Unionized
Oligopoly
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Heterogenous worker in a unionized oligopoly
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Anna K. Goeddeke
University of Erlangen-Nuremberg
October 2008
Unionized
Oligopoly
Motivation
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Firms regularly employ heterogenous workers
Literature concludes:
Substitutable workers are better o¤ in one encompassing
union
Complementary workers bene…t being organized in
di¤erent unions
But: Literature always assumes homogenous bargaining
strengths
Focus of the paper:
Analyzing di¤erent organization and bargaining structures
Impact on wages, union utility, pro…ts, and welfare
How should workers organize themselves: intra–union
degree of heterogeneity vs. degree of centralization of the
union
Craft unions, comprehensive unions vs. …rm speci…c,
industry wide, or even national unions
Unionized
Oligopoly
Literature
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Horn and Wolinsky (1988), The Economic Journal
Dowrick (1993), The Economic Record
Gürtzgen (2003), Labour
Unionized
Oligopoly
Assumptions
Anna
Goeddeke
Introduction
Motivation
Literature
two …rms, four unions
The Model
output: N workers of type n and M workers of type m
Assumptions
Regimes
Negotiations
costs: ci = Nwin + Mwim with i = 1, 2
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
pro…t: π i = (p
ci )xi with i = 1, 2
demand: p = A
x1
x2
unions: U1n , U1m , U2n , and U2m
union utility Ui ,j = jwij xi with j = n, m and i = 1, 2
Conclusion
References
The game:
1
wage negotiations take place
2
…rms set quantities in the product market
Unionized
Oligopoly
Negotiation Regimes
Anna
Goeddeke
Introduction
Motivation
Literature
1
two negotiations in each …rm, unions negotiate separately
2
one negotiation round for each …rm, unions negotiate
separately
3
two industry craft unions, each union bargains in one
negotiation with both …rms over industry wide craft wages
4
two industry craft unions, industry wide craft wages, one
industry wide negotiation
5
two …rm speci…c unions representing two di¤erent types of
workers, one negotiation with each …rm
6
one industry union negotiates with one employers’
association
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Unionized
Oligopoly
Anna
Goeddeke
Craft
Union
Craft
Union
Craft
Union
Craft
Union
Craft
Union
Craft
Union
I
Introduction
Motivation
Literature
Firm
Firm
Craft
Union
Craft
Union
II
Firm
Firm
Firm
Firm
Craft Union
Craft Union
The Model
Assumptions
Regimes
Negotiations
Results
Craft Union
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
Craft Union
III
IV
Firm
Firm
Craft
Union
Craft
Union
Craft
Union
Craft
Union
Firm
Firm
Craft Union
Craft Union
References
Firm Union
Firm
V
VI
Firm Union
Industry Union
Firm
Employers’Association
Unionized
Oligopoly
Stylized Negotiations
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Nash Bargaining Solution
b π c with i = 1, 2
Case 2: N = Uina Uim
i
Case 3: N = Uja π c1 π c2 with j = m, n
Case 5:
1
2
two distinct crafts in one …rm bargain for the internal
distribution of rents. ! relative wage β = win /wim
the merged union bargains with its …rm over absolute
wages.
(a +b ) c
N1i = Ui
πi
a
b
N2i = Uin Uim
Unionized
Oligopoly
Results
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Overview
whether two craft unions merge or negotiate in one round
with the …rms does not matter:
Case 2 = Case 5
CraftU
nion
CraftU
nion
Craft
Union
CraftU
nion
CraftUnion
=
Firm
Firm
CraftUnion
CraftUnion
CraftUnion
Firm Union
Firm Union
Firm
Firm
Case 4 = Case 6
Conclusion
References
Craft Union
Craft Union
Craft Union
=
Firm
Firm
Craft Union
Industry Union
Employers’Association
no decisive advise for complementary and substitutable
workers
Unionized
Oligopoly
Anna
Goeddeke
One negotiation vs. one union
framework
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Case 2: individual utility maximization, no internalization of
the negative external e¤ect of higher wages on craftworkers of
the other craft in the same …rm
[Nwn xi ]a [Mwm xi ]b [(p
Nwin
Mwim )xi ]
c
Case 5: joint utility maximization, internalization of this
external e¤ect
[(Nwn + Mwm ) xi ](a +b ) [(p Nwin
[Nwn xi ]a [Mwm xi ]b
Mwim )xi ]
c
Unionized
Oligopoly
Anna
Goeddeke
Introduction
Motivation
Literature
a+b
30%
The Model
Assumptions
Regimes
Negotiations
a
18%
