Labour Market Institutions and the Personal Distribution of Income in the OECD



Appendix I: Wage and Employment Determination

The Bargaining Model

The bargaining problem is given by

maxL [((i )wu )ρ- (B)ρ](Y - wuL -wsL )1 γ
wuL                    )

(A.1)


The union takes into account the fact that, given the skilled wage ws, the reduction in L due to an
increase in
wu will reduce skilled employment and hence the marginal product of skilled labour. The
resulting first-order condition is

wu


ρ-i


r

ρ(1 )ρ+ (1 )ρ
к



1 L ((1 )ρ wρ- ( bY )ρ )
γ    Y - Hws - Lwu


(A.2)


Using the fact that

Y - Hws - Lwu _ 1 - θ

Lwuu     ^ (1 )θ

we can write (A.2) as

ρ(1 - τ)ρ


—(1 ) rθε L
γ 1


(

I (1 )ρ



(A.3)


Comparative Statics

Consider first a number of comparative statics obtained from the production function. From equation
(1b), we obtain the elasticities of demand for the two types of labour


εL = -


L wu


wu L   1 -(1 )[θ(1 + σ)]


(A.4)


εH = -


H ws


ws H 1 - β[θ(1 + σ) - σ]


(A.5)


From equations (1)-(5), (11), (12), (A.4) and (A.5) we have

sign


θ


= si


(A.6)


L<0,
ω<0,
H
wu<0,
L

ε

L0,
θ


H0,
ω>0,
L


K0,

ω<0,
h


wu
H
εH
θ


w     ∂w     ∂w     ∂w

> 0,   wu0,   ws0,   ws0,   ws0,

K     ∂L     ∂H     ∂K


> 0.


31




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