Chapter 15: Wage and Employment Determination under
Collective Bargaining
Theory of Union Behaviour
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the theory of union behaviour has long been a subject of debate
o most economists have taken an 'economic' approach assuming that the union
maximizes an objective function subject to labour market constraints, such as
the firm's demand for labour
o but other economists, political scientists and industrial relations specialists
have criticized the 'economic' approach for not paying enough attention to the
union as a 'political' institution
the modern approach to union behaviour recognizes some merit in both positions in
that the union is modelled as attempting to maximize a well-defined utility function
subject to labour market constraints, but attention is paid to the political nature of
union decision-making, especially the relationship between the preferences of
individual members and those pursued by union leaders
Union Objectives
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the union's objective function (the union's objectives when it bargains with
management) is assumed to reflect the aggregate labour market preferences of union
members
o we assume that workers are well informed about various labour market
options and that union leaders are democratically elected and wish to remain
in office (if union leaders try to implement an agenda which does not
represent a majority of union members, we assume that they will be voted out
of office and replaced by new leaders who do represent union members)
the two key elements in a union objective function are compensation and employment
(job security)
o while the compensation package includes fringe benefits, such as vacation pay
and pension plans, we assume that wages are the key compensation objective
 what matters to union members is their real wage (W/P), the nominal
wage (W) rate relative to the cost of living (represented by the price
level, P)
 the benefits of belonging to a union depend on the union wage relative
to the best alternative wage; most workers will be unwilling to bear
the cost of union membership (dues) if the union wage is less than
they can earn elsewhere for comparable work
o unions also bargain over a host of other issues, such as working conditions,
grievance procedures, seniority clauses, and severance pay, which are ignored
in the following analysis
the union utility (objective) function is assumed to depend on the union wage
(expressed in real terms), total employment of union members, and the alternative
wage
o the union attempts to maximize wages and job security for its members, but
must trade-off gains in wages against losses in employment for its members
Textbook Figure 15.1 depicts a set of union (U) indifference curves in W/P, E space
the Uo indifference curve represents all combinations of the real wage (W/P)
and employment (E) which provide union members with the same Uo amount
of utility; higher indifference curves, such as U1 and U2, represent higher levels
of utility
o the curvature of the indifference curve reflects the union's preferences for real
wages (W/P) versus employment (E) or job security
 if the union prefers high wages over job security (i.e., is willing to give
up many jobs to gain a small increase in wages), then the indifference
curves will be relatively flat
o the union's indifference curves lie above the alternative wage Wa that union
members could earn elsewhere; if the wage obtained by the union falls below
Wa, union members will leave the union and the firm
some special cases of this union utility function that have been proposed include:
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maximize the (real) wage, which implies that no weight is placed on
employment (job security) in union preferences; as shown in Textbook Figure
15.2(a), this special case is represented by a map of horizontal indifference
curves
maximize employment, which implies that no weight is placed on the wage in
union preferences; as shown in Figure 15.2(b), this special case is represented
by a map of vertical indifference curves
maximize the wage bill (the product of employment and the wage rate),
ignoring the alternative wage; as shown in Figure 15.2(c), this special case is
represented by a set of indifference curves which are rectangular hyperbolas
lying above the employment E axis
maximize the economic rent of union members given what they could earn
elsewhere (the product of employment and the difference between the union
wage and the alternative wage); as shown in Figure 15.2(d), this special case
is represented by a set of indifference curves which are rectangular hyperbolas
lying above the alternative wage
 this latter special case is the most plausible and is analogous to the
union acting as a monopoly seller of labour to the firm and maximizing
the 'total return' to its members
Union Preferences: Some Additional Considerations
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the task of deriving union objectives from the underlying preferences of individual
members is easiest when individual members' preferences are relatively homogeneous
when individual members' preferences are heterogeneous (for example, older
