If nonunion employers set both wages and employment strategically to forestall unionization, the threat of unionization, despite raising wages, increases employment above competitive levels, in contrast with the prediction of standard models.Threat of unionization; Employment determination;

Ruiz-Verdú, Pablo

English

Research Papers in Economics

Threat of unionization and nonunion employment
Pablo Ruiz-Verdú⁎
Universidad Carlos III de Madrid, Department of Business Administration, Calle Madrid, 126. 28903, Getafe, Madrid, Spain
Abstract
If nonunion employers set both wages and employment strategically to forestall unionization, the threat of
unionization, despite raising wages, increases employment above competitive levels, in contrast with the prediction
of standard models.
Keywords: Threat of unionization; Employment determination
JEL classification: J23; J30; J51
1. Introduction
According to the standard union threat model of wage determination, nonunion employers
strategically raise wages when faced with the threat of union organization. The higher wages, in turn,
reduce nonunion employment, as nonunion firms move up along their labor demand curves.
1
While acknowledging that nonunion employers will take into account the effect of their wage choices
on workers' incentives to organize, standard union threat models effectively assume that those same
employers disregard the effect that their employment choices may have on workers' unionization
decision. In this paper, I develop a model in which nonunion firms set both wages and employment
strategically when faced with a threat of unionization. The model shows that if nonunion firms take into
Economics Letters 96 (2007) 109 115
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E mail address: pablo.ruiz@uc3m.es.
1 See Farber (2005) for a recent version of the union threat model and Ehrenberg and Smith (2005) for a textbook exposition.
Pencavel (1991, ch. 6) offers a more general analysis of the interaction between union and nonunion sectors.
0165 1765/$ see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.econlet.2006.12.018
1account the effect of their employment choices on workers' incentives to unionize, the prediction of the
standard threat model is reversed: instead of reducing employment, the threat of unionization increases
employment above competitive levels.
2. Setup
Consider a nonunion firm that hires l workers from a pool of identical workers with reservation wage w ¯
and offers these workers a wage w to be paid after production takes place. Through on-the-job learning,
the l employees accumulate firm-specific skills, thus becoming more valuable for the firm than alternative
workers. If they are not satisfied with the wage w initially offered by the firm, employees can unionize to
renegotiate the wage so as to capture part of the quasi-rents generated by their firm-specific skills.
2
Unionization, however, entails organization costs C(l) for workers.
3 If workers unionize, collective
bargaining takes place, resulting in employment lu≤l and a wage wu.
At the end of the period, revenues are generated and wages paid. The revenues generated by incumbent
workers are described by the function R, with R′≥0 and R″b0. For simplicity, it is assumed that the
firm's revenues would be zero if it employed workerswith no firm-specific skills. Fig. 1 displaysthe time-
line of the model.
3. Collective bargaining
When setting wages and employment, the firm will try to predict the effect of its choices on workers'
incentives to unionize. These incentives, in turn, depend on the wage and employment levels that would
result if workers unionized and bargained collectively with the firm. Therefore, to solve the model, I
proceedby backward induction and first analyze the collective bargaining stage that takes place if workers
unionize.
2 The assumption that workers have no individual bargaining power is made only for simplicity: none of the results would
change qualitatively if we allowed for individual bargaining power, as long as employees' bargaining power is greater if they
bargain collectively.
3 These costs reflect the time and effort workers need to put into organizing (or the fees and dues paid to union officials if
these activities are delegated to an existing union) and the costs stemming from potential retaliatory measures that employers
may take to fight the unionization attempt. See Kleiner (2001) for a recent assessment of these costs and their influence on
unionization.
Fig. 1. Sequence of events.
110 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
2Union-management bargaining is modelled by means of the commonly-used monopoly union model.
According to this model, the union imposes its wage demands on the employer, who then sets
employment at will. I assume that the union's objective is to maximize the total rents accruing to its
members, which is also one of the most usual assumptions in the literature:
Uðwu;luÞ¼luðwu−¯ wÞð 1Þ
As I discuss in Section 5, the particular choiceof bargaining modelor unionobjective functiondoes not
play any essential role in deriving the results.
The well-known outcome of the monopoly union model is the wage–employment pair on the marginal
revenue product curve that yields the highest rents to the union (see Booth, 1995, ch. 4). Below, I extend
the usual model to account for the restriction that the level of skilled employment resulting from the
collective bargaining process (lu) cannot be greater than the number of workers with specific skills (l).
Therefore, once the union has set a wage wu, the firm sets lu≤l such that R(lu)−wulu≥R(l' u)−wul' u, for
any l' u≤l.
The union's problem can then be stated as follows:
4
max
lu;wu
luðwu−¯ wÞð 2Þ
s:t: luVl
RðluÞ−wuluzRðl0
uÞ−wulu V; for any l0
u≤1 ð3Þ
Let wu(l) and lu(l) denote the solutions to this problem, and let ∏U(l)≡R(lu(l))−wu(l)lu(l). The
following lemma describes the properties of wu(l), lu(l) and ∏U(l) (the proof is in the Appendix):
Lemma 1. In the monopoly union model:
(A) wu(l) is nonincreasing in l.
(B) There exists a level of membership lu * such that:
B.1) For l≤lu *,l u(l)=l
(B.2) For l≥lu *,l u(l)=lu * and wu(l)=wu(lu *).
(C) ∏U(l) is increasing in l for lblu *, and constant in l for lNlu *.
Result (A) implies that a larger membership will induce the union to accept a lower wage in exchange
for greater employment. Result (B) shows that for low levels of initial employment, the negotiated
outcome implies the employment, the union is not willing to concede any further reduction in wages and
instead accepts some unemployment (B.2). Result (B) thus implies that lu(l) is nondecreasing in l. Finally,
result (C) means that the profits of a unionized firm are nondecreasing in initial employment. This makes
sense: if the union raises wages and reduces employment, increasing initial employment will, according to
properties (A) and (B) counteract both effects, and should, thus, tend to increase profits. Note, however,
that (A) and (B) do not imply (C).
4 This formulation is equivalent to one in which the union selects wu to maximize lu(wu, l)(wu w ¯), where lu(wu, l) is the
solution to the firm's employment choice problem given wu and l.
111 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
34. Wage setting and union avoidance
Let wT(l) denote worker's expected payoff from unionization (bet of organization costs).
wTðlÞu
luðlÞ
l
wuðlÞþ 1−
luðlÞ
l

