CENTRE FOR ECONOMIC RESEARCH WORKING PAPER SERIES

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1 CENTRE FOR ECONOMIC RESEARCH WORKING PAPER SERIES 2001 Mmum Wages for Roald McDoald Moopsoes: A Theory of Moopsostc Competto by V Bhaskar ad Ted To A Commet Frak Walsh, Uversty College Dubl WP01/18 September 2001 DEPARTMENT OF ECONOMICS UNIVERSITY COEGE DUBIN BEFIED DUBIN 4

2 MINIMUM WAGES FOR RONAD McDONAD MONOPSONIES: A THEORY OF MONOPSONISTIC COMPETITION by V. Bhaskar ad Ted To A COMMENT BY Frak Walsh 1 Ecoomcs Departmet Uversty College Dubl Belfeld Dubl 4. Abstract Bhaskar ad To (1999) develop a model of moopsostc competto ad solve explctly for equlbrum. Whle a mmum age set just above the ucostraed optmum leads frms to crease employmet t also causes frm ext as profts fall. I ths ote I sho that the employmet ad elfare effects of the mmum age hch Bhaskar ad To had thought to be ambguous he frm ext as accouted for are fact uambguously postve. JE classfcato: J42, J30 Keyords: Moopsoy, mmum age, employmet 1 I am grateful to V. Bhaskar for helpful commets o ths ote. Ay errors are me.

3 Itroducto I ther (1999) Ecoomc joural paper V. Bhaskar ad Ted To (BT from o o) develop a model of moopsostc competto the labour market. A mportat cotrbuto of the paper s that t models frms competg for orkers equlbrum. Ths allos BT to model the employmet ad elfare effects of a mmum age ot oly the short ru as other models had doe (eg. Card ad Krueger (1995), Mag (1995) or Rebtzer ad Taylor (1995) but also to explctly model the employmet ad elfare effects of frm ext. I sho ths ote that a mmum age set just above the ucostraed optmum ll uambguously rase employmet ad elfare both the short ru ad the log ru. The employmet ad elfare cosequeces of the mmum age ere take to be ambguous the orgal BT model. The results here are derved th a more geeral producto fucto tha the orgal BT formulato. Aother terestg feature of the dervato belo s that e see that the employmet effects of the mmum age for a dvdual frm s the same partal equlbrum as geeral equlbrum here the effects of other frms ages ad frm ext are accouted for. I. The Model I beg th a geeral Moopsoy model of the labour market. There are Moopsostc frms ho are prce takers o the output market ad have the follog proft fucto: 1 1 Π = PF( [.., ]) [.., ] C (I.1) 2

4 F(.) s a ell behaved producto fucto ad the frms labour supply curve has the follog propertes: > 0, 0, j 0 here j ad fally < 0. There s free etry of frms ho must pay fxed costs C to eter the dustry. Frms choose the age that maxmse profts satsfyg ther frst order codto : π = 0 (I.2) A mmum age mposed just above the equlbrum level ll have the follog mpact o profts of ay frm the log ru: dπ d d = π j + π = 0 (I.3) d j The dervatve of profts th respect to the frms o age ll be zero sce (1.2) holds. The chage other frms age respose to the mmum age ll affect the frm s proft as ll chages the umber of other frms. I the log ru frm ext ll esure that the total mpact o profts s zero ad fxed costs ca be covered. We ca take the partal dervatves (I.3) from the proft fucto: π j j = ( ) (I.4) j PF j π = ( ) (I.5) PF Usg these dervatves (I.3) mples: d = d j j (I.6) Itally e ll look at the mpact of the mmum age o employmet a dvdual frm, accoutg for the mpact of frm ext o employmet th the frm. Dfferetatg 3

5 the frms labour supply fucto th respect to ages ad usg (I.6) e get: 1 (.., ) = j + = (I.7) j= 1 The postve mpact o frm labour supply of frm ext s offset exactly by the mpact o frm labour supply of chages other frms ages. That s the log ru mpact o employmet of a dvdual frm s just the partal dervatve of the frms labour supply curve th respect to the frms o age. Aggregate employmet s the product of frms tmes employmet here s employmet ay of the detcal frms: 1 E = (.., ) (I.8) Dfferetatg th respect to the age ad usg (I.6) ad (I.7) e get: E = + = ( j ) (I.9) j Or a symmetrc equlbrum here each frm starts at the same age ad employmet combato (,): E E ( j ) j = = ε ε j ε ε j (I.10) Where ε s the labour supply elastcty of ay frm th respect to ts o age,ε j s the elastcty th respect to other frms ages ad ε s the elastcty of a frms labour supply th respect to the umber of frms. These last to elastctes are egatve. Bhaskar ad To (1999) develop a model of moopsostc competto here the frms are equdstatly spaced aroud a ut crcle. A ut mass of zero reservato age 4

