Lecture 4 Wage Bargaining and Unionscoin.wne.uw.edu.pl/.../lecture_4.pdf · Lecture4–WageBargainingandUnions Introduction 4/38 Introduction Table1. Unioncoverage–internationalcomparison

Lecture 4Wage Bargaining and Unions

Leszek Wincenciak, Ph.D.

University of Warsaw

Lecture 4 – Wage Bargaining and Unions

2/38

Lecture outline:

Introduction

Some models of trade union behaviourIntroductionThe monopoly model of the trade unionThe ’right-to-manage’ modelThe efficient bargaining model

Corporatism

Summary


Introduction 3/38

Introduction

� Unions are often blamed for unemployment. Is this fair?� Unions influence on unemployment depends upon manyfactors:

� union power within the bargaining unit� the fraction of workers covered by collective bargaining� the degree of centralization of bargaining


Introduction 4/38

Introduction

Table 1. Union coverage – international comparison

Country

Share of workerscovered by

collective contracts

Share of workersin market economybelonging totrade unions Centralization Coordination

Australia 80 35 2 2Austria 97 34 3 4Belgium 82 44 3 4Denmark 52 68 2 4Finland 67 65 5 5France 75 10 2 2Germany 80 25 3 4Sweden 72 77 3 3UK 35 19 1 1USA 13 10 1 1Centralization: 1 – firm level negotiations; 5 – central level negotiationsCoordination: 1 – no coordination or low-level; 5 – negotiations coordinated by a confederation of TU at a centrallevel


Some models of trade union behaviour 5/38

Introduction

Union objectives

Suppose that the representative trade union has a utility functionV (w,L) with the following form:

V (w,L) =L

Nu(w) +

[1− L

N

]u(B), (1)

where N is the fixed number of union members, L is the numberof employed union members (L � N), w is the real wage, B is thevalue of unemployment benefits and u(·) is the indirect utilityfunction.

Two possible interpretations: probabilistic or utilitarian.



Introduction

Firm side

The representative firm is modelled in a standard way. Productionfunction given by Y = AF (L,K), with predetermined capitalstock K is assumed to have constant returns to scale anddiminishing marginal returns (FL > 0, FLL < 0).The short run real profit function is defined as:

π(w,L) = AF (L,K)−wL. (2)

It is worth to capture graphical representation of solutions obtainedin various models. First, labour demand schedule is given by allcombinations of (w,L) for which profits are maximized by thechoice of L. Formally we have:

πL = AFL(L,K)− w = 0 ⇔ LD = LD(w,A,K), (3)

with LDw < 0, LD

A > 0 and LDK

> 0.



Introduction

Firm side

The second graphical device is the iso-profit curve. It represents allthe combinations of w and L for which profits attain certain,constant level. It can be interpreted as the firm’s indifferencecurve. The slope of an iso-profit line can be determined by dπ = 0:

πwdw + πLdL = 0 ⇒(dw

dL

)dπ=0

= −πLπw

. (4)

We know from equation (2) that πw = −L < 0, so that the slopeof an iso-profit curve is determined by the sign of πL. ButπL = AFL − w and FLL < 0, so that πL is positive for lowemployment, zero for optimal employment and negative for toohigh employment.



Introduction

Firm side

Figure 1. Iso-profit curves and labour demand



Introduction

Union objectives

Union objectives can be also represented graphically. Third line tobe derived is the union’s indifference curve. Obviously union willnot supply any workers to the firm at wages below theunemployment benefit. Hence in terms of figure 2, this restrictionthat w � B translates into horizontal line BC (benefit curve). Onthe other hand, the union is unable to supply any more workersthan its current membership. Hence, there is an additionalrestriction L � N , which is the full employment line FE in thefigure 2. Within the feasible region (w � B and L � N), the slopeof an indifference curve is determined by dV = Vwdw + VLdL = 0:

L

Nuwdw +

1

N[u(w) − u(B)]dL = 0 ⇒(

dw

dL

)dV=0

= −u(w)− u(B)

Luw< 0. (5)



Introduction

Union objectives

Figure 2. Indifference curves of the union



Introduction

Three major models of trade union behaviour

� Monopoly union model [Dunlop (1944)]: union exploitsmonopoly power in its labour market

� ’Right-to-manage’ model [Leontief (1946)]: union and firmbargain over the wage. The firm sets the employment level

� Efficient bargaining model [McDonald and Solow (1981)]:union and firm bargain over wage and employmentsimultaneously



The monopoly model of the trade union






This is the oldest model of trade union, proposed by Dunlop(1944). The trade union is assumed to behave like a monopolistseller of labour. It faces the firm’s demand for labour, definedimplicitly by (3) and sets the real wage such that its utility (1) ismaximized. Formally, the problem of a monopoly union becomes:

maxw

V (w,L) s. t. πL(w,A,K) = 0, (6)

where the restriction πL = 0 ensures that the union choosesa point on labour demand line. In other words, the labour demandacts here like a ’budget constraint’ for the monopolistic union.





