A dynamic approach to the tendency of industries to cluster

Since Equation (5) implies that (z22 + z₂₁)/(z ₁₁ + z₁₂) = 1, l can be expressed as a
function of p and ) using (7).

(t^2σp^σ - t^σp^2σ ) -1^1+σp^2σ + tp^σ
(tp^σ -t^{1+ σ} ) +1^2σp^σ - t^σ

Equation (8) gives the distribution of production between the two regions as a
function of transport costs, relative costs and relative consumer expenditure. The
relationship in Equation (8) is dependent on the assumption that n1, n2>0⁷.

2.1 Linkages between manufacturing and producer services

In order to illustrate the location dependence between the two sectors, it is assumed
that the structure of the producer service sector is the same as in the previous section. The
manufacturing sector is denoted by d and the producer service sector by u. (Henceforth,
superscripts will denote sector). The demand for the final products comes from the
consumption expenditure at each location. On the other hand, the demand for the
producer service sector’s output comes from manufacturing since it uses the producer
service sector’s output as inputs. Also, the cost of the manufacturing sector depends on
the producer services sector. These cost and demand linkages imply that the relative cost
of the manufacturing sector (p^d ) and the relative expenditure on the output of the
producer services sector ()^u ) are endogenous. The cost of the producer service sector
and the demand for the final product ( p^u, ) ^d ), though, are exogenous.

Venables (1996) assumes that both industries use labor in production and that the
relative wage between the two locations, ω ≡ w₂ ∕w₁, is exogenous. The producer
service sector uses only labor, implying that it’s relative cost and relative price is (O. As
in Either (1982), Rivera-Batiz (1988) and others, the producer services sector’s output
enters the manufacturing sector’s production function through a CES aggregator.
Specifically, the production function of the manufacturing sector is a Cobb-Douglas over
labor and producer services, with a CES sub-production function for the producer
services sector’s composite output. Since the cost function of the CES sub-production
function is given by the price index, it has already been provided in equation (2) and (3),
(see Appendix A). Due the assumption of a Cobb-Douglas technology, the relative cost of
the producer services industry can be expressed as,

f PU
P^u

к P1

, where γ is the share of the producer service sector’s output used in production.

⁷ Venables (1996) shows that a necessary condition for this to be so is that t> p > 1/1.

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