6 orkers s uformly dstrbuted o the crcle. A mass of µ orkers ho have a postve reservato age v are also uformly dstrbuted o the crcle. Workers face a trasport cost t tmes the dstace to ay frm f they sh to ork for ths frm. BT motvate these trasport costs as prefereces for a varety of frm specfc characterstcs. A frms labour supply curve ths model s: 1 = + ( 1+ 2µ )[ ] t j 2vµ t (I.11) Notg that ths case 1 ε =, the elastcty of employmet th respect to the mmum age (I.10) ca be rertte as: E E ( j ) j = + = ( 1+ 2µ ) (I.12) t (I.12) s postve sce the measure of the labour force 1+ µ caot be exceeded by employmet. If demad s hgh eough relatve to trasport costs, fxed costs ad v frms compete for both types of labour e ould modfy the above labour supply approprately. The oly Nash equlbrum s here each frms employmet s 1 + µ ad there s full employmet. I ths case the age exceeds the margal product ad the mmum age ould have o mpact o employmet (see Kefer ad Neuma (1991) for a smlar example to ths). I ths ecoomy there are frms ad orkers. Frms ear o surplus equlbrum sce there s free etry. Welfare s therefore just the sum of orkers utlty. Clearly therefore f the mmum age creases employmet, elfare also creases. 5

7 Next I apply the aalyss to the partcular case aalysed by BT here they assumed a costat margal product φ ad solve there model explctly. I partcular they sho ther appedx that the sg of the follog expresso determes the sg of employmet: 2 ct 1+ 2µ ( φ v) (I.13) Gve the expresso for optmal employmet * ad the optmal umber of frms * derved the appedx to BT t ca be sho that f employmet s less tha the labour force (1+ µ > * * ) the the follog codto holds: ct 2( 1+ 2µ ) 1+ 2µ > 3 + 4µ ( φ v) (I.14) Isertg (I.14) (I.13) e get the follog expresso hch s postve: 1+ 4µ > µ ( φ v ) (I.15) The postve sg mples that the employmet effect of the mmum age s postve. II. Cocluso Ths ote shos that a mmum age uambguously rases elfare ad employmet the model of moopsostc competto developed by Bhaskar ad To (1999). There rema other argumets agast mmum age polces. A moopsoy model may ot be the approprate model of the labour market or of some sectors of the labour market. Eve f t s the approprate model there may be varyg degrees of moopsoy poer across sectors mplyg that choosg approprate mmum ages may 6

8 be dffcult (see Stgler (1946)). Walsh (2000) shos a moopsoy model that he labour supply depeds o edogeous orkg codtos as ell as the age that a mmum age may reduce employmet ad elfare ad that a employmet subsdy ll be a more effectve polcy. 7

9 Refereces Bhaskar V.,Ted To,(1999) Mmum Wages for Roald McDoald Moopsoes: A Theory of Moopsostc Competto The Ecoomc Joural, 109 (Aprl), Card, Davd ad Ala Krueger (1995), Myth ad Measuremet: the Ne Ecoomcs of the Mmum Wage. Prceto: Prceto Uversty Press. Kefer Ncholas M. ad George R. Neuma (1991) Notes o Moopsoy Models abour Markets Mmeo Uversty of Ioa Mag, Ala (1995) Ho do e Ko that Real Wages are too Hgh? Quarterly Joural of Ecoomcs November. Rebtzer, James ad oell Taylor (1995) The Cosequeces of Mmum Wage as: Some e Theoretcal Ideas Joural of Publc Ecoomcs 56, Stgler, George (1946). The Ecoomcs of Mmum Wage egslato Amerca Ecoomc Reve, 36, Walsh Frak (2001) Moopsoy Poer th Varable Workg Codtos Workg paper WP00/23 Ecoomcs Departmet Uversty College Dubl 8