A Stylised Model with Sanctions

δ=0

>0 ⇔ R⁰(c/Θ) > w₀+ 1−α

α c (6.6)

The second order conditions are fulfilled. After an extensive comparative statics investigation of the model properties (which is of minor interest for us here), Corneo applies this model to the centralisation debate and finds that it predicts gross membership and wages to be larger in a centralised bargaining environment, since an individual firm’s union density has a smaller effect on wages than for local bargaining. Consequently, the gain to the firm associated with the bonus payment shrinks with the number of firms in the economy.

If a central employers’ association cannot enforce the payment of a bonus, each single firm will save this cost, management opposition shrinks and union membership and wages rise. It should be emphasised that Corneo’s argument rests heavily on the fact that bonus payment violates equal treatment laws.

Otherwise bonus payment could be fixed in collective labor agreements and free riders could enforce payment by law. This implies that bonus payments have to be masked in most cases, e.g. the have to take place in biased promotion or firing procedures.

6.3 A Stylised Model with Sanctions

We will provide a short discussion of the question whether the centralisation effect is relevant at all in a section below. Here we contrast Corneo’s manage-ment opposition mechanism with a simple ‘member acquisition’ mechanism.

We claim that Corneo’s reputation function hides an important aspect of the membership decision and the rules of his game are too restrictive for a

7Again we report the corresponding solution in Corneo’s paper (for bonus payments during a strike)

R⁰(c/Θ)> w0+c/α.

A comparison of both conditions and the corresponding first order condition shows that δ^∗ is larger in the unrestricted case.

simulation of reality. Corneo’s workers like high wages and reputation and consume reputation just as they consume bread and fish. Their social pref-erences or fairness conceptions relate only to union membership.⁸ But they are indifferent with regard to discrimination and don’t envy free riders. And – more important – they don’t respond to discrimination.

So we come to the point: The model does not explain why unions try to attract members. We try to show now that a simple model, explaining why workers are not indifferent with respect to membership of their colleagues, can generate contrary predictions of centralisation effects. Since there exist several doubts whether our model captures all relevant aspects of reality, we will devote a section to a short discussion below. Consequently, we have to be cautious interpreting the results. Because of many remaining question marks, we will not believe too much in its predictions. Rather we are happy to show that models with an unclear foundation of its behavioral assumptions should be taken with care.

We expand the repertoire of actions of workers by giving them control on kindness⁹ against members and nonmembers. This is utterly obvious, since reputation is related intimately to kindness. It were even possible to define the reputation of a person by the number of (significant) others being kindly against her, admiring her or holding her in great respect. Of course, as reputation is a complex psychological and social entity, kindness may not capture all its relevant facets, but surely a certain fact. There exist several types of sanctions against free riders: Members could reduce kindness against them, exert social pressure on them or refute to cooperate with them. In some escalated situations even harassment is conciveable. Though picket lines are not violent actions generally¹⁰, they nevertheless generate significant social pressure – especially if the free riders believe in the social norm, but don’t join the union because of monetary rewards.

Of course, there exist also more ‘positive’ types of action. E.g members could organise social events from which nonmembers are excluded or provide legal advice exclusively for members and other services or simply be more friendly to comrades. (We will use only the term ‘kindness’ in the rest of the paper for sake of convenience. But we have to keep in mind that it is only a proxy for other mechanisms.) The allocation of such services is aimed to

at-8Unfortunately, most economic papers using the reputation effect don’t contain a thor-ough discussion of where these effects come from.

9The economic standard vocabulary is more tough. Most economists tend to replace

‘kindness’ by the more distinct term ‘harassment’ (with inverse meaning). We try to enrich the literature here with a somewhat unusual terminology.

10For a description and analysis of picketing action see Batstone, Boraston, & Frenkel (1978).

tract members and not given exogenously. In ourvery simple formulation we assume that union members have control on kindnessk against nonmembers, but that reduction of kindness comes at a psychological costK(k). Formally U_i ={w+ (1−d_i)(δ−k)}L+w₀(1−L) +d_i(r_i−c−K(k)) (6.7) Note that we have defined k negatively for notational convenience, i.e. we define k = 0 as the natural level of kindness of members against members and k > 0 as a lower level of kindness. K(k) represents a psychological cost depending on k. We assume K(.) to be a continuous C² function with K(0) = 0, K(k) > 0 for k > 0, K⁰(k) > 0 for k > 0, and that there exist no fixed costs of reducing kindness.¹¹ Note that we do not make further assumptions regarding the second derivative ofK(.) here. Below we will show that our argument works for concave and convex K(.). This is important since K⁰⁰(k)>0 appears to be the most appropriate assumption.

Some comments and warnings are in order here. Firstly, in a more realistic formulation K(.) should depend on membership M too, since the density of the union matters. A minority of free riders probably may be highly vulnerable by disregard of union colleagues. This may change or even be reverted in a firm where free riders become a majority. We will deal with this issue in an extension of the model but ignore it here for convenience and for the sake of comparability with Corneo’s model. (By the way, this reasoning applies to reputation too, i.e. a more realistic formulation of the reputation function were, for example r_i+ρ_iM.¹²)

As a last problem, it seems artificial and arbitrary to considerr and k as different objects. Of course, we do this only for sake of convenience, since this makes it simpler to identify exogenous given reputation sensitivityrfrom the endogenous action parameter k.

