Transcript Trade unions - Politica Economica Lehmann

Topics in Economic Policy:
Topic 3: Trade Unions
Introduction
•
•
Trade unions are organisations whose aim is to
increase the welfare of their members. They bargain
with employers over wages and employment conditions.
We normally assume that trade unions are able to
negotiate wages that are above the competitive level. In
this introduction we briefly discuss four topics:
1. When is there a surplus that can be divided between
workers and employers?
2. What gives a trade union bargaining power?
3. Orthodox view of the effect of trade unions on
allocative, technical efficiency and on equity.
4. Alternative view of the efficiency enhancing role of trade
unions.
When is there a surplus that can be divided
between workers and employers?
• Trade unions can only bargain, if there is something to
bargain over. So, there must exist a surplus, or there
must exist some “supernormal” profits.
• In the case of imperfectly competitive product markets,
supernormal profits can exist in the short as well as in
the long run. Unfortunately, the literature dealing with
trade unions seldom embeds the analysis into
imperfectly compatible product markets. Most of the
literature assumes competitive product markets.
• In the case of competitive product markets, we can only
have a surplus, or supernormal profits in the short run,
when entry into the industry is limited. In the long run,
entry will erode all supernormal profits.
• So, let’s look at profits in a competitive industry:
Profits in competitive industry
At the competitive wage, wc, profits are
π = pּq(n) – wcּn
Some parts of these profits a trade union can appropriate for its workers
by raising the wage above wc. The maximum wage the trade union can
~ of the trade union will appropriate all profits.
~ . In the case, w
ask is w
What gives a trade union
bargaining power?
• The main lever that gives bargaining power to
trade unions is the threat of a strike.
• This threat of a strike can only work if the trade
union has some control over the labour supply
and if labour demand is not too elastic.
• For, if the trade union does not control the
labour supply employers can easily substitute
union-labour with non-union labour. If, on the
other hand, labour demand is very elastic
employers can probably substitute labour with
other factors of production easily.
Trade union bargaining power, cont.
• Controlling labour supply
• Trade unions are either craft unions or industrial unions.
• Craft unions are controlling and have historically controlled the
labour supply by restricting entry to the craft through an
apprenticeship system or through limited entry to schooling. For
example, the British Medical Association controls entry into the
profession rigorously.
• Industrial unions are, however, more important in modern
economies. Here, the union can only control labour supply if
“union density” is high. Union density is the fraction of workers in
an industry who are members in the trade union. Clearly, if their
fraction is very high, employers cannot easily find a substitute for
union labour.
• What gives established unions also bargaining power is large
“union coverage” of wage agreements. Union coverage refers to
wage agreements that cover workers in the industry who are not
members of the union. Clearly, these workers will not want to be
used as a substitute for union-labour if they benefit from
settlements negotiated by a trade union.
Trade union bargaining power,
cont.
•
•
•
Elasticity of labour demand
The more inelastic labour demand in an
industry the more bargaining power a union
has.
From Marshall’s rules of derived demand (see
lectures on labour demand) we know that the
demand for labour is more elastic, the
a) more elastic is product demand;
b) higher the elasticity of substitution between labour
and other factors of production;
c) larger the share of labour costs in total costs;
d) more elastic is the supply of other factors of
production.
Trade union bargaining power,
cont.
• A trade union can have little impact on
determinants a, c and d. It, however, can
influence determinant b.
• The bargaining process can include manning
requirements in the production process. An
extreme outcome of negotiations over manning
requirements could be a fixed relationship
between machinery (capital) and the number of
workers, giving us a Leontieff-type of production
technology and the following types of isoquants:
Trade union bargaining power,
cont.
The point here is that an already powerful union
that can push through requirements becomes even
more powerful in the bargaining process.
Orthodox view of the effect of trade unions on
allocative, technical efficiency and on
equity.
• First we look at allocative efficiency and at equity using a
simple two-sector model:
Orthodox view, cont.
• In a competitive 2-sector economy in the absence of trade
unions we get an equilibrium where the two value of
marginal product of labour curves intersect resulting in one
economy wide wage, wc.
• Besides the wage, the intersection also determines how
many of workers in the economy will work in sector 1 and in
sector 2. At any rate n = n1 + n2.
• Note: there is perfect labour mobility in this economy.
• Assume now that sector 1 (relatively inelastic labour
demand) becomes unionised. The union can raise the wage
in this sector to w1. Firms in the unionised sector will hire up
to n1′ workers, those workers who previously worked in
sector 1 but are now laid off (n1 – n1′) will migrate to sector
2. Because of the larger supply of workers in sector 2 the
wage will fall to w2 = VMPL of the n2′-th worker.
Orthodox view, cont.
• So, in this model non-unionised workers loose out
from the unionisation in sector one, as their wage is
now less than before (w2 < wc).
• There are two important concepts in connection with
the unionisation in sector 1.
– Wage gain: The difference between the union wage and
the wage that would prevail if trade unions were absent in
the economy, i.e. the competitive wage. The wage gain is
here w1 - wc.
– Wage gap: The difference between the union wage and
the non-union wage. Here the wage gap is w1 – w2.
• The outcome n = n1′ + n2′ is allocatively inefficient.
Too few workers are employed in sector 1 and too
many are employed in sector 2. There is a deadweight-loss to the economy equal to the triangle
CAB.
Orthodox view, cont.
• Looking at equity issues: The distribution of
factor income
Before unionisation
income to labour is
the sum of two
rectangles:
wcABO1 + AwcO2B.
•After unionisation
income to labour is
the sum of two
different rectangles:
w1EGO1 + Fw2O2G.
Before unionisation income to capital After unionisation income to capital is
is the sum of two triangles:
the sum of two different triangles:
CAwc + ADwc.
CEw1 + FDw2.
Orthodox view, cont.
• If (w1EGO1 + Fw2O2G) > (wcABO1 + AwcO2B) labour will
have gained in absolute terms through unionisation in
sector 1 (despite possible loss in sector 2). The picture
does not seem to confirm the above inequality. Because the
union sector is relatively small in this economy, labour as a
whole is worse off than before unionisation.
• If (CEw1 + FDw2) > (CAwc + ADwc) capital will have gained
in absolute terms through unionisation of sector 1 (despite
losing in sector 1, the loss would be more than
compensated by gains in sector 2). From the picture it is not
entirely clear whether capital has gained or not.
• Because of the occurring dead weight loss it is, of course,
possible that both labour and capital loose through
unionisation.
• Thus far we have looked at efficiency and equity issues in
the short-run, i.e. with capital fixed. In the longer run, when
capital is variable, we can also get distortive effects in the
allocation of factors of production.
Distortive effects in partial
equilibrium model
• We can think
of point A as
an efficient
point of
allocation of
capital and
labour. At
point A the
isoquant q1 is
tangent to
isocost curve
1 with slope

