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Monopsony and the Efficiency of Labour Market Interventions

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Implicit in many discussions of labour market policy is the assumption that, in the absence of interventions, the operation of the labour market is well-approximated by the perfectly competitive model. The merits or demerits of particular policies is then seen as a trade-off between efficiency and equality. This paper analyses the impact of a variety of policies – the minimum wage, trade unions, unemployment insurance, progressive income taxation and restrictions on labour contracts – on efficiency when labour markets in the absence of intervention are monopsonistic and not perfectly competitive. A simple version of the Burdett and Mortensen (1998) model is used for this purpose.
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Abstract

Implicit in many discussions of labour market policy is the assumption that, in the absence of
interventions, the operation of the labour market is well-approximated by the perfectly competitive
model. The merits or demerits of particular policies is then seen as a trade-off between efficiency and
equality. This paper analyses the impact of a variety of policies – the minimum wage, trade unions,
unemployment insurance, progressive income taxation and restrictions on labour contracts – on
efficiency when labour markets in the absence of intervention are monopsonistic and not perfectly
competitive. A simple version of the Burdett and Mortensen (1998) model is used for this purpose.

JEL classification: J0
Key words: Labour market policy, Monopsony











Acknowledgements

I would like to thank seminar participants at the University of Essex and the MacArthur Foundation Network on the
Effects of Inequality on Economic Performance for their comments.

Alan Manning is director of the Labour Markets programme at the Centre for Economic Performance, London School
of Economics and Professor of Economics in the Department of Economics, LSE.











Published by
Centre for Economic Performance
London School of Economics and Political Science
Houghton Stre et
London WC2A 2AE

© Alan Manning, submitted August 2001

ISBN 0 7530 1543 9

Individual copy price: £5

Monopsony and the Efficiency
of Labour Market Interventions

Alan Manning






Introduction
1


1.
Monopsony in the Labour Market
2


2.
The Free Market Equilibrium
6


3.
The Minimum Wage and Trade Unions
8

4.
Unemployment Benefits
9


5.
Progressive Income Taxation
11


6.
Restrictions on Labour Contracts
12


7.
Conclusions
16


Figures
17

Appendix
19
References
24









The Centre for Economic Performance is financed by the Economic and Social Research



Introduction

Debates about the desirability and consequences of labour market interventions continue to be at the
heart of many policy debates about the way in which modern industrialised economies should be run.
The most prevalent opinion among economists is that, in the absence of interventions, the operation of
labour markets is well approximated by the perfectly competitive model. This view, when combined
with the fundamental theorems of welfare economics, results in a presumption of efficiency in the free
market unless proved otherwise and an innate suspicion of interventionist policies. To be sure, there are
many individual papers that identify reasons why the free market may not be efficient but these papers
tend to be issue-specific and there is no single unifying model to rival that of the perfectly competitive
model which continues to have a powerful hold over the minds of economists. As a result, debate about
the merits of intervention is often put in terms of a trade-off between efficiency and equality with those
economists favouring a more interventionist approach tending to be those who have a welfare function
that puts greater weight on equality and/or those who believe the efficiency cost of equality is relatively
low.
Empirical research helps to provide evidence on the impact of interventions that informs
economists’ views about the relevant trade-offs, but empirical research finds it hard to say much about
efficiency issues and the presumption that interventions reduce efficiency dominates (explicitly or
implicitly) much thinking. In Samuelsons dictum “in economics, it takes a theory to kill a theory; facts
can only dent a theorists hide” and that view motivates this paper.
It tries (perhaps over-ambitiously) to provide a rival to the perfectly competitive model as a tool
to analyse the efficiency of labour market interventions. It sets up a simple, theoretical, imperfectly
competitive model of the labour market (based on the wage-posting model of Burdett and Mortensen,
1998) and uses that model to address a whole range of labour market interventions, namely:

minimum wages

policies to encourage trade unions

unemployment insurance to support those whose labour market earnings are low or non-existent

progressive tax systems

policies like restrictions on hours or health and safety legislation to limit the form of contracts that
can be signed between employers and workers.
The theoretical model assumes that ‘free’ labour markets are better thought of as monopsonistic
1

