Geography Reference
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and each product c i is produced by a dif erent i rm i =1,. . ., N .
Assumption 1 implies that the N products are substitutes and that s is the mutual
elasticity of substitution (see Dixit and Stiglitz, 1977). The higher s, the more the prod-
ucts are substitutes and the more price dif erences impact on consumers' demand. Since,
because of CES utility, agents value diversity, we have implicitly assumed that each i rm
produces a dif erent product, so that N is both the number of manufacturing i rms and
the number of manufacturing products available for consumption.
The agricultural sector uses only labor as an input under constant returns to scale with
unitary marginal costs. Because of the large number of potential producers, 2 I (1 − μ) at
equilibrium, the agricultural market is perfectly competitive and the agricultural good is
sold at its marginal cost.
Also manufacturing i rms use only labor as input and their technologies are character-
ized by a common, industry-specii c, marginal cost and a local, location-specii c, i xed
cost. Formally this leads to Assumption 2.
Assumption 2 : The labour v i that each i rm i = 1, . . ., N needs to produce an amount y i
of output is given by:
v i 5 b y i 1 a l i
(24.3)
where marginal cost b is constant across i rms and across locations and the i xed costs a l i
depend on the location l i occupied by i rm i .
Assumption 2 implies that we are in the presence of economies of scale, that is, an
increase in output causes a decrease in each i rm's average costs. Firm i proi t is given
by:
p i = p i y i w i v i = y i ( p i w i b) − w i a l i i = 1,. . ., N
(24.4)
where w i is i rm i cost of labor.
Before looking for markets' equilibria notice that, because of perfect competition
and constant returns to scale in agricultural production, agricultural wages are equal to
agricultural prices. Moreover, because of zero transportation costs for the agricultural
goods, agricultural prices, and thus wages, must be the same in both locations. Given
that consumers are not mobile and the economy is at an equilibrium, it should also make
no dif erence for a worker to work in the agricultural or in the manufacturing sector.
As a result wages in the two sectors, and in the two locations, are equal. For this reason
it is convenient to use wages to normalizes prices in the economy and set w i = 1 for
all i .
In order to i nd equilibrium prices, quantities, proi ts in the manufacturing sector, and
the resulting geographical distribution of i rms, one should in principle analyze each of
the N product markets. Nevertheless the problem can be simplii ed by considering only
one representative market for each location. In fact, location by location, i rms produce
using the same technology, face the same demand (because of Assumption 1 all goods are
substitutes), and the same labor supply. This implies that equilibrium prices, quantities
and wages are the same for all the i rms in a given location. We can thus consider only
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