wc
price of labour

r
price of capital
As the price of labour rises through unionisation from wc to w1, isocost
curve 2 becomes relevant for the firm. The new equilibrium occurs at
point B where isocost curve 2, which has a slope  w 1 , is tangent to
r
isoquant q2. Note that q2 < q1!
Distortive effects in partial
equilibrium model, cont.
• Both labour and capital are used less here than before
unionisation. The under use of capital occurs because
the scale effect is greater than the substitution effect
here. At any rate we have an underutilization of factors
of production in this sector compared to the situation
before unionisation (point A).
• Because of unionisation there can also be technical
inefficiencies. We can think of static technical inefficiency
as a loss of output.
• Manning agreements and the establishment of workpace rules brought about by the unions can be thought
of as a fixed capital-labour ratio and as a fixed level of
effort respectively.
• Both will cause a fall in output relative to a non-union
situation, i.e. cause a fall in technical efficiency.
Orthodox theory, cont.
• We can think of dynamic technical efficiency as pushing the
production possibilities curve of an economy outward over time.
• The orthodox theory would say that unionisation can increase
dynamic technical efficiency. As union wages are higher than
competitive ones firms will substitute capital for labour, i.e.
increase investment, pushing the production possibilities curve
outward, i.e. increase dynamic technical efficiency.
• A counter position to this orthodox view starts out with the
important result from a competitive firm that it will continue
producing as long as price is above average variable cost. The
difference between price and average variable cost is termed
“quasi-rents” on fixed capital.
• If a firm invests and has some quasi-rents on the invested
capital the union might want to appropriate part of these quasirents. The firm knowing this ex-ante might decide not to invest
at all; so in this scenario unionisation might lead to underinvestment, i.e. to a decrease in dynamic technical
efficiency.
Alternative view of the efficiency
enhancing role of trade unions
• This role can be seen from many points of view. Here we
look at just three.
a) Transaction costs; the workplace is a very complex
arena whose many details about pay, working
conditions, promotion procedures etc. have to be
negotiated over. For individual workers it would be far
too costly to negotiate with firms individually about all
these matters, and it is much more efficient to have an
agent who does negotiate on workers’ behalf.
b) Raising productivity (union’s “voice”); a complex
workplace also means that management does not
necessarily know what is going on at the shop floor.
Management does not necessarily know the sources of
dissatisfaction of workers and how the situation can be
improved.
Alternative view of the efficiency
enhancing role of trade unions, cont.
Given the imperfect nature of informational flows between
management and workers, workers might react with
“exit” or they might use “voice” to address the
problems they encounter according to their perception.
If they leave the firm (“exit”) management will never
find out what’s wrong at the shop floor level.
If, on the other hand, workers organise and their agent
(union) discusses workers’ problems with
management, workers’ satisfaction might be increased
and production processes might also be improved, i.e.
productivity might be raised.
The rise in productivity thanks to the union’s “voice” might
be so large that even a higher union wage does not
reduce employment:
Alternative view of the efficiency
enhancing role of trade unions, cont.
VMPL1 =
value of
marginal
product of
labour curve
in absence of
trade union.
VMPL2 =
value of
marginal
product of
labour curve
with a trade
union.
Alternative view of the efficiency
enhancing role of trade unions, cont.
c) Enforceability of state-contingent contracts in an uncertain
world
• It is often difficult to know what the state of the world will be
after wage negotiations have taken place.
• Individual workers would find it difficult to enforce contracts
that have been written ex ante and that are contingent on
the state of the world.
• For example, with low demand for the products of the firm
revealed after wage negotiations it might be impossible for
individual workers to press for the negotiated wages (that
are contingent on low demand).