members may want to place more weight on pensions and less on current wages than
younger members), the median voter model may be a good way to represent union
preferences
o in the median voter model, which can be derived under certain conditions from
a political model of union decision-making, the preferences of the organization
as a whole are represented by the median member (for example, a member of
the median age if preferences differ according to the age of the member)
because union utility depends on the preferences of individual members, changes over
time in union membership may lead to changes in union objectives
o for example, an increase in product demand may lead to an influx of new and
possibly younger members, reducing the age and seniority of the median
member
Union Constraints
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assuming that the union maximizes its objective function and the firm maximizes
profits, two different bargaining cases are considered:
o the firm and union only negotiate the wage rate and the firm retains discretion
over the level of employment (the labour demand curve, 'right to manage'
model)
o the firm and union negotiate both the wage rate and the employment level
(the 'efficient' contracts model)
The Labour Demand Curve Model: The Firm and Union Only Negotiate the Wage Rate
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the union wants to maximize its objective function but is constrained by the firm's
labour demand curve; once the wage rate is negotiated, the firm will decide on the
profit-maximizing level of employment (according to the labour demand curve)
o we assume that the union knows the firm's labour demand curve (how much
labour it will hire at various wage rates) and takes this into account in
negotiating the wage rate
given the labour demand curve DL and set of union indifference curves in Textbook
Figure 15.1, the union maximizes its objective function at point a0 where the DL curve
is tangent to the highest possible indifference curve U1
o given the firm's DL curve, the union can not reach a higher indifference curve
than U1 and if the union were to move away from point a0 on the DL curve in
either direction (such as points a1 and a2) union members would have a lower
utility
the firm's labour demand curve DL in Figure 15.1 represents the value of the marginal
product of labour and the area under the DL curve above the negotiated wage
represents the amount of profits the firm makes from hiring labour; as the firm moves
down the DL curve, profits increase
assuming that the firm can not hire any employees if it pays less than the alternative
wage Wa, the firm's optimal bargaining point is the alternative wage Wa
the range of bargaining outcomes is represented by points on the labour demand
curve between the union's optimal bargaining position (point a0) and the firm's optimal
bargaining position (Wa)
o both parties lose if they move up the labour demand curve to a point higher
than a0
depending on the respective bargaining strength (power) of the firm and the union,
the negotiated wage will end up somewhere between point a0 and the alternative wage
Wa
as the union moves from point a0 towards the alternative wage Wa it loses
utility and as the firm moves from alternative wage Wa towards point a0 it
loses profits
o a powerful union, such as the Canadian Automobile Workers (CAW), can
obtain a negotiated wage rate close to its optimal position a0, whereas a weak
union may be forced to accept a wage much closer to the alternative wage Wa
unions may be able to enhance their available wage-employment outcomes by
relaxing the demand constraint, either by increasing labour demand or by making the
labour demand curve more inelastic (as discussed in Chapter 5, the elasticity of labour
demand depends on the elasticity of product demand and the ease of substituting
other inputs for labour)
o union activity is often directed at restricting substitution possibilities by
employers in the labour market (for example, opposing automation and outsourcing) and by restricting substitution possibilities by consumers in the
product market (for example, opposing Free Trade and government deregulation policies which increase competition in the marketplace)
o
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The 'Efficient' Contracts Model: The Firm and Union Negotiate Both the Wage Rate
and the Employment Level
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the firm and union can each benefit from negotiating a contract covering both wages
and employment
o outcomes on the labour demand curve imply unexploited 'gains from trade'
that can be attained by exchanging a lower wage rate for increased
employment such that both firm profits and union utility increase
if the firm and union only negotiate wage rates (and not employment levels), the
outcome will not be Pareto efficient
o if resources are allocated in such a way that no re-allocation of resources can
make anyone better off without making someone else worse off, the allocation
of resources is Pareto efficient or Pareto optimal; Pareto was an Italian
economist (1843–1923) who conducted pioneering research in the field of
welfare economics
