Using (11), we can shown
∂H
∂Kws
dh
dL
ws
∂ws I ∂L
∂ws I ∂H
s
∂ws I ∂K
∂w I ∂H
s
ɪ ∂H H
L ^∂L^ L
= H (1 - β)[θ(1 + σ ) - σk,
L
= H(1 + σ)(1 - Θ∙)Sh > 0
K
--H-(1 + σ)(1 - ff)8H < 0
L2
(A.7)
(A.8)
(A.9)
Write the equilibrium of the bargaining problem (A.3) as p(1 - τ)p = f (θ, Sl, γ)g(L, θ, b), where
1- 1 1 - Y z θ θ
f (θ, 8l , Y) ≡ —γ (1 - β) — + Sl (A.10)
γ 1 - θ
g(L,θ,b) ≡ (1 - τ)p
(A.11)
We define
δ≡ g
f+^L ∂εκ
∂θ ∂ε l ∂θ
∂θ
∂x ’
δ1 ≡δ
∂x ∂x dH
--1---
∂L ∂H dL
+ f ∂g ('Wu
j∂wu ∂L ,
∂x ∂x ∂H
+
∂K ∂H ∂K
+ f ∂g <~w'u
j ∂wu ∂K ,
∆^x-+f
∂H
∂g ∂wu
∂H ∂ws
∂wu ∂H J∂ws ∂B
These expressions can be used to derive the comparative static effects. In fact
dL_ _ ∂f I ∂γ
(A.12)
(A.13)
(A.14)
dγ g ∆1
dL _ ∆ 2
dK ~ ∆7
dL _ f ∙∂g I ∂B + ∆ 3
dB ∆1
The impact of parameter changes may depend on the elasticity of substitution in production. Hence we
need to consider three possible cases.
Case 1: σ > 0
Using (A.6)-(A.9) and the fact that σ> 0 implies ∂θ I∂x > 0, we can establish: ∆< 0, ∆1 <0,
∆2 > 0, while ∆3 may be positive or negative. Hence
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