Residents of other cities are assumed to have a fixed utility level. If utility in the model city is
temporarily lower, model city residents will move to other cities. A population outflow causes
housing prices in the model city to fall, so its remaining residents eventually regain the
equilibrium utility level. Likewise if utility in the model city is temporarily higher than in other
cities, a population inflow results, causing housing prices to increase until the equilibrium utility
level is regained.
Since this model assumes no consumer substitution, residents obtain equilibrium utility if they
can just afford a fixed (exogenous) house size and a fixed (exogenous) consumption level of non-
housing goods. After paying the cost of commuting to the business area, residents must have just
enough money left to afford this fixed consumption bundle. Equilibrium housing prices at all
locations will allow this requirement to be met.
The no-consumer-substitution assumption differs from the indifference curve analysis in the
appendix to Chapter 6. If residents can move along an indifference curve giving them the
equilibrium utility level, house size and non-housing consumption would be endogenous
variables. To eliminate consumer substitution here, we’ll assume the city has a zoning rule. The
rule allows only a fixed housing unit size to be produced by housing firms. That being so,
residents can reach just one point on their equilibrium indifference curve.
Commuting cost is a function of distance between a resident’s housing unit and the
residential/business boundary. Commuting inside the business area is costless.
As in the text, both manufacturing and housing firms are assumed to produce a fixed output
level. Also as in the text, we assume that factor substitution is not possible. In the case of
manufacturing firms, their output is produced using fixed inputs of land, labour, and capital. In
the case of housing firms, their output is produced using fixed inputs of land and capital.
Manufacturing firms ship their output to a highway or port, incurring freight cost along local
roads. The farther they are from the highway or port, the more freight cost they incur. In
equilibrium, land rents will adjust so that firms earn zero economic profit at all locations.
There are no office firms in the model. Manufacturing firms are the only employers. Their