MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 20, 2015

Transcription

1 MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 20, 2015

2 Dixi-Sigliz Model BUILDING THE EQUILIBRIUM Puing hings ogeher impose symmery across all i 1 pz f ( k, n ) r k & 1 pz f ( k, n ) w n & p mc 1 mc implies w r zf( k, n) zf( k, n) n k Symmeric equilibrium relaive price of an inermediae good? Subsiue demand funcions ino DS aggregaor and compue p 1 Wih measure one of inermediae firms, can hink of as a normalizaion bu wha if measure [0,N] of firms? mc 1 < 1 wih ε > 1 and ε < infiniy Monopoly power causes facor prices o fall below marginal producs hence inefficienly low equilibrium facor use hence inefficienly low oal oupu Ocober 20,

3 Dixi-Sigliz Model MONOPOLISTICALLY-COMPETITIVE EQUILIBRIUM Equilibrium Condiions (symmeric across all differeniaed goods) Consumpion-leisure opimaliy condiion Consumpion-savings opimaliy condiion Aggregae resource consrain c k 1 (1 ) k z f ( k, n) (possibly also include g ) (Marke clearing in labor, capial, and goods markes) mc ( < 1 wih ε > 1) 1 Facor prices a markdown of marginal producs 1 1 w z fn( k, n), k z fk( k, n) Ocober 20,

4 Dixi-Sigliz Model THE LABOR WEDGE D S markdown of real wage from marginal produc of labor Labor Wedge MP N w Monopoly disorion in goods marke refleced in disorion in labor (and oher facor) markes L M L F Labor Ocober 20,

5 Dixi-Sigliz Model BUSINESS CYCLES W/ MONOP. COMPETITION Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge and consan markup over ime Time-varying endogenous markup? Ocober 20,

6 Dixi-Sigliz NK Model BUSINESS CYCLES W/ MONOP. COMPETITION Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge and consan markup over ime Quesion: Why do hese firms earn posiive economic flow profis? Ocober 20,

7 Endogenous Enry Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge and consan markup over ime Time-varying endogenous markup? Endogenous enry of produc varieies/firms Ocober 20,

8 Endogenous Enry Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge and consan markup over ime Time-varying endogenous markup? Endogenous enry of produc varieies/firms 10% of U.S. GDP accouned for by new produc creaion 9% of los U.S. GDP accouned for by produc desrucion Based on 50% and 45% for U.S. manufacuring secor respecively (Bernard, Redding, and Scho (2010 AER)) 10% of consumers purchases in a year devoed o new goods no previously available (Produc desrucion less cyclical han produc creaion) Broda and Weinsein (2010 AER) Ocober 20,

9 Endogenous Enry Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge and consan markup over ime Time-varying endogenous markup? Dixi-Sigliz (1977 AER) Benassy (1996 EcLeers) Endogenous enry of produc varieies/firms 1 1 i N y y di 0 N i i 0 y N y d ε measures elasiciy of subsiuion across any wo differeniaed varieies κ + 1 = ε /(ε -1) recovers Dixi- Sigliz κ measures love of variey effec Ocober 20,

10 Endogenous Enry Endogenous enry of produc varieies/firms 1 1 i N y y di 0 N i i 0 y N y d Wihou oher mechanisms, endogenous enry does NOT generae markup flucuaions for hese variey aggregaors Comin and Gerler (2006 AER) Jaimovich and Floeoo (2008 JME) Head and Lampham (1996 JEDC) DO generae endogenous counercyclical markups (NB: All based on Romer (1990) endogenous R&D growh model) Shorcomings No STOCK NATURE of R&D s newly-developed producs No ime-o-build aspec All new produc varieies become obsolee afer one period Ocober 20,

11 BGM Bilbiie, Ghironi, and Meliz (2012 JPE) Time-o-build beween R&D coss and appearance of new variey Ocober 20,

12 BGM Bilbiie, Ghironi, and Meliz (2012 JPE) Time-o-build beween R&D coss and appearance of new variey Represenaive firm wih N independen producion lines Each line auonomously develops is own producs Disney acquired Pixar in 2006 (Pixar operaes auonomously of Disney) Apple acquired Beas in 2014 (Beas operaes auonomously of Apple) Ocober 20,