60%
a
40%
b
+
=
70%
c
70%
b
12%
c
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
negotiation strength of merged union has to be a + b
negative externality is internalized through Nash
Maximization
empirical research showed this in Machin, Stewart, and van
Reenen (1993) and Metcalf (1993) without an explanation
Unionized
Oligopoly
Direct and indirect e¤ects
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
direct e¤ects on quantity:
own costs:
dxi
dw in
< 0,
competitors costs:
dxi
dw im
dxi
dw jn
<0
> 0,
dxi
dw jm
>0
indirect e¤ects on wages:
dw in dxi
dxi dw im < 0
dw in dxi
dw in dxi
dxi dw jn > 0, dxi dw jm
complementary workers, same …rm:
workers in a competing …rm:
>0
Unionized
Oligopoly
Quantity and …rm pro…t
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
CraftU
nion
CraftU
nion
Craft
Union
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
Firm
Firm
Craft Union
Craft Union
=
>
Firm
Firm
Firm
Firm
Craft Union
Craft Union
Firm
Firm
>
Firm
Firm
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
xiII > xiI
xiIV > xiIII
negative e¤ect on the other craft internalized:
! higher quantity
positive external e¤ect on the other …rm not internalized:
! higher quantity
π IIi > π Ii
III
π IV
i > πi
Unionized
Oligopoly
Wages
Anna
Goeddeke
Unambiguous results
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Craft Union
Craft Union
CraftU
nion
CraftU
nion
Craft
Union
CraftU
nion
Firm
Firm
Craft Union
Firm
Firm
CraftU
nion
Craft Union
;
>
CraftU
nion
Craft
Union
CraftU
nion
>
Firm
Firm
Firm
Firm
wjIII > wjII
wjIV > wjII
internalization of negative external wage e¤ects in Case 2
no internalization of positive external …rm e¤ects in Case 2
Unionized
Oligopoly
Wages
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
1
wages are ordered wjIII > wjII and wjIV > wjII for j = n, m.
2
the comparison between wjI and wjII , wjI and wjIII , wjIII
and wjIV is ambiguous and depends on a, b, and c.
3
for a > b, wnIV > wnI and wmI > wmIV , analogously for
b > a, wnIV < wnI and wmI < wmIV . For a = b, wnIV = wnI
and wmIV = wmI .
Unionized
Oligopoly
Case 1 vs. Case 2
Anna
Goeddeke
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
?
wnI > wnII
a πc
Case 1: N = U1n
1
dN
dw 1n
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
CraftU
nion
CraftU
nion
Craft
Union
CraftU
nion
;
=
Firm
a dU1n
U dw
| 1n{z 1n}
direct e¤ect
a U b πc
Case 2: N = U1n
1m 1
+
Firm
Firm
Firm
Firm
Firm
c d π1
!
=0
π dw
| 1 {z 1n}
…rm e¤ect
Conclusion
References
dN
dw 1n
=
a dU1n
U dw
| 1n{z 1n}
direct e¤ect
+
b dU1m
U dw
| 1m{z 1n}
indirect e¤ect
+
c d π1
!
=0
π dw
| 1 {z 1n}
…rm e¤ect
Unionized
Oligopoly
Comparison of wages
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
I (w , w , w ); w II (w , w , w )
w1n
1m
2n
2m
1m
2n
2m
1n
evaluate
dN I
dw 1n
II using
= 0 at w1n
S1 : =
dN II
dw 1n
Opt. Wage
= 0 yields
b
dU1m
>0
U1m dw1n
|{z} | {z }
>0 <0
Marginal
I lies on the right hand side of w II
w1n
1n
Conclusion
References
with upward sloping wage functions: higher equilibrium
!
wages wnI > wnII
Upward sloping
but not necessarily with downward sloping wage functions!
Unionized
Oligopoly
Equilibrium wages
Anna
Goeddeke
Introduction
Motivation
Literature
b dU 1m
U 1m dw 1n ;
Shifts: S1 =
S2 =
a dU 1n
U 1n dw 1m
w1n
The Model
Assumptions
Regimes
Negotiations
wIm(wn)
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
wIIm(wn)
a
Conclusion
References
wIIn
wIn
wII
Employment
effect
b
Wage
effect
wI
wIn(wm)
wIIn(wm)
Emp.
effect
wIIm
Wage effect
wIm
w1m
Unionized
Oligopoly
Case 3 vs. Case 4
Anna
Goeddeke
Craft Union
Craft Union
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Craft Union
Firm
Firm
Case 3:
dN n
dw 1n
=
a dUn
U dw
| n {z 1n}
direct e¤ect
Case 4:
Conclusion
References
Firm
Firm
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Craft Union
;
dN
dw 1n
=
a dUn
U dw
| n {z 1n}
direct e¤ect
S3 : =
b dU m
U m dw 1n
+
+
c d π1
c d π2
!
+
=0
π dw
π dw
| 1 1n {z 2 1n}
…rm e¤ect
b dUm
U dw
| m {z 1n}
indirect e¤ect
+
c d π1
c d π2
+
π dw
π dw
| 1 1n {z 2 1n}
< 0 Similar to Case 1 vs. Case 2
…rm e¤ect
Unionized
Oligopoly
Case 1 vs. Case 3
Anna
Goeddeke
Introduction
Motivation
Literature
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
Craft Union
Craft Union
Firm
Firm
;
Firm
The Model
Firm
Firm
Firm
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Shift: a
1 dU n
U n dw 1n
1 dU 1n
U 1n dw 1n
?
