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



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)8H0

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

δg


f+^L ∂εκ
∂θ ∂ε l ∂θ


∂θ

x


δ1 δ


x x dH

--1---

LH dL

+ f g ('Wu

j∂wuL ,

x  ∂xH

+

KHK

+ f g <~w'u
jwuK ,

∆^x-+f

H


g wu


H ws


wuH J∂wsB


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

(A.12)

(A.13)

(A.14)


dγ   g1

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 Ix0, we can establish: ∆< 0, 1 <0,
2 0, while 3 may be positive or negative. Hence

32



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