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

dL      ∂f / ∂γ

— = - g —--- < 0

dγ        ∆₁

^dL-   ^δ > 0

dK  ∆₁

dL _ f ∙∂g / ∂B + ∆ 3

dB         ∆₁

From (A.6)-(A.9) we can now establish the effects of an increase in union bargaining power:

dL     dH     dx     dθ     dh     dω

— < 0, --< 0, — > 0, — > 0, — > 0, --< 0.

dγ    dγ    dγ    dγ    dγ    dγ

An increase in the capital stock raises both skilled and unskilled employment, dL / dK > 0 ,
dH / dK > 0. However, the impact of K on ω and θ is ambiguous, as the increases in H , L and K
have effects of opposite sign. However, we can obtain

If the elasticity of unskilled labour with respect to capital is less than one, then these two expressions are
positive, implying dω / dK < 0 and dθ / dK > 0 .

The effects of an increase of B are ambiguous. However, if dL / dB < 0, it is then possible to
show that

dH ∂H dL ∂H ∂w

=       + ^s<0

dB ∂L dB ∂w_s ∂B

∂θ ∂x dL ∂x dH
∂x ILdB ∂h dB

Case 2: σ = 0

In this case ∂θ / ∂x = 0, hence ∆ = 0, ∆₁ < 0, ∆₂ > 0, and ∆₃ < 0. Then

dL     dL     dL

— < 0, --> 0, —< 0 .

dγ     dK     dB

It is straightforward to show that the effects on ω are as in case 1, while there is no impact on θ .

Case 3: σ < 0

In this case ∂θ / ∂x < 0 , hence ∆ > 0, ∆₃ < 0, and ∆₁ and ∆₂ can be positive or negative. From the
expressions in (A.12) to (A.14), it is clear that the comparative statics cannot be signed.

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