19. Jahrgang (1993), Heft 4 Wirtschaft und Gcsell!Jchaft
ster pace, with v' (e) > 0 and v" (e) ? 0. Then the local union's payoffs can
by written as
if there is an agreement,
H there is a strike. (71
In addition, the bargairring outcome must sathrfy two constraints. The
first is that profits cannot be negative or the firm will shut the plant
down. The second is that the wage cannot be less than the minimum
wage requircd to attract workers.· Thus the solution must salisfy n ? 0
and u;?: r whcrc r is equal to the utility that workers can obtain by quit
ting and searchirrg for employment elsewhere.
According to starrdard bargairring models, the bargairring outcome
with local bargairring is givcrr by
w = {a [R (e, L, K)/L] + (1 .. a) v (e)
t- r + v (e)
if a [(R!L) - v] > r,
otherwise [8)
where aE (0,1) deperrds on the relative impatience of the two sides to
settl.e (22). lf the wage rate is given by equation [8], it is easy to see that,
with local bargaining, profits are given by
n1• = (I - a) [R ( e, L, K) - v ( e) L./ - C (K)
and the utility of the urriorr is giverr by
u = a [R (e. L I()_ v (e)] I. L
[9]
( I 0]
provided u ;;::: r. Equations (9] arrd [JO] indicate that the union and the
firm share the quasi-rents [R - v (e)] accordirrg to the proportians a and
{1 - a).
For our model of bargainirrg at the industry or national level, we assu
me that that payoffs tu the union are the same as at the local level. For
employers, we assume thal the employers' association seeks to m.aximize
the sum of its members profiLs ::E (R,-wL;-CJ. Then, the bargairring out
come is given by
:ER (e, L. K) (l ,1 ( ) Wc = a I L + - a1 v e llll
where R and L arc summed over all plants that are covered by the
wage rregotiations providcd, as before, that u::::: r. Since a deperrds orr the
relative discourrt rates of thc two sides (see footrrote 22), there is little
reason to expect a to vary. systcmatically with the level of bargainirrg.
Thus, we assume the union's share of thc quasi-rerrts is the same at diffe
rent bargaining levels. What changes is thc definition of the relevant
437