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

max

w_u

^ρ -B^ρ])^γ(Y -wuL -wsH)^1-γ

(8)

(1 -γ θ

ρ(1 -τ)^ρ=∣-^γ (1 -β) -θ- + ε L

V y 1 - θ

(

I (1 -τ)^ρ-

V

B Y∣

w_u J
u / j

(9)

where ε_L is the elasticity of the demand for unskilled labour. Since ε_L , w_u , and θ are functions of H

and L , equation (9) determines w_u as a function of skilled and unskilled employment.

Equilibrium and comparative statics

The equilibrium of the model is then given by equations (2b), (2c), (6), and (9), that is, by

¹~~^γ (1 -β) A + ε L
γ 1-θ

(9)

w_u

= (1 - β)(1 - α)(α + (1 - α)x^σ) ( ^+σ) ^σ x^σ K

L

(10)

= β(1 -α)(α + (1 -α)x^σ) ( ) x^σ H

(11)

w_s

(12)

where φ( B^{, e,} p ) is implicitly defined by (6). Together these four equations determine the equilibrium

levels of skilled and unskilled employment, H and L , and the two wages as a function of model
parameters: the unemployment benefit, B , the bargaining power of the union, γ , the capital stock, K , as

well as the preference parameters, ρ and e , and the technological parameters, α,β, σ , and p .

Let u ≡ 1 - (L + H )/(L + H ) be the unemployment rate, where H is the skilled labour force.

Once H and L are determined, we can obtain our three main variables of interest, the labour share, the
relative wage, and the unemployment rate, which we can express as functions of the stock of capital and
labour market institutions (as well as of the preference and technology parameters):

θ = θ(K,B,γ),
ω = ω(K,B,γ)

(13)

(14)

u = u (K , B, γ).

(15)

All comparative statics are derived in Appendix I. Consider first the effect of union power. It is possible
to show that