• A union, which has the powerful tool of strike threat, might
be more capable to keep firms in line and to ensure that ex
ante agreements are kept. In an uncertain world this
smoothes workers’ income but also production thus
increasing the efficiency of the economy in the medium and
long term.
Preferences of a trade union
• Two types of utility functions are often used to
model the preferences of a trade union:
1. General quasi-concave utility function;
such a function takes usually a specific form, e.g.
the Stone-Geary utility function.
U  w    n    (1)
 and δ are “minimum” or “reference” levels of wages
and employment,
w = wage,
n = number of employed in industry,
θ = parameter for the weight given to aboveminimum-wages relative to employment.

1
Preferences of a trade union, cont.
• Advantages of (1): known from Consumer Theory
and easy to handle econometrically; also, it gives a
sense of the relative importance of wages and
employment in the preferences of the trade union;
finally (1) nests some special cases: 1
1
– a) If   and     0 , then U  (n  w) 2 , which is
2
“wage bill utility function.”
1
1


– b) If
2 , δ=0,  = wc = competitive wage, then U  n(w  wc),2
which is “rent utility function.”
• Problem with (1): the Stone-Geary utility function is
not derived from conventional axioms about
workers’ preferences (e.g. risk averse workers
never maximise a Stone-Geary utility function).
Preferences of a trade union: Expected
utility function or utilitarian function
Expected utility function:
n
mn
U  u w 
u b 
(2)
m
m
where u(∙) = concave utility function of an individual worker;
i.e. u′(w) > 0, u″(w) < 0;
m = number of members in a trade union (for simplicity, for the
moment we assume all workers are unionized);
n = number of employed;
b = level of unemployment benefit or of alternative wage;
n = probability of union member of being employed;
m
m  n = probability of union member of being unemployed.
m The expected utility function maximises the expected utility of
one union member; note that the probabilities are entirely
random, i.e. each member faces a random draw to get
either n or m  n .
m
m
Preferences of a trade union, cont.
Utilitarian function
If m is fixed, then (2) can be multiplied through by m:
m∙U = n u(w) + (m – n) u(b)
or
U = n u(w) + (m – n) u(b)
(3)
where U = m∙U
The utilitarian function maximises the sum of
utilities of union members. So the union treats
people identically and cares about sum of utilities.
(This function is called utilitarian because the
philosophy of utilitarianism by Jeremy Bentham
stated that society’s welfare is maximised when the
sum of individual utilities is maximised!)
Preferences of a trade union, cont.
• Advantages of expected utility or utilitarian
function:
• Individual preferences and size of membership are
explicitly modelled. So it is possible to get a
change in the union’s preferences as members
become more risk averse or as membership size
changes.
• Also, econometric estimation is easy and nesting is
given as well.
• There are some generalisations of the expected
utility or utilitarian function dealing with the issue of
homogeneity of union members. “Seniority” and
“median voter” models of trade union preferences
are touched upon below.
Wage and employment determination
under the trade union monopoly model
• There is one union facing many small firms. The union
can control entry into the profession and/or wage rate. In
this model the union sets unilaterally the wage and firms
then set unilaterally employment.
• Firm’s decision problem: Maximisation of profits given
the wage dictated by the trade union.
Max   pf (n)  wn
n
• So firm chooses n given the wage w in order to
maximise profits.
• p = exogenous price of output,
• f(n) = concave production function,
• w = wage, and n = employment.
Wage and employment determination under
the trade union monopoly model, cont.
• Graph of concave production function:
• Note: capital is fixed here, so we are in the short
run!
Wage and employment determination under
the trade union monopoly model, cont.
Profits are maximised by taking the derivation of the profit
function with respect to n and setting that expression equal
to zero:
(4)
d
 p f' (n) - w  0
dn
p f′(n) = w
or VMPL = w
(4′)
(4′) is labour demand, which we can also write as n as a
function of p and w:
n(w, p).
To find the slope of the labour demand curve we totally
differentiate (4) and solve for :
p f″(n) dn + (-1) dw = 0
dn
1