if the firm and union bargain over both wage rates and employment levels, one party
can be made better off without hurting the other party (a Pareto improvement) and it
is possible to make both parties better off
to demonstrate the Pareto improvement possible by negotiating both wage rates and
employment levels, we make use of firm isoprofit curves (see Textbook Figure 15.3)
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an isoprofit curve plots combinations of wages and employment that yield equal profits
o since the firm reaps more profits as it moves down the labour demand curve,
higher profit levels are represented by lower isoprofit curves (0, 1, 2, and 3)
o each isoprofit curve achieves maximum height where it intersects the labour
demand curve; for any given wage rate, moving left or right from the labour
demand curve will result in a lower profit level (and correspond to a higher
isoprofit curve)
 for example, at the wage rate W* in Figure 15.3, the firm will earn less
profits if it hires fewer employees (points e and f) than E* (the profitmaximizing point b) or if it hires more employees (points g and h)
than E*; compared to point b on the isoprofit curve 2, points e, f, g,
and h all lie on the higher isoprofit curves 0 and 1 representing lower
profit levels
A Pareto Improvement
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point A in Textbook Figure 15.5 represents the union's optimal position if the union
and firm only negotiate the wage rate
point A is the tangency point between the labour demand curve and the
highest possible union indifference curve
o any point above and to the right of A would represents increased utility for
union members
the isoprofit curve passing through point A is also included in Figure 15.5; any point
below this isoprofit curve represents increased profits for the firm
suppose that the firm and union were to negotiate a contract which sets the
employment level as well as the wage rate
points along the isoprofit curve to the right of A (down to the second intersection of
the of union indifference curve and the isoprofit curve) represent a Pareto
improvement for the union; the union is better off (can reach a higher indifference
o
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curve) without making the firm worse off (profit levels remain constant along the
isoprofit curve)
similarly, all points along the union indifference curve to the right of A (down to the
second intersection of the of union indifference curve and the isoprofit curve)
represent a Pareto improvement for the firm; the firm is better off (on a lower isoprofit
curve and has higher profits) without making the union worse off (union utility levels
remain constant along the indifference curve)
all points inside the shaded elliptic area in Figure 15.5 (bounded by the union
indifference curve and the isoprofit curve passing through point A) represent a Pareto
improvement for both the firm and the union
o all points in this shaded area represent a higher union utility level (correspond
to higher indifference curves) and a higher level of firm profits (correspond to
lower isoprofit curves)
Pareto Optimal Points and the Efficient Contract Curve
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a Pareto optimal point occurs when one party can not be made better off without
making the other party worse off
when the union and firm negotiate both wage rates and employment levels, a Pareto
optimal point occurs where a union indifference curve is tangent to a firm isoprofit
curve
consider point A" in Figure 15.5, which is the tangency point of a union indifference
curve and a firm isoprofit curve; if the firm and the union move in any direction from
point A", one or both parties will be worse off
o if they move north of point A" (above the union indifference curve), the union
will be better off but the firm will be worse off (have lower profits)
o if they move south of point A" (below the isoprofit curve), the firm will be
better off but the union will be worse off (on a lower indifference curve)
o if they move northwest or southeast of point A" (between the union
indifference curve and the isoprofit curve), both parties will be worse off
point A", the tangency of a union indifference curve and an isoprofit curve, is a Pareto
optimal point; one party can not be made better off without making the other party
worse off
in Figure 15.5, the CC' line going through point A" and other tangency points between
indifference curves and isoprofit curves is called the contract curve, the locus of all
Pareto-efficient contracts
if the union attaches any weight to job security in its objective function, the union
indifference curves will be downward-sloping and the contract curve (the set of
tangencies between the indifference curves and the isoprofit curves) must lie to the
right of the labour demand curve where the firm's isoprofit curves are also downward
sloping
o the two parties have an incentive to negotiate a wage-employment
arrangement that appears wasteful (i.e., the firm appears to have hired too
much labour at the negotiated wage rate) but such 'featherbedding'
employment practices may be advantageous for both the employer and the
union
the efficient contract curve may be downward-sloping, vertical, or upward-sloping,
