The most common theory to explain spatial interaction is the Gravity Model, whic
ID: 436457 • Letter: T
Question
The most common theory to explain spatial interaction is the Gravity Model, which states in mathematical terms the relationships between “activity at zone j” and “activity at origin zone i,” as governed by the “spatial cost between them:”? ? ?
Employment at zone i = Ei Spatial cost between i and j = dij Proportion of activities from origin i that end up in destination j = ??ij
We can then write
i ij ij Correspondingly, populations Nj are to be distributed among the urban area
and so on. For the following study area:
E ?? (d ) = E ??
i ??kNk/d2ik Nj = ??i Ei ??ij (dij)
according to which, when written for zone 2 in a city of three zones assumes the form
Here,
N2 = E1 ??12(d12) + E2 ??22(d22) + E3 ??32(d32) ??12(d12) = N2/d212
N /d2 j ij
N1/d211 +N2/d212 +N3/d213
From/To Zone 1 Zone 2 Zone 3
Zone1 2 8 6 Zone2 8 3 4 Zone3 6 4 3 Base-yrpop:Nj 480 870 1020
Economic Methods of Analysis CHAPTER 2 79
870/82 ??12(d12) = 480/22 + 870/82 + 1020/62 = 8.3950 x 10??2
(a) Please calculate ??11(d11) and ??13(d13) and verify that the sum of ??11(d11), ??12(d12) and ??13(d13) adds up to the numerical value of unity.
Let us say the total employment in zone 1 is projected to be 500. Accordingly, it means that E1??12(d12) = 500 x 8.3950 x 10??2 = 41.975, or 42 workers from zone 1 will live in zone 2. In order to fore- cast the total number of workers living in zone 2, however, two additional number are needed. They are E2??22(d22) and E3??32(d32). The sum of the three numbers is the total number of employees liv- ing in zone 2, in accordance with the equation Nj = ??i Ei ??ij(dij).
(b) Please calculate the number of employees living in zones 1 and 3.
Similarly, retail employment is located vis-a-vis people's resi- dential choice. The probability that a shopping center will be located at zone 2, given a residential location at zone 1, is given by this formula
ER2/d 212
ER/d2 + ER/d2 + ER/d2
Explanation / Answer
Gravity models are used in various social sciences to predict and describe certain behaviors that mimic gravitational interaction as described in Isaac Newton's law of gravity. Generally, the social science models contain some elements of mass and distance, which lends them to the metaphor of physical gravity. Social science gravity models: Gravity model of trade Trip distribution Gravity model of migration Two-step floating catchment area (2SFCA) method