¯ w−
CðlÞ
l
ð4Þ
For any employment choice, l, the firm has to offer a wage at least as high as wT(l) if it wants to remain
nonunion. If wT(l)≤w ¯, the firm sets w ¯ and avoids unionization. If wT(l)Nw ¯ and the firm offers a wage
below wT(l), workers unionize and profits are ∏U (l)=R(lu(l))−wu(l)lu(l)). If the firm offers wT(l), and
workers accept, profits are:
Pðl;wTðlÞÞ ¼ RðlÞ−lwTðlÞ¼RðlÞ−wuðlÞluðlÞ− ¯ wðl−luðlÞÞ þ CðlÞð 5Þ
For lu * as defined in Lemma 1, it follows from properties (B.2) and (C) in Lemma 1 that ∏U(lu *)≥∏U(l)
for any l. Moreover, luðl⁎
uÞ¼l⁎
u and wTðl⁎
uÞ¼w⁎
u−
Cðl⁎
uÞ
l⁎
u
; so Pðl⁎
u;wTðl⁎
uÞÞ ¼ Rðl⁎
uÞ−l⁎
uwu⁎ þ
Cðl⁎
uÞNRðl⁎
uÞ−l⁎
uwu⁎ ¼ PUðl⁎
uÞ . Therefore if l* is the optimal employment level, it follows that Π(l
*, wT
(l
*))≥Π(lu *, wT(lu *))NΠU(l)f o ra n yl. In words, the firm can guarantee higher profits by setting l=l* and
w=wT(l*) than by setting any employment–wage pair that leads to unionization, Therefore, we obtain the
following result:
Proposition 1. In equilibrium, the firm offers
w⁎ðl⁎Þ¼maxfwTðl⁎Þ; ¯ wg; ð6Þ
where l* is the optimal employment level, and workers accept the wage offer.
As proposed by the standard union threat view, in equilibrium, firms raise wages above w ¯ to eliminate
workers' incentives to organize. Only if C(l) is sufficiently large will the union threat become ineffective,
and the wage remain at the competitive level.
5. Employment determination
Expression (4) highlights that the wage necessary to forestall unionization depends on the level of
employment, l. Therefore, the firm should take this influence into account when choosing its optimal
employment level.
If lblu
*, Property (B.1) in Lemma 1 implies that luðlÞ¼l; so that w⁎
uðlÞ¼wuðlÞ−
CðlÞ
l
and Pðl; w⁎ðlÞÞ ¼ RðlÞ−wuðlÞl þ CðlÞ¼PUðlÞþCðlÞ.
5 Therefore, for low levels of employment, the
maximum profit that the firm can obtain while avoiding unionization is equal to the profit the firm would
obtain if workers unionized plus the costs that workers would have to incur so as to unionize. By property
(C), we know that ∏U(l) is increasing in l for lblu *. Therefore, if C is nondecreasing in l, ∏(l, w*(l)) will
also be increasing in l for lblu *. It follows that if l* denotes the firm's optimal employment choice, l*≥lu *.
5 To simplify the argument, I assume that w*(l) wT(l)Nw ¯ for the relevant range of l.
112 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
4Now, for lzl⁎; luðlÞ¼l⁎
u and w⁎ðlÞ¼
l⁎
u
l
w⁎
u þ
l−l⁎
u
l

