Therefore, an increase in the number of available varieties reduces the manufacturing price
index. Consequently, given that the indirect utility function (9), is decreasing in the
manufacturing price index, the regional welfare increases.
The elasticity of substitution between varieties, σ, determines the responsiveness of the price
index to a change in the available number of varieties.
3.2 Labour supply and human capital externalities
The world farmer’s population employed in the agriculture sector is 1 - μ. Since farmers
cannot regionally relocate, the supply in each region is (1 - μ)Z2.
The manufacturing sector employs two types of workers (i) low-skilled workers, and
(ii) high-skilled workers. 8 Both types of workers are endowed with one unit of labour, and
may move between regions. We assume that the global population of workers of each type is
normalised to 1. The total population of manufacturing workers therefore sums to 2.
The existence of localised human capital externalities implies that the interaction
between high-skilled workers in a region increases the productivity of each skilled worker by
a knowledge diffusion process. The productivity of high-skilled workers, i.e. the efficiency
unit of labour supplied, depends upon the number of workers with similar characteristics in
the regional labour force. In the model the skill premium si is endogenous, and may differ
between regions according to the size of the regional highly skilled population si = f (Si ),
where Si represents the population of high-skilled workers in region i. We formalise the
positive interaction between high-skilled workers in a region as:
s =( Si )λ (10)
8 In this model, labour provided by low and high skilled is qualitatively homogeneous. Manufacturing workers
of the two types are perfect substitutes.
13