0
dw pf ' ' (n)
, which can write also as nw(w, p) < 0
Wage and employment determination under
the trade union monopoly model, cont.
• So, the labour demand curve is downward-sloping, i.e.
there is a trade-off between wages and employment,
when w , n . Also note, that labour demand is
downward sloping because of the well behaved concave
production function, which gives f″(n) < 0.
• Now, the union will take the trade-off of waged and
employment into account when it sets the wage, which
maximises the union’s utility:
• Union’s decision problem, using utilitarian form of utility
function:
(5)
Max U  u(w)·n(w, p)  [m - n(w, p)] u(b)
w
• Doing this maximisation is equivalent to finding the
highest indifference curve of the union, which is tangent
to the labour demand curve.
Wage and employment determination under
the trade union monopoly model, cont.
• IC2 cannot be reached given the location of the labour
demand, but IC1 can be reached. Equilibrium occurs at
point A, where IC1 is tangent to the labour demand curve
giving wu and nu.
Wage and employment determination under
the trade union monopoly model, cont.
• Assuming an interior solution, we get the following first-order
condition (F.O.C):
dU
 U w  u' (w) n(w, p)  u(w) nw(w, p) - u (b) nw(w, p)  0
dw
{ recall that = nw (w, p) }
or Uw = u′(w) n(w,p) + [u(w) – u(b)] nw(w, p) = 0 (F.O.C) (6′)
Let’s look at the two terms in (6′):
The first term, u′(w)∙n(w, p), gives the additional utility going to all
employed union members when the wage is raised. This is the
total marginal benefit accruing to the union when wages are
raised.
The second term, [u(w) – u(b)] nw(w, p), has to be negative for (6′)
to be equal to zero. Note that nw(w, p) is negative (when the wage
rises employment falls); nw(w, p) gives us the number of workers
laid off for a unit rise in the wage; [u(w) – u(b)] has to be positive
for the whole second term to be negative.
Wage and employment determination under
the trade union monopoly model, cont.
• What is u(w) – u(b)? It is the difference in utility
between an employed and unemployed member of
the union. Any laid-off worker bears the cost of this
utility difference when s/he becomes unemployed.
• [u(w) – u(b)] nw(w, p) is therefore the total loss in
utility brought about by a rise in the wage. It is total
marginal cost borne by the union when wages are
raised. In equilibrium total marginal benefit = total
marginal cost.
Wage and employment determination under
the trade union monopoly model, cont.
Some important results coming from the monopoly
union model:
1. b  will w 
•
Proof:
•
dw
So db
•
(comparative static 1)
d
(U w )  U wb  - u' (b)·n w (w, p)  0
db
 
