dL dH du dθ dh dω
— < 0, --< 0, — > 0, — > 0, — > 0, — < 0.
dγ dγ dγ dγ dγ dγ
As in the standard wage bargaining model, the direct effect of greater union bargaining power is to
reduce unskilled employment. This reduces the marginal product of skilled labour, and skilled
employment falls in order to maintain the skilled wage at Ws. Since both types of employment are
reduced, the unemployment rate increases. Furthermore, under the assumption that σ > 0, the labour
share also increases, the reason being that lower levels of employment result in a higher capital-labour
ratio. The effect of an increase in γ on unskilled employment can be shown to be stronger than that on
H , implying an increase in relative skilled employment, and hence a reduction in the relative wage.
Concerning an increase in the stock of capital, we have
dL dH du
---> 0, ----> 0, ---< 0.
dK dK dK
A higher capital stock raises the marginal product of labour (both unskilled and skilled), leading to
greater employment of both types of workers for a given wage. In the case of unskilled workers, unions
react by demanding higher wages, which results in an increase in wu . In case of skilled workers, given a
constant efficiency wage, the increase in the capital stock leads to an expansion of skilled employment so
as to maintain the marginal product of labour constant. Moreover, the indirect effects on L through the
change in H and vice versa reinforce these direct impacts. Under reasonable conditions (see appendix),
we can also show that
dθ dh dω
---> 0, ---> 0, ---< 0.
dK dK dK
A greater capital stock has a direct positive effect on θ , as a higher K increases the marginal product of
labour, and indirect negative impacts through the increase in both types of employment. The positive
effect dominates, implying that a greater stock of capital increases the labour share. The effect on skilled
employment can also be shown to be greater than that on unskilled employment, resulting in a higher h
and hence a lower relative wage.
A higher unemployment benefit has two effects. On the one hand, it increases the outside option
for unskilled workers, hence unions will bargain for a higher wage and accept a lower level of
employment. On the other, it increases the efficiency wages that the firm must pay to skilled workers,
which requires the firm to employ fewer skilled workers in order to increase their marginal product. The
reduction in H tends to reduce the marginal product of the unskilled and hence partially offsets the
reduction in L . If the direct effect dominates, so that dL / dB < 0, it is then possible to show that
dH du dθ
--< 0, — > 0, — > 0.
dB dB dB
That is, a higher unemployment benefit reduces both skilled and unskilled employment, increasing the rate
of unemployment and raising the labour share. The effect on the relative wage is ambiguous, as both the
skilled and the unskilled wage increase.