PRODUCTIVE PUBLIC EXPENDITURE AND IMPERFECT COMPETITION WITH ENDOGENOUS PRICE MARKUP: COMMENT

Transcription

1 PRODUCTIVE PUBLIC EXPENDITURE AND IMPERFECT COMPETITION WITH ENDOGENOUS PRICE MARKUP: COMMENT Luís F. Costa (ISEG, Unversdade Técnca de Lsboa and UECE) Nuno Palma (London School of Economcs) ABSTRACT In a recent artcle Chen et al. (2005) analyse the role of government expendture n an mperfectly compettve statc model, ntroducng a government-expendture externalty through the producton functon. Our purpose n the present paper s to argue that the clam from the authors that ther model generates an endogenous markup s n our vew ncorrect. We argue that ther model does not contan an endogenous markup, but a fxed one and that ther clam s based upon an ncorrect nterpretaton of what s the margnal cost n ther own model. JEL Classfcaton: E12, E62, H54 Keywords: Endogenous markup. Insttuto Superor de Economa e Gestão Unversdade Técnca de Lsboa Rua do Quelhas LISBOA Portugal Tel.: Fax: E-mal: lukosta@seg.utl.pt London School of Economcs and Poltcal Scence Houghton Street, WC2A, 2AE Unted Kngdom E-mal: n.p.palma@lse.ac.uk Ths verson: October 2006

2 PRODUCTIVE PUBLIC EXPENDITURE AND IMPERFECT COMPETITION WITH ENDOGENOUS PRICE MARKUP: COMMENT by Luís F. Costa and Nuno Palma In a recent artcle Chen et al. (2005) analyse the role of government expendture n an mperfectly compettve statc model, ntroducng a governmentexpendture externalty through the producton functon. Our purpose n the present paper s to argue that the clam from the authors that ther model generates an endogenous markup s n our vew ncorrect. We argue that ther model does not contan an endogenous markup, but a fxed one and that ther clam s based upon an ncorrect nterpretaton of what s the margnal cost n ther own model. 1. Introducton In a recent artcle n Oxford Economc Papers, Chen et al. (2005) analyse the role of government expendture n an mperfectly compettve statc model, followng the Dxon (1987), Mankw (1988), and Startz (1989) approach, but ntroducng a government-expendture externalty through the producton functon. The authors clam ths gves rse to an endogenous ( ) markup, whch s used to measure the degree of monopoly - Chen et al. (2005), p The purpose of ths paper s to Correspondng author. Nuno Palma s a research assstant at UECE. 1

3 2 LUÍS COSTA AND NUNO PALMA argue that ther model does not contan an endogenous markup, but a fxed one, and that ther clam s based upon an ncorrect nterpretaton of what s the margnal cost n ther own model. Secton 2 presents the markup defntons used n the lterature and dscusses the mportance of a varable markup. Secton 3 presents the mcro-foundatons of the orgnal paper and compare ther markup measure wth the standard ones. Secton 4 concludes. 2. Markup Defntons and Usage When frms have the power to set prces facng downward-slopng demand curves, monopoly (market) power can be measured by the wedge between the margnal cost of producton (MC) and the prce pad by the buyer (p), wedge that the seller can keep to hm/herself. In order to quantfy t, there are two man measures of market power n the lterature: - the Lerner ndex, more popular n the IO lterature, that s defned as λ = (p - MC)/p [0, 1]; - the prce-cost wedge, used more often n the Macroeconomcs lterature, that s defned as z = p/mc [1, + ]. Both measures are connected by the monotonc relatonshp λ = 1 1/z, and a larger value for ether λ or z mples a hgher degree of monopoly power. As notced by Barro and Tenreyro (2006): 2

4 COMMENT ON PRODUCTIVE EXPENDITURE AND IMPERFECT COMPETITION 3 From the standpont of generatng fluctuatons n aggregate economc actvty, movements n markups reflectng shfts n the extent of competton work smlarly to the technologcal dsturbances usually stressed n real busness cycles (RBC) models. For an excellent survey on the mportance of endogenous markups n macroeconomcs see Rotemberg and Woodford (1999). However, markup fluctuatons are not the only source of endogenous varablty n the overall effcency level n the economy avalable n the macroeconomc lterature. Several types of externalty also affect observed total (prvate) factor productvty, as measured by the Solow resdual, and they are not due to fluctuatons n market power. 3. Mcro-Foundatons and Markup n Chen et al. (2005) The orgnal artcle here dscussed presents a closed economy populated by n - a large number of - Dxt and Stgltz (1977) monopolstc producers, each one usng the followng technology to generate a dfferentated product varety: (1) y f ( L, G) =, = 1, 2,, n where y represents the output of frm, L s ts labour nput, and G s government expendture (on nfrastructure). Here, frm obtans ts labour n a compettve labour market at a wage rate w, and G s a publc good avalable to all frms a zero prce. Furthermore, we know that f L > 0, f LL < 0, f G > 0, f GG < 0, and f LG 0, where f u = f/ u and f uv = 2 f/( u v), wth u, v = L, G. Thus, government expendture works as a postve externalty n producton as t s a non-rval non-excludable nput for frms. 3

