Subcontracting and Economic - Indian Institute of Public Administration

A Theoretical Model of Subcontracting for High Quality
perfectly at the end of the first period and they will purchase
the product again if the quality is high, that is, q=q h
.
It is assumed that the product becomes obsolete at the
end of the second period. The utility function of an individual
is defined as
}
u =θq - p If consumer purchases one unit of
product with quality q and price p 2
=0 Otherwise
Assume p 1
and p 2
be the prices charged by the monopolist
in periods 1 and 2 respectively and x 1
and x 2
are the corresponding
demands.
p
Thus x 1
= 1
p θ − and x 2
= θ − 2
for q=q h
in previous
q qh
and current period and x 2
= 0 otherwise.
In this case the subcontractor undertakes the first stage of
production of each unit of output and the quality level is
determined at this stage of production. However, the
monopolist cannot observe the quality level supplied by
the subcontractor. In the second stage of production, the
monopolist finishes the product and supplies it to the market.
Let ‘c’ be the monopolist’s per unit finishing cost of
the product. It is assumed that ‘c’ is constant and independent
of the level of output and quality level of the product.
It is assumed that there are a large number of identical
competitive contractors and each can produce one unit of
output in a particular period. Each subcontractor maximises
the present value of his two periods’ incomes. Let `π’ be
the income that a contractor in each period gets from his
alternative source of employment. If he works under the
monopolist, he earns income r 1
per unit of output in the
first period. If he produces high quality goods his unit cost
of production is c h
and if he produces low quality product,
his unit cost of production is c l
where c h
>c l
. If the
subcontractor produces a high quality product in the first
period only then does the monopolist give the contract in
the second period and pays r 2
per unit of output produced,
to the subcontractor. It is further assumed that subcontractors
make their quality decision in the first period
only 1 . The subcontractor will accept the offer of the
monopolist and produce a high quality product if and only
if the present value of his two periods’ income is at least
as great as the present value of his income from alternative
source of employment, that is, if
_________________3.
This is the individual rationality or reservation constraint
(IR) of a subcontractor. Here δ is the discount factor. A
subcontractor will actually produce high quality if and
only if his earnings from producing low quality goods is
less than what he gets by producing high quality goods,
that is, if
or
____________4.
This is the incentive compatibility constraint (IC). It is assumed
that the monopolist first announces r 1
and r 2
. If
contractors accept the offer, they supply the product to
the firm. Given the demand function, and r 1
, in the first
period the monopolist maximises his profit to determine
his price p 1
. If the final product is a high quality one in the
second period, the monopolist will give the contract to the
subcontractor again. The subcontractor will supply the
product and receive r 2
in the second period. In the second
period, quality is common knowledge. Given r 2
and p 1
,
the monopolist determines p 2
and p 2
is equal to full information
monopoly price.
However, if quality supplied at the initial period is poor,
the monopolist faces zero demand in the second period.
Thus, the monopolist’s profit when high quality is supplied
in the first period is given as
---------------- 5
In this case the monopolist is dealing with a large number
of identical agents. It is a two-period model. So he cannot
employ new agents in the second period, because the new
agent will supply a low quality product. There are two
reasons for this situation. Firstly there is no future and secondly
the monopolist cannot observe the quality level served
1
If a contractor firm takes quality decision in each period then in the last period, that is, in the second period he will obviously cheat, as there is no future.
15