rather than perfectly competitive. As many (if not most) labour economists are sceptical about the
relevance of monopsony, some justification for this assumption is needed. Manning (2001) provides a
lengthy and detailed argument but the basic argument can be summarised very briefly: the perfectly
competitive model makes the unbelievable assumption that a wage cut of a cent immediately causes all
workers to leave the firm. However, there are good reasons to believe that labour markets have
substantial frictions as it is costly for workers to change jobs and employers to find workers. These
frictions mean there are generally rents in the employment relationship and that cutting the wage will not
lead to an immediate quit giving employers some monopsony power.
The paper shows that, in monopsonistic labour markets, one can prove surprisingly strong
results about the beneficial efficiency effects at the margin of most (though not all) of the labour market
interventions listed above. This should not be taken to imply that these policies are always good, just
that they are not always bad. The presumption of economists should be that these policies are desirable
and the debate about the appropriate level of intervention.
The plan of the paper is follows. The next section outlines the basic model of a monopsonistic
labour market that we will use in the theoretical part of the paper. It is a simplified version of a model
by Burdett and Mortensen (1998). We then use this model to analyse the impact of a number of typical
social democratic interventions: the minimum wage, trade unions, welfare benefits, progressive income
taxation and restrictions on the legal form of labour contracts. We show that ones view of these policies
is always more positive if one starts from a monopsonistic perspective though this should not be taken to
mean that these policies are always good, just that one should not have the instinctive reaction that they
are automatically bad.


1.
Monopsony in the Labour Market

If there are rents from frictions, one needs to have some view of the way in which they are divided. The
wage-posting model of Burdett and Mortensen (1998) assumes that employers set wages and the
model of this paper is based on theirs.1

1 Perhaps the most common alternative model used is ex post bargaining between worker and employer (e.g.
Pissarides, 1990 or Burdett and Mortensen, 1998, for a comparison). In many situations, the bargaining and
wage-posting models have the same predictions but there are cases (see below) where there are important
differences. For low-wage labour markets, wage-posting seems a more appropriate as sumption: e.g. Machin and
2


We will start with the case where the number of workers and employers are fixed and in which
the wage offer distribution is exogenously fixed. The basic assumptions are:
(A1) Workers: There are Mw workers all of whom are equally productive and attach equal
value, b, to leisure. They seek the job with the highest wage.
(A2) Employers : There are Mf employers, each of which is assumed to be infinitesimally small
in relation to the market as a whole. All employers have constant returns to scale, the productivity of
each worker being p. For future use, denote the ratio of firms to workers by M=Mf/Mw.
(A3) Matching Technology: Both employed and unemployed workers receive job offers at a
rate ?(M) where ?’(M)>0 and ?
<1. Job offers are drawn at random from the set of firms.
M
?
Employed workers leave their jobs for unemployment at an exogenous job destruction rate du. All
workers, both employed and unemployed, leave the labour market at a rate dr, to be replaced by an
equal number of workers who initially enter unemployment. Define d=du+dr.
(A4) Wages: For reasons that are explained in more detail in Burdett and Mortensen (1998),
(and will be briefly discussed later) the equilibrium will have a wage distribution. Denote the cumulative
density function of wages across employers by F(w) and the associated density function by f(w). For
future use, denote the inverse of F(w) by w(F). For the moment, treat this as exogenous though the
bulk of the paper will be about how different interventions affect the wage offer distribution. In some of
what follows, taxes will drive a wedge between the wage paid by employers and that received by
workers: so denote by wc(F) the consumer wage received by workers in an employer at position F in
the wage distribution.
These assumptions have been chosen to be the simplest possible whilst retaining the essential
features of a monopsonistic labour market in which a higher wage reduces the separation rate and raises
the recruitment rate. The following Proposition provides some useful preliminary results.

Proposition 1
In the labour market with fixed numbers of workers and employers:
1.
Employment in the firm at position F in the wage distribution is given by:
??(M)

N(F) =

(1)
2
M[ ? + (M)(1-F)
?
]

Manning (1997) found that one-third of UK residential care homes chose to pay all their care assistants exactly
the same hourly wage, an outcome that would be hard to explain in terms of ex post bargaining.
3



2.
The employment rate, n, in the economy is given by:
?(M)

n =

(2)
? + ?(M)
3.
The expected level of profits, E(? ) , is given by:
?[ p ? E(w)]

E(? ) =

(3)
M (? + ?)