13 BGM Bilbiie, Ghironi, and Meliz (2012 JPE) Time-o-build beween R&D coss and appearance of new variey Represenaive firm wih N independen producion lines ρ is relaive price of variey Each line auonomously develops is own producs Disney acquired Pixar in 2006 (Pixar operaes auonomously of Disney) Apple acquired Beas in 2014 (Beas operaes auonomously of Apple) max E ( mc ) q N mc f N 1, NE, 0 { N } 0 0 E, E, 0 N 1 (1 )( N Law of moion for number of NE, ) produc varieies, which urn over a rae δ f E he produc developmen cos, in erms of labor unis Ocober 20,

14 BGM FOCs max E ( mc ) q N mc f N 1, NE, 0 { N } 0 0 E, E, 0 s.. N 1 (1 )( N Law of moion for number of NE, ) produc varieies, which urn over a rae δ f E he produc developmen cos, in erms of labor unis N +1 : N E, : Ocober 20,

15 BGM FOCs max E ( mc ) q N mc f N 1, NE, 0 { N } 0 0 E, E, 0 s.. N 1 (1 )( N Law of moion for number of NE, ) produc varieies, which urn over a rae δ f E he produc developmen cos, in erms of labor unis N +1 : N E, : Produc creaion condiion Characerizes opimal invesmen in R&D/produc developmen Free-enry condiion for produc developmen mc f (1 ) E ( mc ) q( ) mc f E, E, 1 Ocober 20,

16 BGM Differen forms of final goods aggregaors Dixi-Sigliz (1977 AER) 1 1 i N y y di 0 ε measures elasiciy of subsiuion across any wo differeniaed varieies Benassy (1996 EcLeers) N i 0 y N y di κ + 1 = ε /(ε -1) recovers Dixi- Sigliz κ measures love of variey effec Ocober 20,

17 Endogenous Enry MARKUPS, RELATIVE PRICE, & LOVE OF VARIETY Symmeric equilibrium across differeniaed produc varieies Dixi-Sigliz Benassy Markup µ(n ) µ = ε/(ε-1) µ = ε/(ε-1) Relaive price ρ(n ) = N µ-1 = N κ Love of variey є(n ) = µ 1 = κ Ocober 20,

18 BGM Differen forms of final goods aggregaors Dixi-Sigliz (1977 AER) 1 1 i N y y di 0 ε measures elasiciy of subsiuion across any wo differeniaed varieies Benassy (1996 EcLeers) N i 0 y N y di κ + 1 = ε /(ε -1) recovers Dixi- Sigliz κ measures love of variey effec Translog aggregaor No closed-form aggregaor exiss Primiive is expendiure funcion (expendiure minimizaion) See Feensra (2003 Economics Leers) for deails Ocober 20,

19 Endogenous Enry Translog uni expendiure funcion on differeniaed inermediae varieies ln P ln pd ln pln p ln p dd 2 N N N 2N Noaion N mass of poenial se of varieies ha could ever exis price elasiciy of spending share on an individual variey Ocober 20,

20 Endogenous Enry Translog uni expendiure funcion on differeniaed inermediae varieies ln P ln pd ln pln p ln p dd 2 N N N 2N Noaion N mass of poenial se of varieies ha could ever exis price elasiciy of spending share on an individual variey ( N ) 1 ranslog markup Depends on number of produc varieies 1 N vs. D-S or Benassy markup Love of variey ( N ) ( N) ( N) 1 2 N 2 = µ - 1 for Dixi-Sigliz = κ for Benassy Ocober 20,

21 Endogenous Enry Translog uni expendiure funcion on differeniaed inermediae varieies ln P ln pd ln pln p ln p dd 2 N N N 2N Noaion N mass of poenial se of varieies ha could ever exis price elasiciy of spending share on an individual variey ( N ) 1 1 N ranslog markup Profi-desrucion exernaliy inheren in ranslog aggregaor Causes OVER-producion of varieies Scope for correcive policy Model-consisen MRTs (Chugh and Ghironi, 2015) BGM II (2008 NBER WP) Ocober 20,

22 Endogenous Enry MARKUPS, RELATIVE PRICE, & LOVE OF VARIETY Symmeric equilibrium across differeniaed produc varieies Dixi-Sigliz Benassy Translog Markup µ(n ) µ = ε/(ε-1) µ = ε/(ε-1) µ = 1 + 1/(σN) Relaive price ρ(n ) = N µ-1 = N κ = exp Love of variey є(n ) = µ 1 = κ = 1/(2σN) = ½ (µ(n) 1) Ocober 20,