MATCHING MARKET CLEARING OCTOBER 15, 2015

Size: px

Start display at page:

Download "MATCHING MARKET CLEARING OCTOBER 15, 2015"

Osborne Cox
5 years ago
Views:

1 MATCHING MARKET CLEARING OCTOBER 15, 2015

2 Iroducio TIMING OF EVENTS Macig mare clearig e wage deermiaio Focu ju o exeive margi Ocober 15,

3 Employme Margi LABOR SUPPLY (LFP) Repreeaive oueold max E u( c ) 1 c,, 0 0 lp c (1 ) w (1 ) b (1 ) x 1 lp (1 ) Coumpio-LFP opimaliy codiio '( lp ) x '( lp 1) u '( x 1) b 1 1 (1 ) w (1 ) b (1 ) E1 u'( c ) u' ( x 1) 1 Ocober 15,

4 Employme Margi LABOR SUPPLY (LFP) Deiiio: Houeold opimaliy i a e o ae-coige ucio or c,, a aiy Coumpio-LFP opimaliy codiio '( lp ) x '( lp 1) u '( x 1) b 1 1 (1 ) w (1 ) b (1 ) E1 u'( c ) u' ( x 1) 1 Houeold budge corai c (1 ) w (1 ) b Perceived law o moio o employme (aa job-idig corai) (1 ) x 1 aig a give exogeou procee ad -1, w, Ocober 15,

5 Employme Margi LABOR DEMAND (JC) Repreeaive irm D max E0 0 ( ) D z w v v, 0 D x.. (1 ) v D 1 Job-creaio codiio D D x z '( ) w (1 ) E 1 1 Ocober 15,

6 Employme Margi LABOR DEMAND (JC) Deiiio: Firm opimaliy i a e o ae-coige ucio D v, a aiy Job-creaio codiio D D x z '( ) w (1 ) E 1 1 Perceived law o moio o employme (aa job irig corai) (1 ) v D x D 1 aig a give exogeou procee ad -1, w Ocober 15,

7 Employme Margi MATCHING MARKET CLEARING Deiiio: Equilibrium opimaliy i a e o ae-coige ucio, v,,, c a aiie aggregae RC, Coumpio-LFP opimaliy codiio '(1 Job-creaio codiio ( )) u'( c ) ( )(1 ) w (1 ( )) b '( lp ) u'( x ) b 1 ( )(1 x ) E 1 u' ( x 1) ( 1) D D x z '( ) w (1 ) E1 ( ) ( ( ) 1 ) Ocober 15,

8 Employme Margi MATCHING MARKET CLEARING Deiiio: Equilibrium opimaliy i a e o ae-coige ucio, v,,, c a aiie aggregae RC, Coumpio-LFP opimaliy codiio Job-creaio codiio Aggregae LOM or employme AND '(1 ( )) u'( c ) D D x z '( ) w (1 ) E 1 ( ) ( ( )(1 ) w (1 ( )) b '( lp ) u'( x ) b 1 ( )(1 x ) E 1 u' ( x 1) ( 1) (1 ) m(, v ) x 1 ( ) 1 ) Ocober 15,

9 Employme Margi MATCHING MARKET CLEARING Deiiio: Equilibrium opimaliy i a e o ae-coige ucio, v,,, c a aiie aggregae RC, Coumpio-LFP opimaliy codiio '(1 ( )) u'( c ) Job-creaio codiio Aggregae LOM or employme ( )(1 ) w (1 ( )) b '( lp ) u'( x ) b 1 ( )(1 x ) E 1 u' ( x 1) ( 1) D D x z '( ) w (1 ) E 1 ( ) ( (1 ) m(, v ) x 1 ( ) 1 ) Macig-mare clearig ( ) ( ) v m(, v ) Ocober 15,

10 Employme Margi LABOR SUPPLY (LFP) Coider ρ x = 1, b =0 Deiiio: Houeold opimaliy i a e o ae-coige ucio or c,, a aiy Coumpio-LFP opimaliy codiio Houeold budge corai '(1 ) u'( c ) (1 ) w c (1 ) w Perceived law o moio o employme (aa job-idig corai) aig a give exogeou procee ad -1, w, Ocober 15,

11 Employme Margi LABOR SUPPLY (LFP) Coider ρ x = 1, b =0 Deiiio: Houeold opimaliy i a e o ae-coige ucio or c,, a aiy Coumpio-LFP opimaliy codiio Houeold budge corai '(1 ) u'( c ) (1 ) w c (1 ) w Perceived law o moio o employme (aa job-idig corai) aig a give exogeou procee ad -1, w, Ocober 15,

12 Employme Margi LABOR SUPPLY (LFP) Coider ρ x = 1, b =0 Deiiio: Houeold opimaliy i a e o ae-coige ucio or c, a aiy Coumpio-LFP opimaliy codiio ' (1 ) w u '( c ) Houeold budge corai c (1 ) w aig a give exogeou procee ad -1, w, Ocober 15,

