the technological disturbances
usually stressed in real business cycles (RBC) models.
1Chen et al. (2005), p. 527.
2For an excellent survey on the importance of endogenous markups in macro-
economics see Rotemberg and Woodford (1999).
However, markup ￿ uctuations are not the only source of endogenous variabil-
ity in the overall e¢ ciency level in the economy available in the macroeconomic
literature. Several types of externality also a⁄ect ￿ observed￿total (private) fac-
tor productivity, as measured by the Solow residual, and they are not due to
￿ uctuations in market power.
3 Micro-Foundations and Markup in Chen et al.
(2005)
The original article here discussed presents a closed economy populated by n
(a large number of) Dixit and Stiglitz (1977) monopolistic producers, each one
using the following technology to generate a di⁄erentiated product variety:
yi = f(Li;G) ; i = 1;2;:::n (3)
where yi represents the output of ￿rm i, Li is its labor input, and G is
government expenditure (on infrastructure). Here, ￿rm i obtains its labor in
a competitive market at a wage rate w, and G is a public good available to
all ￿rms at zero price. Furthermore, we know that fL > 0, fLL < 0, fG > 0,
fGG < 0, and fLG R 0; where fu =
@f
@uand fuv =
@
2f
@u@v with u;v = L;G. Thus,
government expenditure works as a positive externality in production as it is a
non-rival non-excludable input for ￿rms.
Here, ￿ labor demand￿for ￿rm i can be written as
Li = ￿(Yi;G) ; i = 1;2;:::n (4)
where ￿1 =
@￿
@yi = 1
fL > 0 and ￿2 =
@￿
@Gi = 1
fL > 0 = ￿
fG
fL < 0.
In the model produced by Chen et al. (2005), neither of the two measures
mentioned above (￿ or z) is used. In fact, the authors use a price-wage ratio:2
￿ ￿
pi
w
=
￿
￿ ￿ 1
:￿i(yi;G) > 1 (5)
where ￿ is the price (pi) elasticity of demand faced by producer i. This
approach is incorrect, as the wage rate does not correspond to the marginal cost
of the model (in which case the measure used would be the price-cost wedge,
which we believe the authors were trying to calculate).
We will now discuss why the marginal cost is not equivalent to the wage rate
in this model. In a model where labor is the only private input acquired by ￿rms,
as in this case, total cost is given by TCi = w:Li = w:￿(yi;G) and consequently
the marginal cost is MCi = @TCi
yi = w
fL = w:￿1(yi;G). Note that the marginal
2See equation (9) and the following line in page 527 of the original article.
3cost would only be equal to the wage rate if and only if the production function
was yi = 1:Li (no externality and unit average labor productivity).
Some additional issues need clari￿cation at this point. First, there is no
mathematical reason why ￿ (the reciprocal of the real wage in a symmetric
equilibrium) should be bounded below by 1, with the general production func-
tion chosen. The value of ￿1 is expressed in units of labor per unit of good i,
thus its numerical value clearly depends on the choice of units which does not
guarantee the expression is larger than one.
Second, and more importantly, using an appropriate markup measure we ob-
tain ￿ = 1
￿ and z = ￿
￿￿1, a ￿xed markup. Despite the fact that labor is the only
private input, and that labor demand is a⁄ected by ￿scal policy, the monopoly
power is not a⁄ected by ￿scal policy. This should be clear when we observe the
demand function faced by ￿rm i in equation (3) of the original article, and the
market structure assumed (Dixit-Stiglitz monopolistic competition): the price
elasticity of demand faced by each producer is ￿xed and there is no way the
market share of each producer can vary under a symmetric equilibrium.
It is important to remember that ￿ is nothing else than the reciprocal of
the real wage. What the authors have in this paper is a ￿ uctuating real wage:
the real wage depends positively on government expenditure in infrastructure,
and the markup remains ￿xed. What does vary with ￿scal policy here is the
marginal cost. However, this also happens (indirectly) in all general-equilibrium
models, even in perfectly competitive ones. What is new in Chen et al. (2005)
is the positive externality in production that may decrease the marginal cost
instead of increasing it via equilibrium production and wages.
Finally, notice that ￿ still varies with G when ￿ ! 1, i.e. when there
is perfect competition. Obviously, it does not make any sense to have an en-
dogenous markup under perfect competition. In fact, the results in Chen et
al. (2005) have nothing to do with markup variation: they are driven by an
externality that is closer to the e⁄ects of increasing returns to specialization
as in Devereux et al. (1996) or love for variety in Heijdra and van der Ploeg
(1996). For a model studying the e⁄ects of a really endogenous markup (entry
in a Cournotian model) within the Dixon-Mankiw-Startz framework see Costa
(2004).
4 Concluding Remark
The model in Chen et al. (2005) contains a ￿xed markup, due to an incor-
rect identi￿cation from the authors of the marginal cost for their typical ￿rm.
Therefore, the claim that government expenditure in infrastructure a⁄ects the
markup in this model is incorrect. Changes in labor e¢ ciency are solely due
to the direct e⁄ect of government expenditure on the production function (a
positive externality).
4References
[1] Barro R., and S. Tenreyro (2006) "Closed and Open Economy Models of
Business Cycles with Marked Up and Sticky Prices" Economic Journal
116, 434-456.
[2] Chen J.-H., J.-Y. Shieh, C.-C. Lai, and J.-J. Chang (2005) "Productive
Public Expenditure and Imperfect Competition with Endogenous Price
Markup" Oxford Economic Papers 47, 522-544.
[3] Costa L. (2004) "Endogenous Markups and Fiscal Policy" Manchester
School 72, 55-71.
[4] Devereux M., A. Head, and B. Lapham (1996) "Monopolistic Competition,
Increasing Returns, and the E⁄ects of Government Spending" Journal of
Money, Credit, and Banking 28, 233-254.
[5] Dixit A., and J. Stiglitz (1977) "Monopolistic Competition and Optimum
Product Diversity" American Economic Review 67, 297-308.
[6] Dixon H. (1987) "A Simple Model of Imperfect Competition with Walrasian
Features" Oxford Economic Papers 39, 134-160.
[7] Heijdra B., and F. van der Ploeg (1996) "Keynesian Multipliers and the
Cost of Public Funds under Monopolistic Competition" Economic Journal
106, 1284-1296.
[8] Mankiw N.G. (1988) "Imperfect Competition and the Keynesian Cross"
Economic Letters 26, 7-14.
[9] Rotemberg, J., and M. Woodford (1999) "The Cyclical Behavior of Prices
and Costs" in Handbook of Macroeconomics by J. Taylor and M. Woodford,
Eds., Amsterdam: Elsevier, 1051-1135.
[10] Startz R. (1989) "Monopolistic Competition as a Foundation for Keynesian
Macroeconomic Models" Quarterly Journal of Economics 104, 737-752.
5

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