depending on the strength of the union's preference for job security
o higher wages that generally accompany unionization may not be associated
with reduced employment (if the union has a strong preference for job security
and union indifference curves are very steep)
unions and firms negotiating a Pareto-efficient contract which sets both the wage rate
and the employment level will bargain along the contract curve; depending on the
respective bargaining strength (power) of the firm and the union, the negotiated
wage, and employment level will lie somewhere on the contract curve
o
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the upper limit of the bargaining range is determined by the zero isoprofit
curve and the lower limit is determined by the alternative wage; moving down
the contract curve increases firm profits and decreases union utility
a powerful union may be able to negotiate a contract settlement further up the
contract curve than a relatively weak union (which may be forced to accept a
settlement on the lower end of the contract curve)
Obstacles to Reaching an Efficient Contract
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although in principle both the employer and the union can be made better off by
negotiating both wage and employment levels, in practice there are several obstacles
to reaching an efficient contract
to sign a Pareto-efficient contract, both parties must know each other's objective
function; without full information about each other's objective function it is difficult to
know whether a Pareto improvement is possible (whether you are on or off the
contract curve)
o in non-cooperative bargaining, each side typically tries to conceal (or
misrepresent) information about its objective function (for example, firms are
reluctant to open the books and reveal profit relationships to unions)
because demand may shift during the term of the agreement altering the contract
curve, the contract must stipulate the efficient levels of wages and employment for a
variety of different possible economic conditions; it is very difficult and expensive to
negotiate and enforce a 'contingent' agreement, which depends on different economic
conditions that may prevail
o one has to define all possible economic conditions in legally enforceable
language and for each possible economic condition the firm and union have to
negotiate a Pareto-efficient wage-employment contract
there is a need for costly monitoring because for any given contract the firm has an
incentive to reduce employment back to the labour demand curve, where profits are
maximized for a given wage rate; given the firm's incentive to cheat on employment
levels, the union must be able to enforce (in a court of law) the specified employment
level
o while it is easy to enforce the wage provisions in a contract (any employee can
use a pay stub as evidence of the wage paid by the employer), enforcing total
employment levels in a contract is more difficult (for example, do you adjust
for the number of hours worked per week)
the costs of negotiating, monitoring, and enforcing efficient 'contingent' contracts may
be too high to make the effort worthwhile
while it may not be possible to specify an exact employment level in a contract, unions
and firms may be able to approximate the employment level clause in a Paretoefficient contract by tying employment to the output of the firm or to the use of other
inputs
o unions often negotiate work rules which restrict the firm's flexibility in reducing
employment, say by specifying the minimum number of workers required for a
particular task (for example, the minimum number of pilots per aircraft and
the maximum class size for teachers); such restrictive employment practices
allow employment levels to change in response to shifts in demand but
constrain the employer to hire more workers than implied by the demand for
labour curve
o excess labour (workers watching other workers), restrictive work rules and
featherbedding practices are consistent with a Pareto-efficient contract
Empirical Applications
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empirical studies of union wage and employment determination face several
challenges:
o choosing an appropriate specification for union preferences
the presence of two alternative models of wage and employment
determination, the labour demand curve and efficient contract models, that
are plausible on a priori grounds
o the need for a theory of firm-union bargaining to predict the specific wageemployment outcome (which point on either the labour demand curve or on
the efficient contract curve) chosen by the parties
the earliest empirical studies assumed that observed wage-employment outcomes lie
on the labour demand curve and that the union is sufficiently powerful to achieve its
preferred outcome; another set of studies assumed that observed outcomes lie on the
efficient contract curve; recently scholars have begun the difficult task of incorporating
bargaining theory into the empirical analysis of wage and employment determination
o while several studies have attempted to test between the 'labour demand
curve' and 'efficient contracts' models using contract-level data for specific
