MEASURING THE EFFECTS OF MONOPOLIES IN A PARTIAL MONOPOLY MODEL

Date01 November 1981
Published date01 November 1981
DOIhttp://doi.org/10.1111/j.1467-9485.1981.tb00089.x
AuthorGerald Makepeace
Scofnsh
Journal
of
Polrrrcal
Economy,
Vol
20,
No
3, November
1981
0
1981
Longman Group
Limited
0036- 9292/81/00250236 502.00
MEASURING THE
EFFECTS
OF
MONOPOLIES
IN
A PARTIAL MONOPOLY
MODEL
GERALD
MAKEPEACE*
University
ojHul1
I
INTRODUCTION
The main purpose of this paper is to develop a solution to the partial
monopoly model which will enable one to calculate the effects of monopolies
on
the allocation
of
resources.’ Normally, the output
of
a monopoly
is
compared indirectly with the output
of
a competitive industry by the
measurement of the consumer surplus lost when a monopoly takes over.’ Like
most
of
these investigations, the present study is
a
partial equilibrium analysis
of the effects
of
profit maximising firms and does not concern itself with general
equilibrium problems (see Bergson, 1973), or with the extra losses
of
output
due to factors such as x-inefficiency. In contrast with previous work, the
present study is not an empirical investigation but is based on a theoretical
model which includes a labour market and a variable size
for
the monopolistic
sector.
The basic model considered here consists of a product and a labour market.
The only variable input in the production process is labour and firms act as
price takers in the labour market. Four variants
of
the model are then
examined. In the first two, the labour market is competitive but the product
market is in turn a competitive industry and a partial monopoly. The last two
models have partially monopolistic and competitive product markets respec-
tively but the labour supply is controlled by a trade union which seeks to
maximise the difference between the revenue received by its members and the
costs
of
supplying labour. These models are described in the second section
of
the paper.
The substance ofthe paper is contained in the third section where the outpul
*
I
am grateful to Phil Lewis, John McCombie, John Treble and an anonymous referee for their
helpful comments
on
earlier drafts
of
this paper.
The comparative static properties
of
a partial monopoly model with a linear demand curve
and quadratic cost functions have been studied in some detail by Reid
(1977)
in a previous issue
of
this journal. Reid was concerned with the analytic properties
of
his model while the present paper
concentrates on the numerical solution of
a
partial monopoly model. This places the present paper
more
in the tradition of the “monopoly welfare
loss”
literature, although it does,
of
course, provide
a link between the two approaches.
*See,
for
example, Cowling and Mueller
(1978)
and the references quoted in their introduction.
Date of receipt of
final
manuscript:
30
April
1981.
3
?h
MEASURING THE EFFECTS
OF
MONOPOLIES
237
produced in the various models is compared. Let
Y*
be the output produced
when there is perfect competition in the product and labour markets,
Y
be the
output produced when there is a partial monopoly in the product market and
perfect competition in the labour market and
Y’
be the output produced when
there is a partial monopoly in the product market and union activity in the
labour market. Section three reports the values of
Y/Y*,
Y’/Y
and
Y/Y*
for
different values of the parameters. The main parameters considered are
:
(i)
the fraction of the capital stock owned by the partial monopoly
(ii) the capital elasticity of output
(iii) the elasticity of the product demand curve
(iv) the elasticity of the labour supply curve.
The penultimate section of the paper draws some parallels between the
present results and traditional studies of monopoly losses. Put simply, it is
argued that traditional measures of the aggregate welfare loss conceal
significant transfers which cannot be ignored in any discussion of the effects of
monopolies. The paper is completed by a short conclusion.
I1
THE
PARTIAL
MONOPOLY
MODEL
The impact of monopoly forces
on
the production of output is investigated
in
a
standard model known variously as the partial monopoly, dominant firm
or price leadership model. Good discussions of this model are available in
Scherer
(1971)
and Reid
(1977).
In the present version, the firms in the industry have a fixed capital stock but
are free to vary their labour input through purchases in the labour market. The
firms are organised into
a
price-setting, ‘‘monopolistic’’ sector and a price
taking, “competitive” sector. The firms in the monopolistic sector act in
collusion to maximise their joint profits and, for
our
purposes, can be regarded
as a single, monopolistic firm. This firm acts as
a
price leader for the industry
and sets its price in the knowledge that whatever price it announces will be
taken as the market price by the remaining firms.
At any price set by the monopolist, the price taking firms will supply the
quantity
of
output given by their aggregate supply curve. The partial
monopolist’s demand is, therefore, the residual demand curve obtained by
subtracting the total supply of the competitive firms from the market demand
at each price. The monopolist will maximise its profits by employing the
quantity of labour which makes the marginal revenue product of labour, based
on the derived demand curve, equal to the marginal cost of labour. It is
assumed that all firms are price takers in the labour market
so
that the
marginal cost of labour is constant and equal to the money wage. The profit
maximising behaviour of firms, described above, implies
a
demand for labour
at each value of the money wage. The model is closed by assuming the supply

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