Though most readers will consider it trivial then, and refute to go on reading,¹³ we anticipate the underlying mechanism. Purposeful disregard of free riders increases membership which in turn (through improvement of the bargaining position) raises wages. This effect vanishes in a centralised bargaining environment since local membership looses its impact on wages.

We end with negative effects of centralisation on membership and wages.

It suffices to show that equilibria with k^∗ > 0 exist and that centralisation reducesk^∗.

11Also the ‘no fixed cost’ - assumption is made for sake of convenience in order to avoid additional case differentiations. Nevertheless it seems to be plausible.

12Booth & Chatterji (1993) specify reputation by the termr_iM.

13It is probably efficient to skip the rest of this section and to proceed with the conclusion if the basic idea is clear.

In our model we assume that the firm is restricted to set δ = 0, i.e.

cannot use a bonus scheme to fight the union. We do this for the sake of convenience, since the more general case renders the model much more complicated. Consequently, our model cannot characterise the conditions for inner and corner solutions, whenboth parties can make use of their strategic instruments (k and δ).

The timing of our model is completely analogous to Corneo’s: In the first stage, the (future) union members decide on kindness, then workers decide on membership (given kindness), and in the last stage the union bargains with the firm over (employment and) wages. Again some remarks are in order here.

Firstly, the threads associated with harassment and kindness are not sub-game perfect. If negotiations are finished, rational unionised workers have no incentive to harass free-riders, rendering the thread implausible. Below we will report experimental evidence suggesting that behaviour of people apply and enforce non subgame perfect threads in everyday live.

Secondly, this game seems to require or contain schizophrenic workers.

Potential union members of a not yet existing union set the level of kindness against potential free riders. And an implication of the model is that the marginal union member which plans to disregard free riders could become a disregarded free rider due a small parameter change. Again the model is not realistic in this respect, since the entry into a union will change the way how workers perceive labour relations and other relevant issues.¹⁴ It will furthermore change the cannels of information available to him. Eventually the worker can predict these influences and take them as constraints for his membership decision. Similar (symmetric) forces are at work for free riders.

If they believe in the custom, cognitive dissonance mechanisms will urge them to reinterpret their conception of labour relation and seek for another free-rider friendly ideology.¹⁵

Our model probably underestimates the true ex post heterogeneity of the workforce due to its static nature. But – again for sake of simplicity – we ignore these effects. Anyway, we claim that the sequence of the game captures an central aspect of reality: It represents the fact that the behaviour of union

14A large strand of psychological experimental evidence shows that group membership affects the perception of group members and outsiders significantly even if these groups are artificial ones and membership is determined by highly arbitrary or trivial criteria (e.g.

similar estimation of the number of dots on a screen). The classical paper is Taifel et al.

(1971), Haslam (1995) provides a survey (chapter 2) with several interesting applications to organisational psychology.

15Similar problems arise in Akerlof & Dickens (1982), where the economic consequences of cognitive dissonance are analysed.

members is given for the individual worker at the time when he decides on membership.

With this at hand we can proceed by solving the wage bargain.¹⁶ Substi-tution of the utility function and the profit function into the Nash product and solution of the first order condition gives

w^∗ =w₀(1−α M) + (1−α)K(k) +α{R(1)−R(1−M)}. (6.8) The formula shows that membership has a positive impact on wages.¹⁷ Of course, this comes from the fact that higher membership reduces the firm’s threat point.

The membership decision is based now on a comparison of U^U =w+r− K(k)−c and U^F =w−k giving the reputation for the marginal member

˜

r=c+K(k)−k

with the simple interpretation that the reputation effect must compensate the sum of union fees and disutility (−k) of kindness reduction less costs of being disregarded by colleagues. Evaluation of the membership decision yields

M =

1−(c+K(k)−k)/Θ if c+K(k)−k < Θ

0 otherwise (6.9)

The derivative of M with respect to k, ∂M/∂k = −(K⁰(k)−1)/Θ is posi-tive for K⁰(k) <1, meaning that the cost of being unfriendly for the union member is less than the harm of being treated unfriendly to nonmembers.

At the first stage of the game a democratic union maximises the utility of the median member. In the case of the uniform distribution the median reputation r^m is simply

r^m = (˜r+ Θ)/2 = (Θ +c+K(k)−k)/2

after insertion into the utility function we obtain the first order condition

∂U^m

∂k = dw^∗

dk +∂r^m

∂k −K⁰(k)

=−1

2(K⁰(k) + 1) + (1−α)K⁰(k) +α(K⁰(k)−1){R⁰(1−M(k))−w₀} Θ

(6.10)

16We replicate Corneo’s efficient bargaining assumption here for sake of comparability.

17To state it formally, the derivative ∂w^∗/∂M = α(R⁰(1−M)−w₀) is positive for R⁰(1−M)> w₀which is the case for the plausible assumption w₀≤R⁰(1).