where E(w) is the expected wage paid by employers.
4.
The value of being unemployed, Vu, is given by:
? E w ? b
u
[ (
)
]

c
? V = b +

(4)
r
? + ?
where E(wc) is the expected wage received by workers.
Proof: See Appendix.
The intuition behind Proposition 1 is simple. (1) says that employment in a firm is determined by
the overall ratio of firms to workers (M) and by the position in the wage distribution (as high-wage firms
have lower separation rates and find it easier to recruit). The overall employment rate as given by (2) is
simply determined by inflow and outflow rates. (3) and (4) say that both expected profits and value of
being in the labour market are determined by expected wages. The expression for workers in (4) has a
simple intuition. The employment rate is given by (2) so the final term in (4) is the probability of being in
employment multiplied by the expected surplus when in employment.
Now consider the case (not analysed by Burdett and Mortensen, 1998) where the supply of
both workers and employers to the labour market is not completely inelastic. For firms, we will assume
that there is a cost of entry Cf which, to give some flexibility in the model about the elasticity in the
supply of firms, will be assumed to vary across potential employers. Denote by Cf(Mf) the value of Cf
for the marginal employer if there are Mf employers. Then, in the free entry equilibrium, and using (3),
we must have:
?(M )[p ? E(w)]

E(? ) =
= C (M )
(5)
f
f
M (? + ?(M ))
On the worker side, we will use an analogous method of introducing some elasticity into the
labour supply by assuming that there is a ‘participation’ cost of Cw that must be paid each period. If the
worker does not pay it then they cannot be employed or get a job offer. This is a stylised way of
introducing some elasticity into labour supply but one could imagine it as the (amortised) cost of
acquiring skills necessary for employment before labour market entry. We will assume that Cw varies
4


across workers: denote by Cw(Mw) the value of Cw for the marginal worker if there are Mw workers in
the labour market. The free entry condition for workers can be derived as follows.
Let us distinguish between the value of being unemployed Vu and the value of non-participation
Vn which, as non-participants are always unemployed and save the cost of participation, can be written
as:

n
? V = b +

(6)
r
C w
Free entry of workers means that, in equilibrium, we must have Vu=Vn for the marginal worker so that,
using (4), the ‘free entry’ condition for workers can be written as:
?(M )[E(w ) ?b]

c
= C (M )
(7)
w
w
? + ?(M )
For fixed wages, the free entry equilibrium then involves solving (5), (4) and (8) for Mw and Mf.
The simplest way to see that there is a unique equilibrium (for a given level of average wages) is to note
that (7) implies a positive relationship between M and Mw as the greater the ratio of employers to
workers the higher is the employment rate. And, as long as the elasticity of ?(M ) with respect to M is
less than one, (5) implies a negative relationship between Mf and M as the greater the ratio of employers
to workers the lower is employment per firm. Using M=Mf/Mw we can eliminate Mf from (5) to have a
negative relationship between Mw and M. The supply of firms (5) is represented by FF in Figure 1 and
the supply of workers in (7) by WW.
The distribution of the entry costs for employers and firms determines the elasticity of the FF
and WW lines. For example, if all firms have the same entry costs then the supply of firms to the market
is perfectly elastic and the FF lines are vertical. If, on the other hand the supply of labour to the market
is inelastic then WW will be horizontal. But, it should be apparent that the set-up used here
encompasses a wide range of possibilities: this helps to ensure that none of the conclusions will be
sensitive to assumptions made about elasticity in the supply of firms or workers to the market.
One might wonder about the efficiency of the equilibrium. We will not worry about
distributional issues and will just focus on the total surplus, S. This can be written as:
M
?(M)(p-b)
M
f

w
S =
?
?
M - (
C m )dm
? C (m )dm
(8)
w
0
w
w
w
0
f
f
f
? + ?(M)
The first term is the surplus from employment and the other terms the costs of participation of employers
and workers. The following Proposition provides some first-order conditions for the efficient levels of
Mf and Mw.
5


Proposition 2
1.
The first-order conditions for the efficient numbers of employers and workers can be written as:
??(M)[p-b]

?? = C ( M )
(9)
M
f
f
2
M[ ? + ?(M) ]

2
?(M ) [p-b] ? ?
?

1+
(1-
?
?? ) = C ( M )
(10)
M
w
w
2
?
[? + ?(M)] ?
?
?
where e?M is the elasticity of ?(M) with respect to M.
2.
If the expected producer and consumer wages are equal then both efficiency conditions will be
satisfied if:
?

E( )
w = p ?
? (p ? b)
(11)
M
?
? + ?
Proof: see Appendix.
This shows that an appropriate level of average wages can satisfy the efficiency conditions for
both the entry of firms and the entry of workers. If the expected wage is higher (lower) than the efficient
level there will be excessive entry of workers (firms) and insufficient entry of firms (workers).
So far, the distribution of wages has been treated as exogenous. But, let us now consider
whether the free market attains these efficiency conditions or whether wages will be too high or too low.


