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“Central Place Theory
and Zipf's Law” (Job Market Paper)
This paper provides a
theory of the location of firms and, as cities are groups of firms, the
emergence of cities. Using both a model of spatial price discrimination, this
paper provides a microfoundation for central
place theory and the conditions under which Zipf's law for cities
emerges. Central place theory describes how a hierarchical city system
with different layers of cities serving different sized market areas
forms from a uniformly populated space. Zipf's law for cities, that is,
the size distribution of cities following the Pareto distribution with a
tail index close to 1, is a robust empirical regularity. In the model,
the main force driving the size difference of cities is the tradeoff
between transportation cost and scale economies, which differs across
goods due to different fixed costs of production. Since a central place
hierarchy also implies a hierarchy of firms, Zipf's law for firms is also
approximated. The theory is also consistent with a newly discovered
empirical regularity, the Number-Average Size rule, which is a log-linear
relationship between the number of cities and the average size of cities
where an industry is located.
“On the
Structure of Distribution”
To
explain a recent phenomenon of “disintermediation,” this
paper presents a general equilibrium model of the distribution sector
that intermediates goods from manufacturers to consumers. The model is
the first in the literature that features multiple layers of middlemen. A
case of infinite layers is fully examined in the paper. The approach to
modeling is to embed the recursive structure of intermediation in the
standard Dixit-Stiglitz (1977) model of monopolistic competition. The
friction that creates the recursive structure of the distribution sector
is multi-fold: uncertainty upon entry, the retail cost which induces
economies of scale, and the entry cost that shrinks at the same rate of
the expected gross profit over layers. In particular, the interaction
between the uncertainty and the retail cost creates cutoff rules for the
middlemen to choose between retailing and wholesaling, and the shrinking
entry cost enables a recursive structure that permits the existence of
infinite layers.
Other work in progress:
“On the Optimality of Central Place
Hierarchies,” March, 2008
“Group Formation and Cultural
Transition,” September, 2006
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