¯ w−
CðlÞ
l
, so that the wage bill is w*(l)l=
lu *wu *+(l−lu *)w ¯−C(l). Notice that, if we abstract from the last term, this expression implies that, for any
l≥lu *,ifthefirmwantstohireanextraworkerwhileavoidingunionization,itonlyhastoincreasethewage
bill by w ¯. The reason is that, when l≥lu *, any additional worker hired only increases workers' total payoff
in case of unionization by w ¯: since the new hire would not affect the union-negotiated wage or
employmentlevel,itwouldonlyincreasethenumberofskilledworkerswholosetheirjob–and,thus,earn
w ¯ – after unionization. Therefore, for l≥lu *, ∏(l, w*(l))=R(l)−w*(l)l=R(l)−lu *wu *−(l−lu *)w ¯+C(l), so:
PVðl;w⁎ðlÞÞ ¼ RVðlÞ− ¯ w þ CVðlÞð 7Þ
In the absence of a union threat, the firm would choose the level of employment lc such that R′(lc)=w ¯.
It follows from this last expression and Eq. (7) that, as long as C′≥0, ∏′(lc, w*(lc))≥0 and, by strict
concavity of R, ∏′(l, w*(l))N0 for lblc. Therefore, l*≥lc, and l*Nlc if C′(lc)N0. The following
proposition summarizes the argument.
Proposition 2. Let l* be the optimal employment level and lc the competitive employment level. Then
l*≥lc.
It is worth noting that the overemployment result in Proposition 2 does not depend on the specific
choice of bargaining model. It can be shown that the result holds for more general specifications of the
union's objective function and for a large family of bargaining models that includes the two other
main collective bargaining models, namely the right-to-manage and the efficient bargaining models.
6
What drives the overemployment result are properties (A)–(C) in Lemma 1, which, essentially, follow
from the assumption that the marginal revenue product of labor is decreasing in the level of
employment.
Although the standard union threat model predicts that employment will fall as a consequence of the
threat of unionization, it should be noted that there is a precedent for the positive threat effect in
Proposition 2. Using a different modelling strategy (in which coalitions of workers can form a union and
select a wage–employment pair from a set of exogenously-given possible bargaining outcomes), Dickens
(1986) showed in a working paper that the threat of unionization could lead to an increase in employment
under certain conditions regarding the ability of coalition workers to discriminate against noncoalition
workers.
6. Conclusion
Ithaslongbeenrecognizedthatthethreatofunionizationislikelytoaffectnonunionfirms'wagepolicies.
Inparticular, unionthreat models haveproposedthatnonunionfirms will increasewages abovecompetitive
levels to dissuade workers from joining unions. In this paper, I argue that the same logic applies to
employment choices: nonunion firms should set their employment levels taking into account the impact of
their choicesonworkers' incentives toorganize.Tothe extentthatemployers dotakeinto accounttheeffect
ofemploymentonprospectiveunionization,Ishowthatthethreatofunionization,despiteraisingwagesasin
6 For a review of theses models, see Booth (1995, ch. 5).
113 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
5standard union threat models, will increase employment above the competitive level, in contrast to the
prediction of those models.
Acknowledgements
The author thanks Edward Lazear, Robert McMillan, John Pencavel and Steve Tadelis for extremely
