A Comment on Increasing Returns and Spatial. Unemployment Disparities

Transcription

1 The Society fo conomic Studies The nivesity of Kitakyushu Woking Pape Seies No.06-5 (accepted in Mach, 07) A Comment on Inceasing Retuns and Spatial nemployment Dispaities Jumpei Tanaka ** The nivesity of Kitakyusyu Abstact By intoducing the efficiency age hypothesis into a simple ne economic geogaphy model, Suedekum (005) agued that loe (highe) unemployment ates and highe (loe) eal ages hold in the highe (loe) population egion hen okes ae immobile acoss egions and that the okes fee mobility inceases such egional dispaities. We sho, hoeve, that his agument about the stability of equilibia is questionable and unde the valid stability analysis his esult no longe holds. JL Classification: F4, J6, R Keyod: Regional unemployment, economic geogaphy, inceasing etuns, age cuve, migation, labou mobility. Intoduction Blanchfloe and Osald (996) empiically demonstated that in many counties egional ages ae negatively elated to egional unemployment ates in the long un and they called the elationship the age cuve. Afte thei study, many eseaches have offeed vaious models hich can explain such a phenomenon, and Suedekum (005) is one of such attempts. Constucting an analytically solvable geneal equilibium model in hich eal ages ae detemined though the efficiency age hypothesis and diffeentiated intemediate goods ae poduced unde the IRS (inceasing etun to This eseach is financially suppoted by the JSPS KAKNHI Gant Numbes JP6K ** -mail: j-tanaka@kitakyu-u.ac.jp

2 scale) technology, he agued that in the shot un (namely, hen okes ae immobile acoss egions) loe (highe) unemployment ates and highe (loe) eal ages hold in the highe (loe) population egion, and that in the long un (namely, hen okes ae mobile acoss egions) such egional dispaities divege. In this note e eexamine his agument and sho it is not coect. Suedekum (005) shoed that in the shot un thee ae to equilibia (one is chaacteized ith high eal age and lo unemployment ate and the othe is chaacteized oppositely) and claimed that the stable equilibium is the fome. Hoeve, he pointed out it by the intuitive explanation only, and omitted the igoous stability analysis. By eexamining the stability of equilibia, e sho that the stable equilibium is the latte (not the fome), and that the opposite of Suedekum (005) s esult holds in the latte equilibium; namely, in the shot un loe (highe) unemployment ates and highe (loe) eal ages hold in the loe (highe) population egion and in the long un such egional dispaities convege. This esult means that Suedekum (005) did not succeed in explaining the age cuve phenomenon theoetically.. Reexamination and its esult Suedekum (005) s model is compised of the folloing to equations concening the elationship beteen the eal age ( ) and the unemployment ate ( ) in the egion : () [ V es, =V en, () [ N l = ( ) L = ( L γ γ e = e + b + t +, ( δ = ( R / ) R ) )( ) δ ( / B) ( ( θ ) / θ ( θ ) / θ ), ( B: a constatnt) hee the notation is basically the same as the oiginal pape. The equation () epesents the efficiency age as a function of a given unemployment ate, hich is deived by equalizing the value of non- shiking okes ( V en, ) to that of shiking okes ( V es, ). This elationship is called the VV schedule. The equation () epesents the elationship beteen and that cleas the labo maket, hich is deived by equalizing the labo demand ( N l ) to the labo supply ( ( ) L ). This elationship is called the BB schedule. Fom () and () e can calculate the equilibium pai of and in the shot un in hich okes ae immobile acoss egions. When θ >/ holds, these equations can be depicted as Figue, and the to equilibia ( and ) can exist as Suedekum (005) shoed. He claimed that in to equilibia the stable one is, but he pointed out it by the intuitive explanation only and omitted the igoous

