ABSTRACT
In this section we shall show that wage rates will tend to increase with
city size at a decreasing rate. The argument is a continuation of that in
the preceding section,,
We use as a tool of analysis the concept of the set of bid price curves
introduced by Alonso (1964)» A bid price curve connects the set of points
indicating rents and locations between which a household is indifferent•
A household's preferences are described by an infinite set of bid price curves
just as in the usual analysis of consumer behaviour a household's preferences
are described by an infinite set of indifference curves. However whilst the
household prefers to consume the bundles of goods represented by points on
higher indifference curves to those represented by points on lower indifference
curves, since it obviously prefersto pay a lower rent to a higher rent at
any given distance from the centre, it must prefer locations and rents
represented by points on lower bid price curves to those represented by points
on higher curves» At its optimal location therefore the rent gradient will be
tangential to the lowest attainable bid price curve from above. In Figure 4
we reproduce one half of Figure 1 but show in addition one of the bid price
curves of a representative household*
May 25th 1971
- 10 - Evaûs
The curve XYZ is the lowest bid price curve attainable by the household;
the point Y indicates the optimal location and rent. Suppose now that the
household, with an unchanged schedule of preferences, is transferred to a
larger city where the rent surface is that indicated by the curve R'P'^ R1
in Figure 2. The bid price curve XYZ is no longer attainable since R^'R'
lies everywhere above RFR and therefore lies everywhere above XYZ. The lowest
bid price curve which is now attainable by the household is one which is
The household is made worse off by an increase in city size because of the
increase in its rent and/or travel costs. If migration between cities is
possible at a negligible cost, some benefit must accrue to residents of the
larger city which compensates them for the higher rent and/or travel costs
payable in the larger city and prevents them migrating to the smaller city.