2.
The Free Market Equilibrium

In this section we assume that employers set wages to maximise profits. This is the equilibrium
considered by Burdett and Mortensen (1998) so we shall only discuss it briefly here. They show that
the only possible equilibrium is a wage distribution without mass points: the reason being that if there is a
mass point in the wage distribution then an employer who deviates by paying a wage ? higher will have
only infinitesimally lower profits per worker but a much higher level of employment as they will now be
more attractive to all the workers in the firms at the mass point.
As all firms must, in equilibrium, make the same level of profits, the wage paid at position F in
the wage offer distribution, w(F), must satisfy:

[ p ? (
w F )]N (F ) = [ p ? (0)
w
]N (0)
(12)
6


where w(0) is the wage offered by the lowest-wage firm. Taking expectations of (12) we have that:

[ p ? E( )
w ]E (N ) = [ p ? w(0)]N (0)
(13)
Using (1) and (2), (13) can be solved to yield the following expression for the average wage in the free
market equilibrium:
?

E( )
w = p ?
[ p ? (0)]
w

(14)
? + ?
so the average wage is a weighted average of marginal product and the lowest-wage offered.

Burdett and Mortensen (1998) show that the lowest wage offered in the free market equilibrium
will be the reservation wage of unemployed workers. The reason is simple: there is no point in offering a
lower wage as no workers will accept the job and there is no point in offering a higher wage (if one is
the lowest wage firm) as one can lower wage costs without affecting the supply of labour to the firm.
And, with job offers arriving at the same rate whether employed or unemployed, the reservation wage is
simply equal to b, the value of leisure. Hence, in the free market we will have w(0)=b and (14)
becomes:
?

E( )
w = p ?
[ p ? b]
(15)
? + ?
so that the average wage is a weighted average of marginal product and the reservation wage. But, is
the free market level of wages the efficient level: comparison of (14) and (11) readily leads to the
following Proposition.

Proposition 3
If ?
<1 then average wages are too low in the free market equilibrium.
M
?
Proof: Simple comparison of (14) and (11).
For a given value of M, this Proposition implies that there are too many firms in the market, the
reason being that excessive entry is encouraged by the monopsony profits on offer. In contrast, there
are, for a given level of M, too few workers in the market as they receive less than their marginal
product.
However, one should not conclude that there are too few workers in the market compared to
the first-best. Figure 2 makes it clear why. The line F’F’ represents the entry conditions for firms when
average wages are at their efficient level and FF when they are at the free market level. Similarly,
W’W’ represents the efficient entry condition for workers and WW the free market condition. M, the
7


ratio of firms to workers, is clearly too high in the free market but Mw may be too high or too low. For
example, if e?M=0 then Mw is too low, but if e?M is close to one then Mw is too high.
The rest of this paper is about whether we can restore efficiency through a suitable set of
policies.


3.
The Minimum Wage and Trade Unions

First, let us consider the introduction of a minimum wage of wm in this model. As long as this is above b,
this will be binding on the lowest wage firm in the market and will become the lowest wage paid. The
expected wage distribution will be given by (14) with w(0) replaced by wm . As the minimum wage
raises average wages and free market wages are too low, it is not surprising that an appropriately
chosen minimum wage can restore efficiency: the following Proposition tells exactly the wage that is
necessary.

Proposition 4
A minimum wage, wm, which satisfies:
p - w

m = ? ?
(16)
M
p - b
will lead to the socially optimal outcome.
Proof: This is the value of wm that makes (14) the same as (11).
The rule in (16) is similar to the result of Hosios (1990) for the efficient distribution of surplus in
matching models with ex post bargaining rather than wage-posting. The Hosios rule for efficiency is that
the workers share of the surplus should be equal to e?M: (16) says that this should be the workers’ share
of the surplus in the lowest-wage firm. But, importantly, workers in all other firms in the wage-posting
model get a higher level of the surplus and this does affect one’s interpretation. The Hosios result is
often interpreted to say that the workers share of the surplus may be too high or too low for efficiency
and there is no a priori reason to believe one case or the other. In contrast, this result says that, with
wage-posting, there is an a priori case to believe that the workers’ share of the surplus is too low and
should be raised even though the share of the total surplus may be very high. Note, that this result does
not say that minimum wages can be raised without limit without eventually reducing efficiency. If
8


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