- 
>0
When unemployment benefits rise, we get a new equilibrium
with a higher wage. This result is intuitive; when b goes up
unemployment becomes less costly, so the trade union will
push for a higher wage.
2. p no effect on desired wage w (comparative static 2),
as long as the elasticity of labour demand is constant.
Wage and employment determination under
the trade union monopoly model, cont.
3. A change in the membership does not affect the wage
(comparative static 3)
dw
Proof: m does not appear in F.O.C.  Uwm = 0, i.e. dm = 0
This comparative static is a particularly unpopular prediction of the
model.
4. The wage is higher and employment is lower at the
“monopoly union equilibrium” than at the competitive
equilibrium.
Proof: competitive equilibrium we have
p f′(n) = b = wc
By F.O.C. [u(w) – u(b)] > 0
u(w) > u(b) w > b = wc w > wc
Then compare p f′(nc) = wc
to
p f′(n) = w
Since wc < w f′(nc) < f′(n)
By concavity of production function this then implies that nc > n.
Wage and employment determination under
the trade union monopoly model, cont.
Relationship between “monopoly union model” and “right-tomanage models” is quite close. In the latter models the wage
is not set by the union but bargained over; given the
bargained wage the firm then sets unilaterally the
employment level (firm has “right-to-manage” employment).
The predictions of the “right-to-manage” models are quite
similar to those of the union monopoly model.
Efficient bargaining models
• Remember that:
– If f(n) is a well-behaved concave short-run production function (i.e.
f′(n) > 0 and f″(n) < 0 ); p is exogenous price; w wage and n
employment.
 Profits are π = p f(n) – wn
(7)
If firm is a profit maximiser it is indifferent between combinations of w
and n that leave p f(n) – wn constant. The locus of all combinations of
w and n that keep profits the same is called an isoprofit curve.
The labour
demand curve
is locus of all
points where
for each wage
the slope of
the isoprofit
curves is zero.
Efficient bargaining models, cont.
• Revisiting the union monopoly model:
•At point A the union’s indifference
curve IC1 is tangent to the labour
demand curve, nd → not Pareto
optimal.
•For example, we can move from
point A to point B. This move will
increase the utility of the union (will
make the unions better off) and will
give the firm the same profits like at
A (will not make the firm worse off).
We could also move from point A to point C. This move will increase the profits of the
firm (will make the firm better off) and will keep the union’s utility at the same level
like at A (will not make the union worse off). Any move from A to a point in the shaded
area (excluding points B and C) will make both union and firm better off.
Points B and C are Pareto optimal since if we moved from these points we would
make either the union or the firm or both worse off.
Efficient bargaining models, cont.
• When unions bargain over both wages and employment,
efficient outcomes occur, where isoprofit curves are tangent
to the union’s indifference curves. As long as the union’s
indifference curves have a negative slope throughout, as
shown in the graph below, the efficient outcomes are to the
right of the labour demand curve.
Efficient bargaining models, cont.
•
The locus of all tangency points of isoprofit curves and
indifference curves is the set of efficient, Pareto optimal
outcomes. This locus is called the contract curve (CC).
Note two important points about the way the contract curve
is drawn:
1. it coincides with the labour demand curve only at
one point, namely at the competitive wage and
employment level (wc, nc);
2. the contract curve has a positive slope.
•
•
Points 1) and 2) together  employment levels on the
contract curve CC are greater or equal to the competitive
employment level nc. So, efficient bargaining models
generate over-employment (i.e. more than full employment,
which we have defined as nc).
We now need to derive the contract curve mathematically in
order to really prove points 1) and 2).
Efficient bargaining models, cont.
•
To get a mathematical expression for the contract curve we
set the slopes of the union’s indifference curve and of the
isoprofit curve equal to each other.
π = p f(n) – w n
isoprofit curve
U = u(w)∙n + (m – n)∙u(b)
indifference curve
Recall slope of π:
Slope of U: =
dw pf ' (n)  w

dn
n
dw u ( w)  u (b)

dn
u ' ( w)  n
Setting the two slopes equal to each other:

u ( w)  u (b)
 pf ' (n)  w
u ' ( w)
(9)
The slope of the indifference curve is definitely negative, since
u(w) – u(b) > 0 and also u′(w) > 0  efficient equilibrium
occurs where the slope of the isoprofit curve is negative. So,
efficient outcomes are here to the right of the labour
demand curve, where VMPL < w !
Efficient bargaining models, cont.
•
Multiplying (9) through by (-1) gives then the equation of the
contract curve
u ( w)  u (b)
(10)
 w - p f' (n)
u ' ( w)
Note that the r.h.s. of (10) becomes zero on the labour demand
curve (w = p f′(n) on the labour demand curve). The l.h.s. of
(10) becomes only zero when w = b = wc.
• The contract curve intersects the labour demand curve at
the competitive equilibrium. This proves point 1)!
• To show that the slope of the contract curve is positive, we
first multiply (10) through by u′(w):
u(w) – u(b) = [w – p f′(n) ] u′(w)
(10′)
• Then, we totally differentiate (10′) with respect to w and n:
u′(w)dw = 1∙u′(w)dw+[w – p f′(n) ] u″(w) dw + [– p f″(n) u′(w)] dn
 [(w – p f′(n)) u″(w)] dw = [p f″(n) u′(w)] dn
Efficient bargaining models, cont.
 