helpful discussions. The usual disclaimer applies. The financial support of Spain's Ministry of Education
and Science (SEJ2005-06655/ECON) is gratefully acknowledged.
Appendix A
Proof of Lemma 1. The standard monopoly union problem with no restrictions on lu can be stated as:
max
lu;wu
luðwu− ¯ wÞ
s:t: RðluÞ−wuluzRðl0
uÞ−wul0
u; for any l0
uV0 ðPAÞ
Concavity of R implies that the restriction can be replaced by the F.O.C.: R′(lu)=wu, so problem (PA)
can be rewritten as
max
lu
luðRVðluÞ− ¯ wÞð P0
AÞ
Making the standard assumption that problem (P′ A) is concave, its solution, lu *, is given by
RVðl⁎
uÞ − ¯ w þ l⁎
uRWðl⁎
uÞ¼0 ð8Þ
Let w*≡R′(lu *) and let lc be defined by R′(lc)=w ¯. Strict concavity of R implies that wu *Nw ¯ and lu *blc.
If lu is constrained to lie below l, the union solves problem (PB):
max
lu;wu
luðwu− ¯ wÞ
s:t: luVl ð9Þ
RðluÞ−wuluzRðlV
uÞ−wul0
u; for any l0
uV1 ð10Þ
Foranywu≤R′(l),R″b0andEq.(10)implythatlu=l.Therefore,itcannotbeoptimalfortheuniontoset
w
u≤R′(l), (since wu=R′(l) guarantees the same level of employment). Now, if the union sets wu≥R′(l)f o r
any l,t h e nlu will satisfy R′(lu)=wu, so the union's problem becomes:
max
lu
luðRVðluÞ− ¯ wÞð P′BÞ
s:t: luVl ð9Þ
Problem (P′ B) is identical to problem (P′ A) with the addition of constraint (9). Therefore, if lu * satisfies
Eq. (9), then it is a solution to problem (P′ B). Thus lu(l)=lu * and wu(l)=wu * for l≥lu *, proving (B.2). Now,
114 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
6the concavity of problem (P' A) ensures that R'(lu)−w ¯−luR"(lu)N0 for lublu *. That is, the marginal benefit
for the union of increasing employment is positive for lublu *. Therefore, for lblu *, lu(l)=l and wu(l)=R'(l),
proving (B.1). (A) follows from the concavity of R and the fact that for lblu *, wu(l)=R′(l), and, for l≥lu *,
wu(l)=wu *.
Finally, note that for lblu *, ∏U(l)=R(lu(l))−lu(l)wu(l)=R(l)−lR′(l), which is increasing in l due to the
concavity of R; and, for l≥l*, ∏U(l)=R(lu(l))−lu(l)wu(l)=R(l*)−l*R′(lu *), which is constant in l. This proves
(C). □
References
Booth, A.L., 1995. The Economics of the Trade Union. Cambridge University Press, Cambridge.
Dickens,W.T.,1986.Wages,Employment,andtheThreatofCollectiveBargainingbyWorkers.NBERWorkingPaper,vol.1856.
Ehrenberg, R.G., Smith, R.S., 2005. Modern Labor Economics, Ninth ed. Addison Wesley, Boston.
Farber, H.S., 2005. Nonunion wage rates and the threat of unionization. Industrial and Labor Relations Review 58, 335 352.
Kleiner, M.M., 2001. Intensity of management resistance: understanding the decline of unionization in the private sector. Journal
of Labor Research 22, 519 540.
Pencavel, J.H., 1991. Labor Markets Under Trade Unionism: Employment, Wages and Hours. Basil Blackwell Inc., Oxford.
115 P. Ruiz Verdú / Economics Letters 96 (2007) 109 115
7

Intensity of management resistance: understanding the decline of unionization in the private sector.

Labor Markets Under Trade Unionism: Employment, Wages and Hours.

Nonunion wage rates and the threat of unionization.

Ruiz Verdú /

The Economics of the Trade Union.

Threat of unionization and nonunion employment.

http://e-archivo.uc3m.es/bitstream/10016/12725/1/threat_ruizverdu_EL_2007_ps.pdf

Threat of unionization and nonunion employment.

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