2. Modeling location dependence between producer
services & manufacturing
In this section, the basic structure of a model developed by Venables (1996) is
presented. The model is based on the following theme: vertical linkages between sectors
imply that the location of the sectors is interdependent. Since the downstream sector
creates a market for the upstream sector, the latter is attracted to locations where there are
relatively many upstream firms. (The author denotes this as the demand linkage). At the
same time, the downstream sector experiences lower costs if it operates in a location in
which there are relatively many upstream firms. (The author denotes this linkage the cost
linkage). This model is of relevance in the present context because it shows how and why
the locations of two vertically linked sectors are simultaneously determined. Here,
downstream will be interpreted as manufacturing and upstream as producer services. This
may be conceived as a very ad hoc assumption, but in a world where product attributes,
such as design, technological refinement, branding and so forth, constitute an important
part of the product value, manufacturing firms have inevitably to rely upon various
producer service providers to sustain their market shares and competitiveness, (see for
instance Reich, 1991 and Hansen, 1993 earlier referred to). Hence, producer services can
be seen as an important input in the production function for manufacturing firms.
In Venable’s (1996) model, there are two regions and three sectors; (i) a perfectly
competitive sector, whose product is used as numeraire, (ii) a monopolistically
competitive sector, which produces for final consumption and (iii) a monopolistically
competitive intermediate sector, here the producer service sector, which supplies inputs to
the final manufacturing sector. The two latter sectors are modeled using the common
monopolistic competition model in Dixit & Stiglitz (1977) 5. The presentation of the
model follows the original presentation in Venables (1996). It starts by describing the
manufacturing sector and then goes on to describe its linkages to the producer service
sector.
2.1 Manufacturing - the final sector
1 and 2 denote the two regions in the economy. All manufacturing firms in the
industry supply both locations. Consumers in region 1 (2) can consume varieties
produced in the same region, z11 (z22), or varieties produced in the other region, z21 (z12).
For varieties transported from the other region, the consumer price is the price of the
variety at the origin multiplied by an ad valorem transport cost of t >1. All consumers in
both locations have a love-of-variety and their preferences are identical. The latter makes
it possible to treat each region as one representative consumer. The problem for region 1,
then, can be expressed as in Equation 1.
(1)
max
{zi 11,zi 21≥0}
( n 1 σ-1 n 2 σ-1 ʌ σ -1
U1 = ∑ zn σ +∑ znσ
4i=1 i=1 y
n1 n2
s.t. m 1 =J pnzi 11 +J pι2 tzi21
i=1 i =1
5 For a comprehensive and pedagogical presentation of the monopolistic competition model with extensions see
Matsuyama (1995).