unions and groups of firms, there is not a consensus on which model performs
best
studies of several unions and industries based on the labour demand curve model
generally agree on a number of findings:
o employment and wages are both important to unions
o union preferences display a diminishing marginal rate of substitution between
wages and employment
o union preferences are sensitive to the alternative wage
o unions generally place more weight on employment than wages
o
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Theory of Bargaining
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bargaining theory seeks to predict the outcome in any given bargaining situation and
explain what factors this outcome depends on
in any bargaining situation there are incentives for both cooperation and conflict
o the incentives for cooperation arise because of 'gains from trade;' there is a
set of feasible outcomes that make both parties better off than if no
agreement is reached
o the incentives for conflict arise because once all the mutually advantageous
trades have been made, actions that make one party better off make the other
party worse off
theories of the bargaining process not only predict the outcome but also model the
process by which the outcome is reached
o theories of the bargaining outcome specify a number of properties or axioms
that the solution should obey
two principal solutions to the bargaining problem have been proposed by Nash and
Rubinstein
Nash's Bargaining Theory
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Nash's bargaining theory, for which he won the Nobel prize in economics, specified
four axioms (Pareto-efficiency, symmetry, transformation invariance, and
independence of irrelevant alternatives) the bargaining solution should obey
together these four properties imply a unique solution to any bargaining situation: the
outcome that maximizes the product of the two parties' utility increments from the
disagreement point (the utility of each party if no agreement is reached)
o as illustrated in Figure 15.7 on page 455, the Nash solution (point N) has the
maximum rectangular area (NfNdUN) in the set of feasible outcomes
Nash's solution to the bargaining problem is widely used in theoretical and empirical
work, and has been tested in laboratory experiments
the life of John Nash has recently been depicted in the movie 'A Beautiful Mind'
Rubinstein's Bargaining Theory
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Rubinstein's solution to the bargaining problem uses non-cooperative bargaining
theory, and assumes a process of alternating offers that the receiving party can either
accept or reject
given that there are costs of delay, the size of the 'pie' to be shared by the two parties
shrinks the longer it takes to reach agreement (see Textbook Figure 15.8)
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even though under full information the two parties would never delay reaching an
agreement, the relative magnitudes of the delay costs facing each negotiator influence
the Rubinstein outcome
o if the union's disagreement costs are less than the firm's, the Rubinstein
outcome is more favourable to the union and less favourable to the firm (see
Figure 15.8(b))
in collective bargaining this implies that the relative costs of a work stoppage (strike or
lockout) influence the negotiated outcome even though a strike or lockout may not
occur
Union Bargaining Power
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two possible meanings of the term 'union bargaining power' are implied by the
analysis in this chapter and are illustrated in Textbook Figure 15.9
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one meaning is related to the elasticity of the labour demand curve and is associated
with the willingness to raise wages
o a union facing an inelastic demand for labour can raise wages substantially
with only minor adverse employment consequences
a second meaning is associated with the ability to raise wages; a powerful union is one
that can obtain a negotiated outcome close to its most preferred outcome
o this aspect of union power depends not on the elasticity of labour demand but
principally on the relative costs of disagreement to each party
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Union Power and Labour Supply
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most unions attempt to improve the wages and working conditions of their members
directly by bargaining with the employer
however, craft unions and professional associations can raise wages and improve
working conditions indirectly by controlling labour supply
mechanisms for restricting labour supply include limiting entry through:
o an apprenticeship program in craft unions
o a closed shop: the worker has to be a member of the union before being hired
(the union controls the hiring hall)
o
o
certification: only those who have been certified have the right to use the
professional designation or title (such as 'Chartered' accountant); others can
practise in the profession but cannot use the professional title
occupational licensing: only those with a licence can practise in the profession
and licences are controlled by the profession (doctors and lawyers)