13 Employme Margi LABOR SUPPLY (LFP) Coider ρ x = 1, b =0 Deiiio: Houeold opimaliy i a e o ae-coige ucio or c, a aiy Coumpio-LFP opimaliy codiio ' ( ) ( )(1 ) w u'( c ) Houeold budge corai c (1 ) w aig a give exogeou procee ad -1 ( ), w, Ocober 15,

14 Employme Margi LABOR DEMAND (JC) Deiiio: Firm opimaliy i a e o ae-coige ucio D v, a aiy Job-creaio codiio D z'( ) w Perceived law o moio o employme (aa job irig corai) v aig a give exogeou procee ad -1 D, w Ocober 15,

15 Employme Margi LABOR DEMAND (JC) Deiiio: Firm opimaliy i a e o ae-coige ucio D v, a aiy Job-creaio codiio ( ) z' ( D ) w Perceived law o moio o employme (aa job irig corai) D v ( ) aig a give exogeou procee ad -1 ( ), w Ocober 15,

16 Employme Margi MATCHING MARKET CLEARING Deiiio: Equilibrium opimaliy i a e o ae-coige ucio, v,,, c a aiie aggregae RC, Aggregae RC c v z ( ) Coumpio-LFP opimaliy codiio Job-creaio codiio ' ( ) ( )(1 ) w u' ( c ) Aggregae LOM or employme ( ) z' ( ) w m(, v ) Solve or θ uig job idig corai Solve or θ uig irm job irig corai Macig-mare clearig ( ) ( ) v m(, v ) Ocober 15,

17 Employme Margi MATCHING MARKET CLEARING Fucioal orm m 1 (, v) v m v v m (, v ) (1 ) v (1 ) (, ) v ( ) ( ) 1 ( ) 1 ( ) 11/ ( lp ) lp 1/ '( lp ) 1 lp uc ( ) 1/ c u'( c ) 1 ' ( ) z '( ) w ( ) w ( ) u' ( c ) Subiue (ad e ax rae = 0) Ocober 15,

18 Employme Margi MATCHING MARKET CLEARING I (θ, ) pace 1 1/ 1 1 w z w ad olve or θ LFP ad θ JC LFP 1/ 1 ( 1 )(1 1/ ) w JC 1 z w 1 Ocober 15,

19 Employme Margi MATCHING MARKET CLEARING I (θ, ) pace 1/ 1 1 w z 1 w ad olve or θ LFP ad θ JC LFP 1/ 1 ( 1 )(1 1/ ) w JC 1 z w 1 Areeau ad Cug (2012 JPE, Propoiio 1 (p. 950)) Eicie allocaio caracerized by '( lp ) m (, v ) u'( c ) m (, v ) MRSc, lp MRTc, lp v Give ucioal orm, aed i (θ, ) pace?... Ocober 15,

20 Employme Margi MATCHING MARKET CLEARING I (θ, ) pace 1/ 1 1 w 1 z w ad olve or θ LFP ad θ JC LFP 1 ( 1 )(1 1/ ) w 1/ JC 1 z w 1 Areeau ad Cug (2012 JPE, Propoiio 1 (p. 950)) Eicie allocaio caracerized by '( lp ) m (, v ) u'( c ) m (, v ) MRSc, lp MRTc, lp v Give ucioal orm, aed i (θ, ) pace LFP JC Obviou i (deceralized equilibrium a uppor ) eicie allocaio. Ocober 15,

21 Employme Margi MATCHING MARKET CLEARING I (θ, ) pace 1/ 1 1 w 1 z w ad olve or θ LFP ad θ JC LFP 1 ( 1 )(1 1/ ) w 1/ JC 1 z w 1 Areeau ad Cug (2012 JPE, Propoiio 1 (p. 950)) Eicie allocaio caracerized by '( lp ) m (, v ) u'( c ) m (, v ) MRSc, lp MRTc, lp v Give ucioal orm, aed i (θ, ) pace LFP, EFF JC, EFF Obviou i (deceralized equilibrium a uppor ) eicie allocaio. Ocober 15,

22 Employme Margi MATCHING MARKET CLEARING Aggregae macig-mare clearig Aggregae macig mare clearig v m(, v) ew employee Ocober 15,

23 Employme Margi MATCHING MARKET CLEARING Aggregae macig-mare clearig Experime 1: labor icome ax rae τ > 0 * LFP, EFF VC, EFF ( ; ) ( ; ), LOW i i i WEDGE d Aggregae macig mare clearig v m(, v) ew employee Ocober 15,

24 Employme Margi MATCHING MARKET CLEARING Aggregae macig-mare clearig Experime 2: uemployme beei b > 0 HIGH WEDGE ( ; ) ( ; ) d LFP, EFF VC, EFF b, * i i i Aggregae macig mare clearig v m(, v) ew employee Ocober 15,

25 Employme Margi MATCHING MARKET VS. WALRASIAN MARKET Suppoe eicie * (e.g., CSE or Na-Hoio bargaiig) Ceeri paribu: icreae i labor ax rae Queio: are labor wedge ideical? Ocober 15,

Economics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017

Economics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017 Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy