Ž .
If wageremployment bargaining coexists with right-to-manage b F 0.5 , how does aggregate employment vary with the unions’ bargaining power? Restricting
Ž .
Ž .
attention again to ex-ante symmetric firms A s A s A , we get from Eq. 16
i j
Ž
U U
U
. the aggregate employment level Y s y q y
,
C 1
2
Y
U
s 6 y 5b q b
2
q 6 bw y b
2
w a y Aw
r2G
Ž .
Ž .
C
Contrary to the Universal right-to-manage bargaining, aggregate employment in this case may increase, or decrease, with the unions’ bargaining power, b,
depending on the value of the parameter w. In fact, if the unions’ members are Ž
. sufficiently risk-averse e.g., w - 0.6 , aggregate employment increases with b.
Ž The opposite is true if the unions’ members are closer to being risk neutral e.g.,
. Ž
. w
0.8 . For intermediate values e.g., w s 0.7 , aggregate employment initially decreases, and then increases with b. Finally, for b s 0.5, under Universal
U
Ž . Ž
. right-to-manage bargaining, aggregate employment is Y s 4 a y Aw r 6 q w ,
R U
Ž .Ž
. Ž
while under coexistence of institutions it is Y s 15 q 11w a y Aw r2 9 q 8w
C 2
.
U U
q w , with Y Y for all values of w. Summarizing, as the unions’ bargaining
C R
power decreases, aggregate employment increases continuously initially, then jumps up for b s 0.5. For further decreases of b, however, aggregate employment
may decrease or increase, depending on the degree of risk aversion of the unions’ members.
4. Extension to a symmetric oligopoly
Consider a n-firm homogeneous Cournot oligopoly. Firms are endowed with Ž
. identical linear one-factor labor production functions; that is, firm i’s production
function is y s N rA with 1rA being the productivity of labor. The rest of the
i i
specification of the model is as in Section 2. The following proposition summa- rizes the results.
Proposition 4: In a n-firm symmetric homogeneous Cournot industry, i UniÕer- sal right-to-manage bargaining is the equilibrium institution if, and only if,
b G 1 y 1 r n. ii UniÕersal wage r employment bargaining can neÕer be sus- tained as an equilibrium institution.
iii If b F 1 y 1 r n, then a subset of
firm r union pairs conducts wage r employment bargaining with the rest conduct- ing right-to-manage bargaining.
19
19
The proof of Proposition 4 is along the lines of the proofs of Propositions 1 and 2, and thus is not included in the present version of the paper. It is available from the authors upon request.
Universal wageremployment bargaining cannot be sustained as an equilibrium institution for the same reasons as in the duopoly case. Further, Universal
right-to-manage is the equilibrium institution only if the unions’ bargaining power is sufficiently high. The critical value of b is increasing in the number of firms in
the industry. As the number of firms increases, the gains from becoming the unique Stackelberg leader in the product market increase. Then a firm’s incentive
to include employment on its negotiations agenda becomes stronger, provided that
Ž . all its rivals negotiate over wages alone. Indeed, as part i of the proposition
indicates, when n is sufficiently high, all firmrunion pairs conducting right-to- Ž
. manage bargains is an equilibrium institution only in case of almost Monopoly
Ž .
Unions. That is, only if unions possess almost all the power to set wages, are a firm’s extra labor costs from moving away from its labor demand curve higher
than its gains from becoming the unique Stackelberg leader. It is only in this rather extreme case that no firm has incentive to revert to wageremployment bargaining,
and Universal right-to-manage is the equilibrium institution. Otherwise, the equi- librium configuration of scope of bargaining institutions involves some firmrun-
ion pairs conducting wageremployment bargaining, while the rest conduct right- to-manage bargaining.
5. Conclusions