?0
calculate equilibrium wages!
III > w I
for a wide parameter space: w1n
1n
I > w III
low a, low c, and high b w1n
1n
Unionized
Oligopoly
Case 1 vs. Case 4
Anna
Goeddeke
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
Firm
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Craft Union
Craft Union
Firm
Firm
;
Introduction
S := a
|
1 dUn
Un dw1n
{z
1 dU1n
U1n dw1n
sub. worker e¤ect
Firm
+
}
Firm
Firm
b
|
1 dUm
Um dw1n
{z
}
70
comp. worker e¤ect
negative indirect e¤ect on comp. workers: Only appears in
Case IV and not under I : ceteris paribus lowers w IV but
not w I . Depends on b.
sub. worker e¤ect positive: 1/Un dUn /dwn : ceteris
paribus higher w IV than w I
which e¤ect predominates? Depends on a and b:
for a = b: w IV = w I
for a > b, sub. worker e¤ect dominates and w I < w IV
for b > a, comp. worker e¤ect dominates and w IV < w I
Unionized
Oligopoly
Case 1 vs. Case 4
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
comparing Case 1 and Case 4 the employment e¤ect due
to asymmetric shifts of the wage functions of
complementary workers does not matter:
Shift wim :
a dUn
U dw
| n {z 1m}
comp. worker e¤ect
+ b
|
1 dUm
Um dw1m
{z
1 dU1m
U1m dw1m
sub. worker e¤ect
7 0,
}
they reinforce each other: A right shift for workers of type
n results in a left shift for workers of type m and vice versa.
Unionized
Oligopoly
Case 1 vs. case 4
Anna
Goeddeke
Introduction
Motivation
Literature
w1n, wn
The Model
wIm(wn)
Assumptions
Regimes
Negotiations
wIVm(wn)
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
wIVn
Conclusion
References
wIVn(wm)
w In
wIn(wm)
wIVm
wIm
w1m, wm
Unionized
Oligopoly
Unions
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
1
UjIV > UjII for all j = n, m.
2
Comparing UjI and UjII , UjI and UjIII , UjIII and UjIV ,and UjII
and UjIII with j = n, m depends on bargaining strengths a,
b and c.
3
For a > b UnIV > UnI and UmI > UmIV , analog for b > a
UnIV < UnI and UmI < UmIV , if a = b UnIV = UnI .
Unionized
Oligopoly
Welfare
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
W =
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
CraftU
nion
1
(A
2
CraftU
nion
Craft
Union
p ) (x1 + x2 ) + π 1 + π 2 + U1n + U2n + U1m + U2m
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
CraftU
nion
Firm
Craft Union
Firm
Firm
=
>
Firm
Craft Union
Firm
Firm
Firm
Firm
Craft Union
Firm
Firm
>
Conclusion
References
W II > W I
Craft Union
W IV > W III
Unionized
Oligopoly
Conclusion
Anna
Goeddeke
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
no di¤erence occurs between a one union or a one
negotiation framework.
no veri…cation for:
Complementary workers: di¤erent unions
Substitutable workers: encompassing unions
di¤erent union strengths: unambiguous results
di¤erent union utility functions
di¤erent union sizes
Unionized
Oligopoly
Anna
Goeddeke
Introduction
Motivation
Literature
References
Dowrick, S. (1993).
Enterprise bargaining, union structure and wages.
The Economic Record 69 (207), 393–404.
The Model
Assumptions
Regimes
Negotiations
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
References
Gürtzgen, N. (2003).
Revisting the impact of union structures on wages:
Integrating di¤erent dimensions of centralisation.
Labour 17 (4), 519–542.
Horn, H. and A. Wolinsky (1988).
Worker substitutability and patterns of unionisation.
The Economic Journal 98, 484–497.
Machin, S., M. Stewart, and J. van Reenen (1993).
The economic e¤ects of multiple unionism: Evidence from
the 1984 workplace industrial relations survey.
Scandinavian Journal of Economics 95 (3), 279–296.
Metcalf, D. (1993).
Industrial relations and economic performance.
British Journal of Industrial Relations 31 (2), 255–283.
Unionized
Oligopoly
Anna
Goeddeke
U1n
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
Umax1n
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
Conclusion
w1n
References
w*1n
Back
Unionized
Oligopoly
Anna
Goeddeke
I
U’
1n
Introduction
Motivation
Literature
The Model
Assumptions
Regimes
Negotiations
>0
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
0
wI1n(wII1n)
Conclusion
References
Back
wI*1n
w1n
Unionized
Oligopoly
Anna
Goeddeke
w1n
wII2n(w1n)
Introduction
wI2n(w1n)
wI1n(w2n)
Motivation
Literature
The Model
wI1n
Assumptions
Regimes
Negotiations
wII1n(w2n)
Results
Overview
Equal Cases
Basic results
Quantity and
pro…t
Wage e¤ects
Unions
Welfare
wII1n
Conclusion
References
w2n
wII2n
Back
wI2n