3 stability analysis. Concening the adjustment pocess aound the BB schedule he stated belo: Fo all points belo the BB-schedule, ages ae too lo fo any given unemployment ate. Poduces in the Y-secto (the final goods secto) makes positive pofits that induces othes to ente the maket. This expansion of the Y-secto tanslates into ising pices fo intemediate poducts, hich subsequently must be absobed by highe ages fo the manufactuing okes in the X-secto (the intemediate goods secto). (p73) (Figue aound hee) Is this statement coect? If it is the eal ages (not the unemployment ate) that is adjusted hen the economy is not on the BB schedule, such an adjustment pocess must be fomulated as φ [ l (3) / = N - ( ) L θ /( θ ) =φ [ B - ( ) L, hee φ (>0) is an exogenous paamete about the adjustment speed of the eal age. The equation (3) shos that the eal age inceases hen the excess demand is positive ( N l > ( ) L ). We can easily confim that unde (3) the excess demand is negative and the eal age dops (the diection of the phase ao is donad) in all points belo the BB schedule. This contadicts Suedekum s claim quoted above. This means that even if e accept his claim that it is the eal age (not the unemployment ate) that cleas the labo maket, the coect diection of the phase ao is opposite of his claim and theefoe is no longe the stable equilibium. Hoeve, the moe fundamental poblem is that his claim itself is questionable, fo in his model the eal age is detemined not by the labo maket cleaing condition but by the efficiency age hypothesis. In his model fims pull up the eal age to da okes effot hen V es, > en V, holds, hich means that the eal age is adjusted hen the economy is not on the VV (not BB) schedule. Consideing this, the valid adjustment pocess of the eal age must be fomulated as (4) / =ψ [ V es, -V en, ψ γ δ ) e = ( )( γe + b + t + ( γ )( δ ), 3

4 hee ψ (>0) is the an exogenous paamete. Given (4), V es, > en V, holds and the eal age inceases fo all points belo the VV schedule. Since the eal age is detemined to satisfy () (the VV schedule), it is the unemployment ate that cleas the labo maket (namely, that satisfies ()). So the adjustment equation of the unemployment ate can be fomulated as (5) / =ψ [ ( ) L - N l θ /( θ ) =ψ [ ( ) L - B hee ψ ( > 0) is an exogenous paamete. The equation (5) means that the unemployment ate inceases hen the labo supply (= ( ) L ) exceeds the labo demand (= N l). Gaphically, the diection of the phase ao is ightad belo the BB schedule as depicted in Figue. Accodingly, e can conclude that in to equilibia ( and ) the stable equilibium is. (Figue aound hee) We can also deive this conclusion by intepeting both VV and BB schedules as the eaction functions. See Figue 3 fo this point. When the initial unemployment ate is given by, then the eal age set by fims accoding to the efficiency age ule is on the VV schedule. And hen the eal age is given by ate hich cleas the labo maket is, the ne unemployment on the BB schedule. By iteating this induction, e can easily see that the economy appoaches to. (Figue 3 aound hee) As is depicted in Figue 4, at the stable equilibium loe (highe) unemployment ate and highe (loe) eal age hold in the loe (highe) population egion in the shot un. This esult is opposite of Suedekum (005) s one. Futhemoe, since okes move fom the highe population egion ith loe eal age to the loe population egion ith highe eal age in the long un ith fee mobility, the egional dispaities deceases and finally the eal ages ae equalized beteen to egions. This is also diffeent fom Suedekum s esult that egional dispaities divege by fee labo migation. Ou esult, theefoe shos that Suedekum (005) s model does not succeed in explaining the age cuve phenomenon. (Figue 4 aound hee) Refeence Blanchfloe, O. and A. Osald (996) The age cuve (second edition), MIT Pess, Cambidge, MA 4

5 Suedekum, J. (005) Inceasing etuns and spatial unemployment dispaities, Papes in Regional Science, Vol.84(), pp59-8 BB schedule VV schedule (Figue ) BB VV (Figue ) 5

6 BB VV (Figue 3) BB (high population) BB (lo population) (lo population) (high population) VV (Figue 4) 6