 
dw
pf ' ' (n) u ' ( w)

0
dn [ w  pf ' (n)] u ' ' ( w)
 
•
•
•
 
This proves that given a well behaved production function and a
well balanced utility function, the contract curve has a positive
slope (establishing point 2).
To get a unique equilibrium in the wage-employment plane with
efficient bargaining models, we need an additional curve, since
the contract curve gives us an infinite number of efficient
bargaining outcomes. McDonald and Solow in their paper
introduce an “equity locus.” The trade union considers it equitable
if it receives a fair share (proportion) of total revenues, so the
wage bill should be a certain fraction of total revenues:
w n = k p f(n)
0<k<1
w
k p f(n)
n
(11)
(11) is the equation for the equity locus; it is downward sloping, when
n , w .
Efficient bargaining models, cont.
•
In the graph below point A gives a unique equilibrium, with
both the wage and employment larger than the competitive
levels (wc, nc). So equilibrium occurs to the right of the
labour demand curve.
Efficient bargaining models, cont.
Efficient unique equilibrium at A (we, ne).
•
Three important problems with this type of efficient bargaining models:
1.
We have overemployment in a world of unemployment. This is the
most serious problem.
2.
Empirical evidence seems to point to the fact that firms unilaterally
determine employment.
3.
Firms have an incentive to renege on the bargained deal and jump at
the bargained wage to the demand curve:
Efficient bargaining models, cont.
•
•
•
It would increase profits if a firm jumped at w1 back to the
labour demand curve as π2 > π1. If the firm does this, it
could destroy its reputation as a reliable employer, that’s
why firms might refrain from this kind of cheating.
The advantages of the efficient bargaining model is that
unions do bargain over wages and that we have a Pareto
optimal outcome, something economists like very much.
One way to get an efficient bargaining outcome without
overemployment is to get an efficient outcome on the labour
demand curve.
We can get such an outcome if we model the union’s
preferences differently.
Let’s look at the utilitarian function of the union’s utility function:
U = n u(w) + (m – n) u (b)
(3)
Efficient bargaining models, cont.
•
•
•
•
Add m u(w) and subtract m u(w) from eq. (3):
U = m u(w) – m u(w) + n u(w) + (m – n)u(b)
U = m u(w) + [u(b) – u(w)] (m – n)
(3′) has 2 components, m∙u(w), which is the total benefit the
union get from wage w, and term [u(b) – u(w)] (m – n),
which is the cost of not having employment for unemployed
members of union. It is negative as long as m > n, i.e. as
long as some union members are unemployed. So, given
this utility function we see two things:
1) The union cares about employment, the smaller m–n, i.e.
the larger n, the better off is the union.
2) There is a trade-off between the wage and employment; the
higher w, the lower n and the larger m–n, i.e. the larger the
cost of a high wage.
Efficient bargaining models, cont.
•
If not all workers were unionized, and all unionized workers
were employed, we could have m < n.
• i.e. this specification would not make any sense, as m–n
would become negative and the whole second term
positive. Now, cost of unemployment appears as a benefit
to the union.  It makes more sense to have a specification
that whenever n ≥ m there is no trade-off between the wage
and employment and the union cares only about wages.
U = m u(w) + [u(b) – u(w)] max[0, m–n]
When m–n > 0, we keep the second term and we have a tradeoff, i.e. indifference curve is downward sloping.
When m–n < 0, the second term drops out and the indifference
curve becomes horizontal for n > m:
Efficient bargaining models, cont.
Since n1 > m, the
union does not care
about employment (it
does not care for
example
about
outsiders’
employment) and we
have
an
efficient
outcome on the labour
demand curve at
(w1, n1).
Efficient bargaining models, cont.
•
In the real world, there are some union members who are laid-off.
So, a more realistic scenario is one where we have non-random
lay-offs. For example, in many countries we have the “last-in-firstout” principle (LIFO principle). With this principle the median
seniority member (median voter model) will never be affected by
layoffs and if the median voter makes the decisions in the trade
union, the union’s indifference curves will have a zero slope
beyond ns in the following graph:
•
Efficient bargains on the labour demand curve
ns = employment up to
median seniority
member of trade union.