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2017 | OriginalPaper | Chapter

4. The Mills Model

Author : John R. Miron

Published in: The Organization of Cities

Publisher: Springer International Publishing

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Abstract

Mills (1967)—a widely cited paper in its area—was among the first to present a model of an urban economy operating under perfect competition. Even by today’s standards, the model is bold in scope; it contains 4 industry sectors, 3 factors of production, and two geographic zones (CBD and suburb). In terms of the global economy, this is an open model; factors flow freely into or out of the city in response to market prices. My intention here is to simplify and clarify the model so that we can better understand its significant implications. Mills implicitly assumes that the state has already enabled competitive markets locally in commodities, housing, transportation, land, labor, and capital. The state has decentralized its authority by empowering property and labor rights and creating incentives for individuals to participate in markets fully enough for everyone in a given market to be a price taker (small player). In market equilibrium, the city reaches a size where the unit cost of production (including land rent, wages, and paid and imputed interest)—the same for each firm in the sector—is just equal to price. No firm is able to earn any profit. Workers who in-migrate to the city are implicitly no better off as a result than those who did not in-migrate. Each unit of capital that flows into the city earns the same rate of return: presumably the same as it could earn outside the city. Despite its elegance, the absence of an algebraic solution make the Mills model difficult to understand. Further, the lengthy set of assumptions made make it difficult to separate out the significance of any one assumption.

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Footnotes
1
Mills (1967) is referenced, for example, in Henderson (1974), Hamilton (1975), Fujita and Thisse (1996), Anas et al. (1998) and Quigly (1998).
 
2
Modeling of rates of change and/or flows from date to date.
 
3
Production technology by which the firm is able to increase its output only by a similarly proportional increase in all its inputs.
 
4
For an elastic supply curve, quantity supplied increases quickly as price is increased.
 
5
Mills used a fixed price elasticity model here. To me, a linear model is simpler.
 
6
Mills allowed for increasing or decreasing returns to scale. I use constant returns to scale for ease of exposition.
 
7
Mills appears to treat the transporter pricing parameter a as a constant (i.e., exogenous). However, if the market for transportation is in perfect competition, new keep adding to the supply of land for transportation until there is no excess profit to be earned. In this Chapter, I treat a as just another price whose equilibrium level is to be determined; hence, a is endogenous.
 
8
As my students look at me (first quizzically then disappointedly), I describe calculations such as the above as demonstrating the beauty of a model. What I mean by “beautiful” here is, of course, how a set of just 16 seemingly innocuous parameters translates into a full and consistent picture of an urban economy in operation.
 
9
The hypothetical area below the consumer’s demand curve out to the quantity demanded and above market price.
 
10
The hypothetical area below the consumer’s demand curve out to the quantity demanded.
 
11
This excludes nonlabor costs incurred by the other sector.
 
12
Measure of the carrying capacity of a vehicle or vessel: e.g., tonnage or passengers.
 
Metadata
Title
The Mills Model
Author
John R. Miron
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-50100-0_4