Appendix I: Wage and Employment Determination
The Bargaining Model
The bargaining problem is given by
max∣ L [((i -τ)wu )ρ- (B)ρ]∣ (Y - wuL -wsL )1 γ
wu < L )
(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 -τ)ρ+ (1 -τ)ρ
к
1 -γ L ((1 -τ)ρ wρ- ( bY )ρ )
γ Y - Hws - Lwu
(A.2)
Using the fact that
Y - Hws - Lwu _ 1 - θ
Lwuu ^ (1 -β)θ
we can write (A.2) as
ρ(1 - τ)ρ
—(1 -β) rθ→ε L
γ 1-θ
(
I (1 -τ)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 -β)[θ(1 + σ)-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
L > 0,
∂θ
∂H < 0,
∂ω>0,
∂L
∂K > 0,
∂ω<0,
∂h
∂wu
∂H
∂εH
∂θ
∂w ∂w ∂w ∂w
> 0, wu > 0, ws > 0, ws < 0, ws > 0,
∂K ∂L ∂H ∂K
> 0.
31
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