5 4 LUÍS COSTA AND NUNO PALMA Here, labour demand for frm can be wrtten as (2) L φ ( y, G) =, = 1, 2,, n where φ 1 φ/ y = 1/f L > 0 and φ 2 φ/ G = -f G /f L < 0. In the model produced by Chen et al. (2005), nether of the two measures mentoned above (λ or z) s used. In fact, the authors use a prce-wage rato - see equaton (9) and the followng lne n page 527 of the orgnal artcle: p σ =. 1, > 1, w σ 1 (3) µ φ ( y G) where σ s the prce (p ) elastcty of demand faced by producer. We beleve ths approach s ncorrect, as the wage rate does not correspond to the margnal cost of the model (n whch case the measure used would be the prce-cost wedge, whch we beleve the authors were tryng to calculate). We wll now dscuss why the margnal cost s not equvalent to the wage rate n ths model. In a model where labour s the only prvate nput acqured by frms, as n ths case, total cost s gven by TC = w.l = w.φ(y,g) and consequently the margnal cost s MC = TC / y = w/f L = w.φ 1 (y,g). Note that the margnal cost would only be equal to the wage rate f and only f the producton functon was y =1.L (no externalty and unt average labour productvty). Several addtonal ssues need clarfcaton at ths pont. Frst, there s no mathematcal reason why µ (the recprocal of the real wage n a symmetrc equlbrum) should be bounded below by 1, wth the general producton functon chosen. The value of φ 1 s expressed n unts of labour per unt of good, thus ts 4

6 COMMENT ON PRODUCTIVE EXPENDITURE AND IMPERFECT COMPETITION 5 numercal value clearly depends on the choce of unts whch does not guarantee the expresson s larger than unty. Second, and most serously, s the fact that usng an approprate markup measure we obtan λ = 1/σ and z = σ/(σ 1) a fxed markup. Despte the fact that labour s the only prvate nput, and that labour demand s affected by fscal polcy, the monopoly power s not affected by fscal polcy. Ths should be clear when we observe the demand functon faced by frm n equaton (3) of the orgnal artcle, and the market structure assumed (Dxt-Stgltz monopolstc competton): the prce elastcty of demand faced by each producer s fxed and there s no way the market share of each producer would vary under a symmetrc equlbrum. It s mportant to note, once agan, that µ s nothng else than the recprocal of the real wage. What the authors have n ths paper s no more than a fluctuatng real wage: the real wage depends postvely on government expendture n nfrastructure, and nevertheless the markup remans fxed. What does vary wth fscal polcy here s the margnal cost. However, ths also happens (ndrectly) n all general-equlbrum models, even n perfectly compettve ones. What s new n Chen et al. (2005) s the postve externalty n producton that may decrease the margnal cost nstead of ncreasng t va equlbrum producton and wages. Fnally, notce that µ stll vares wth G when σ,.e. when there s perfect competton. Obvously, t does not make any sense to have an endogenous markup under perfect competton. In fact, the results n Chen et al. (2005) have nothng to do wth markup varaton: they are drven by an externalty that s closer to the effects of ncreasng returns to specalsaton as n Devereux et al. (1996) or love for varety n 5

7 6 LUÍS COSTA AND NUNO PALMA Hejdra and van der Ploeg (1996). For a model studyng the effects of a really endogenous markup (entry n a Cournotan model) wthn the Dxon-Mankw-Startz framework see Costa (2004). 4. Concluson In ths comment t s shown that Chen et al. (2005) produced a model where the markup s fxed due to an ncorrect dentfcaton of the margnal cost for ther typcal frm. Therefore, ther clam that government expendture n nfrastructure affects the markup s ncorrect and changes n labour effcency are solely due to the drect effect of government expendture on the producton functon (a postve externalty). Acknowledgements The authors would lke to thank Huw Dxon for hs comments on an earler verson. UECE (Research Unt on Complexty and Economcs) s supported by FCT (Fundação para a Cênca e a Tecnologa, Portugal). The usual dsclamer apples. References Barro R., and S. Tenreyro: "Closed and Open Economy Models of Busness Cycles wth Marked Up and Stcky Prces," Economc Journal, 116 (2006), Chen J.-H., J.-Y. Sheh, C.-C. La, and J.-J. Chang: "Productve Publc Expendture and Imperfect Competton wth Endogenous Prce Markup," Oxford Economc Papers, 47 (2005), Costa L.: "Endogenous Markups and Fscal Polcy," Manchester School, 72 Supplement (2004),

8 COMMENT ON PRODUCTIVE EXPENDITURE AND IMPERFECT COMPETITION 7 Devereux M., A. Head, and B. Lapham: "Monopolstc Competton, Increasng Returns, and the Effects of Government Spendng," Journal of Money, Credt, and Bankng, 28 (1996), Dxt A., and J. Stgltz: "Monopolstc Competton and Optmum Product Dversty," Amercan Economc Revew, 67 (1977), Dxon H.: "A Smple Model of Imperfect Competton wth Walrasan Features," Oxford Economc Papers, 39 (1987), Hejdra B., and F. van der Ploeg: "Keynesan Multplers and the Cost of Publc Funds under Monopolstc Competton," Economc Journal, 106 (1996), Mankw N. G.: "Imperfect Competton and the Keynesan Cross," Economc Letters, 26 (1988), Rotemberg, J., and M. Woodford: "The Cyclcal Behavor of Prces and Costs," n Handbook of Macroeconomcs, ed. by J. Taylor and M. Woodford. Amsterdam: Elsever, Startz R.: "Monopolstc Competton as a Foundaton for Keynesan Macroeconomc Models," Quarterly Journal of Economcs, 104 (1989),