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

Using (11), we can shown

Write the equilibrium of the bargaining problem (A.3) as p(1 - τ)^p = f (θ, S_l, 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

We define

∂x ∂x dH

--1---

∂L ∂H dL

₊ f ^∂g ⁽'^Wu

^j∂w_u ∂L ^,

∂x  ∂x ∂H

+

∂K ∂H ∂K

₊ f ^∂g <~^w'u
^j ∂w_u ∂K ^,

These expressions can be used to derive the comparative static effects. In fact
dL_ _ ∂f I ∂γ

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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