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
|
dh 1 dH H dL H ____ —_____— / ] -Lrrwl _ A IO ____ |
Γ1 - dL K |
|
dK LdK L2 dK" H LK dθ ∂θ Γ∂X dL ∂x dH ∂x "I ∂θ x ---=---+--+--- =--(1 dK ∂x ∂L dK ∂H dK ∂K ∂x K |
_ dK L -β)ε h 1 |
_
dL K
dK L
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 ∂ws ∂B
dθ
dB
∂θ ∂x dL ∂x dH
∂x ILdB ∂h dB
>0
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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