By substituting the labour demand into the union’s utility function,the optimization problem becomes very simple:

maxw

V(w,LD(w,A,K)

). (7)

The first order condition is:

dV

dw= 0 : Vw + VLL

Dw = 0, (8)

This implies that Vw/VL = −LDw , which means that in the

optimum the slope of union’s indifference curve has to be equalizedwith the slope of firm’s labour demand. Solution is presented inthe figure 3.





Figure 3. Wage setting by the monopoly union





How does real wage respond to productivity shock in a monopolyunion model? In competitive solution the real wage would beunaffected, unless the productivity shock is very large. In order tograsp the effects in the monopoly union model let’s rewritecondition (8) in the following form:

Vw + VLLDw =

L

Nuw +

1

N[u(w)− u(B)]LD

w = 0

=L

wN

[wuw + [u(w) − u(B)]

wLDw

L

]= 0

⇒u(w) − u(B)

wuw=

1

εD, (9)

where εD ≡ −wLDw/L is the absolute value of labour demand

elasticity.





If this elasticity is constant, then any productivity shock will affectonly employment, but not real wages. This can explain real wagerigidity.

If all members of the union are employed (L = N), then union’sobjective function simplifies to V (w,L) = u(w) and is independentof L. The union is then interested in setting the highest possiblewage, which is set according to w = AFL(N,K). This is the pointof intersection of labour demand line and FE line. Any positiveproductivity shock will drive wages further up.



The ’right-to-manage’ model





The bargaining theory

� The union never gets everything it wants. It bargains� In more realistic setting the union and the firm bargain overwages. What determines the outcome of the power strugglebetween a union and its employer?

� Key element – ability of both sides to halt production� Firm may lock-out or fire workers� Union may organize and go on strike� Costs of firing and hiring together with a human capitalspecific to the firm may give the union considerable bargainingpower

� Both sides have an incentives to settle (firm losses revenue,workers may lose wages)





� The problem of bargaining is analogous to that of dividinga continuous supply of cake between two parties

� If the parties do not agree, they get no cake at all� It can be shown (using game theory) that this would drivebargainers to split the cake:

� If the discount rates differ, the party with higher discount ratewill be less willing to go without the cake, so will accepta reduced share of it in order to prevent it from happening

� If one side gets some extra income from elsewhere as a resultof a dissagreement (e.g. unemployment benefits), that partywill be more willing to tolerate a dissagreement and thus willbe able to insist on a higher share of cake. This party is said tohave a higher ’fallback’





It can be shown that if Yi is the cake which one party receives perperiod, ri its discount rate, and Y i its fallback income per period,the supply of cake Y will be divided between the two parties tomaximize (so called Nash maximand):

(Y1 − Y 1)1/r1(Y2 − Y 2)

1/r2 s.t. Y1 + Y2 = Y .





If we apply this outcome to the problem of bargaining betweena union and a firm, the problem is to maximize:

(V − V )β(π − π)1−β s.t. relevant constraints,

where V is the union objective function, π the firm’s profit perperiod and V , π are relevant fallbacks.

In this context, β can be viewed as a measure of the bargainingpower of the union. β is the relative discount rate of the firm, so βis increasing if discount rate for the firm increases (this makesa union relatively more patient).





The firm is assumed to have free choice of employment (hence thename ’right-to-manage’) but there is bargaining between the firmand the union over wage. In this kind of models it is moreconvenient to use Nash maximand function (Ω) in logarithmicterms.

The fallback position of the union is V = u(B), while the fallbackposition of the firm is π > 0 (to cover capital costs).

ln Ω = β ln(V (w,L) − V ) + (1− β) ln(π(w,L) − π).





The problem of bargaining can be written in the following way:

maxw

ln Ω s. t. πL(w,A,K) = 0, (10)

If we substitute labour demand (3) into (10) we obtain:

maxw

β ln(V (w,LD(w,A,K))− V

)+(1−β) ln

(π(w,LD(w,A,K))− π

)(11)

F.O.C.:

d ln Ω

dw= β

Vw + VLLDw

V − V+ (1− β)

πw + πLLDw

π − π= 0. (12)





The numerator Vw + VLLDw can be expressed in the following way

(by using (9)):

Vw + VLLDw =

L

wN[wuw − εD[u(w)− u(B)]] . (13)

And by the envelope theorem we have:

πw + πLLDw = πw = −L, (14)

since πL = 0, because solution lies on labour demand curve.





