## first

We noted in subsection 5.2.3 above that the residential location model needed to be disaggregated by both person type (say using an index w) and house type (say using k). A typical example of such a model would be

(5.26)

This follows the argument of Wilson (1970) and Senior and Wilson (1974), though once again, it is simply being taken as a typical example of a disaggregated model and others could be substituted without affecting the essential argument about dynamics to be presented later. In this model, T~~ is the num-

lJ ber of type w people resident in a type k house in zone i and working in zone j. (We neglect here all the discussions which are needed to build in non-workers, households with varying numbers of workers and so on. For a more general review of residential location, see Senior, 1973, 1974.)

H~ is the number of type k houses in i. E~ is the number 1 J

of type w jobs in j (person type being assumed to derive from job type - for example in relation to income). b~; is the bid rent for a type k house in i by a w-type person working in j. The other terms are as before. or are obviously parameters. An equilibrium condition based on this model would take the form

(5.27)

(5.28)

L T~~ = kHkq ijw lJ for a suitab1e constant, qk The different equations in (5 0 26) are coupled in the usua1 way through the nature of the ba1ancing factors, which in this case are

(The model has been presented in sing1y constrained form, which is more useful as the basis for dynamica1 ana1ysis, though this parti cul ar mode1 is often presen ted in doubly constrained form.) 1

The next obvious step in the argument is to investigate how the two sets of diaggregated mode1s wou1d combine together in a Lowry-like structure. As formu1ated, the most obvious connection wou1 d be to make per capita expenditure terms 1ike e~,

1 dependent on the population mix in a particular zone, which is availab1e as

p~ L T~~ (5.30) 1 jk lJ

using an obvious notation. The other features of linkage turn on a more detailed discussion of attractiveness factors and so this is postponed until the next subsection.