186 C
. Fuest, B. Huber Journal of Public Economics 78 2000 171 –192
bargaining at the firm level. In the next section, we consider the case of the right-to-manage model of wage bargaining.
6. Capital subsidies in the right-to-manage model
In the present section, we consider the welfare effect of capital subsidies in a right-to-manage model. Thus, we now assume that bargaining between unions and
firms is over wages only, whereas the level of employment is set unilaterally by firms. To keep the following analysis simple, we normalise the parameter z to
zero, which implies that we abstract from firm heterogeneity and the possibility of
19
firm liquidations. The sequence of decisions is now as follows. As in the
preceding analysis, the investment decision is taken at stage one and union–firm bargaining takes place at stage two. The crucial new aspect is now, of course, that
unions and firms bargain over wages only. At stage three, firms unilaterally set employment.
We determine the equilibrium beginning with stage three. As in the preceding
20
analysis, we first abstract from taxes. At stage three, for a given capital stock, the
representative firm maximizes the term P 5 YL, K 2 wL
23 over L. The firm’s optimal employment decision is
Y 5 w. 24
L
At stage two, firms and unions bargain over wages. The objective function of the representative union is given by
U 5 wL 1 N 2 L c 25
and the union’s reservation utility is cN. The firm’s objective function is given by 23, and its reservation profit is 11r K. The Nash maximand is thus
V 5 b logLw 2 c 1 1 2 b logYL, K 2 wL 2 1 1 r K. 26
The wage rate emerging from the bargaining process is derived by maximizing 26 over w. The first-order condition
V 5 0 can be rearranged to yield
w 21
L 1 2
b L
w
]] ]]]]]]]] ]
w 2 c 5 2
. 0. 27
F G
b L
YL, K 2 wL 2 1 1 r K
19
In the preceding section, the liquidation of low productivity firms was required to have an equilibrium with an inefficiently low level of employment, given the capital stock. Here, the level of
employment will be too low even without firm liquidations.
20
In Appendix B, we show how taxes enter the model.
C . Fuest, B. Huber Journal of Public Economics 78 2000 171 –192
187
Eq. 27 shows that the equilibrium wage rate exceeds the marginal disutility of working w . c. Eq. 27 also defines the wage rate as a function of the capital
stock, i.e., w 5 wK . At the first stage, the entrepreneurs choose the level of investment, taking into
account that the size of the capital stock will affect the outcome of wage bargaining at stage two. The profit function at stage one is
I 5 YL, K 2 wK L 2 1 1 rK. 28
Maximizing 28 over K yields ≠w
] Y 5 1 1 r 1
L. 29
K
≠K Eq. 29 shows that, if an increase in the capital stock raises the wage rate
21
emerging from the bargaining process , entrepreneurs will set K such that the marginal productivity of capital exceeds the ‘social cost’ of capital 11r, which
means that underinvestment occurs. It is now straightforward to determine the welfare effect of introducing a capital subsidy, financed by a labour tax. Overall
welfare is
R 5 YL, K 2 cL 2 1 1 rK. 30
Let dL and dK denote the change in investment and employment induced by the introduction of a capital subsidy. The change in welfare is then
dR 5 Y 2 1 1 r dK 1 Y 2 c dL.
K L
Using 24 and 29, this can be written as ≠w
] dR 5
L dK 1 w 2 c dL. 31
≠K Eq. 31 shows that the welfare effect of introducing a capital tax is determined by
the resulting equilibrium changes of K and L induced by the introduction of the capital subsidy. In a first-best world, a marginal capital subsidy would, of course,
not affect welfare. In this model, both investment and employment decisions are distorted such that marginal changes in K and L have a first-order welfare effect.
In general, the welfare effect of introducing the capital subsidy financed by a labour tax is now ambiguous. In Appendix B, we provide a simple example for a
positive welfare effect. If bargaining is over wages only, the case for capital subsidies is thus weaker, but they may still induce a welfare gain.
21
In Appendix B, we provide an example where this is indeed the case see also Van der Ploeg, 1987.
188 C
. Fuest, B. Huber Journal of Public Economics 78 2000 171 –192
7. Conclusions