By substituting (13) and (14) into (12) we get:

β

V − V

[Vw + VLL

Dw

]=− 1− β

π − ππw

L

wN[wuw − εD[u(w) − u(B)]] =

(1− β)(V − V )

β(π − π)L

wuw − εD[u(w)− u(B)] =(1− β)wL

β(Y − wL− π)[u(w) − u(B)],

(15)

where V − V = (L/N)[u(w) − u(B)].





Finally, by simplifying, we get:

u(w)− u(B)

wuw=

1

εD + φ, φ ≡ (1− β)γL

β(1− γL − γπ)� 0, (16)

where γL = wL/Y is the share of labour income in total incomeand γπ = π/Y is the share of the minimum profit in total income.From (16) we can see that the wage markup is lower than in themonopoly model. Clearly, the monopoly model is the special caseof RTM when we set β = 1 with φ = 0. The other extreme isfound by setting β = 0, when we have competitive solution.





Figure 4. Wage setting in the right-to-manage model




Conclusions

� In the ’right-to-manage’ model, the increase of bargainingpower by the union reduces employment, so it results in higherinvoluntary unemployment

� In both models however, the pair (w,L) is inefficient in Paretosense. It is possible to obtain higher utility level for at leastone side without reducing the utility of the other

� These models are treated by economists with caution, becauseof their inefficient outcomes

� A simultaneous bargaining over wages and employment maylead to efficient contracts



The efficient bargaining model






The model proposed by McDonald and Solow (1981) assumes thatthe firms and the union bargain over wages and employmentsimultaneously. Again, the bargaining problem can be solved bymaximizing the Nash product with respect to w and L. Theproblem becomes:

maxw,L

ln Ω ≡ β ln(V (w,L)− V ) + (1− β) ln(π(w,L) − π). (17)

F.O.C.:

∂ ln Ω

∂w=

β

V − VVw +

1− β

π − ππw = 0, (18)

∂ ln Ω

∂L=

β

V − VVL +

1− β

π − ππL = 0. (19)





By combining these two F.O.C. we get so called contract curve,which represents all combinations of (w,L) for which efficientbargaining solutions are obtained. There is no combination of(w,L) along this contract curve which makes one side better offwithout making the other one worse off. It can be easily seen thatthe contract curve is given by:

VL

Vw=

πLπw

. (20)

In graphical terms the contract curve represents all points oftangency between the union’s indifference curves and firm’siso-profit lines.





From (20) we can see that πL = VLπw/Vw, which is clearlynegative, because of Vw > 0, VL > 0 and πw < 0. This means thatalong the contract curve wages will exceed that marginal productof labour (πL < 0), so efficient bargains will generally lie off thelabour demand line (except for the competitive solution). Thismeans that efficient contracts will not generally be efficient inproduction sense.We can see that (20) can be expressed in the following way:

w − FL(L,K) =u(w)− u(B)

uw. (21)





By calculating total derivative of (21) we can find the slope of thecontract curve:

dw

dL=

AFLL(L,K)uw

uww[w − FL(L,K)].

Because the sign of FLL(L,K) is negative (by diminishingmarginal product) the slope of contract curve is determined by thesign of uww. If workers are risk averse then the slope of contractcurve is positive. Risk neutrality would yield vertical contractcurve, and finally, if workers are risk lovers employment decreaseswith the bargaining power of the union.





Figure 5. Wages and employment under efficient bargaining


Corporatism 36/38

Corporatism

Key idea (Calmfors and Driffill): it is best for unemployment tohave either many very small and weak unions (as in the US, Japan,and Canada) or to have few large and strong unions (as in Swedenand Austria). Avoid the intermediate case. Reasons:

� Weak unions do not impose much damage� Strong unions internalize the external effects of high wageclaims [high wages → high unemployment → (in a welfarestate) high unemployment benefits → high taxes on workingpopulation → low after-tax wage for workers]

� Intermediate case: unions large enough to do damage but notlarge enough to internalize the government budget constraint


Corporatism 37/38

Corporatism

Figure 6. Unemployment, real wages and corporatism


Summary 38/38

Summary

� Unions and firms bargain over wages and possibly otherattributes of a contract. In more general setting, bargainingcould be over employment conditions, hours of work,severance payments and so on

� Generally higher bargaining power of a union results in loweremployment if bargaining is over wages only. In efficientbargaining, when workers are risk averse, increased bargainingpower would lead to higher employment

� Level of centralization of wage bargaining is important for thelabour market performance

Lecture 4 Wage Bargaining and Unionscoin.wne.uw.edu.pl/.../lecture_4.pdf · Lecture4–WageBargainingandUnions Introduction 4/38 Introduction Table1. Unioncoverage–internationalcomparison

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