S.A. Stouffer, an American sociologist, introduced one such modification in the gravity model. Stouffer formulated his intervening opportunity model in 1940, and claimed that there is no necessary relationship between mobility and distance (Stouffer, 1940:846). Instead, the observed decline in the volume of migration is due to an increase in the number of intervening opportunities with increasing distance. Stouffer’s model suggests that the number of migrants from an origin to a destination is directly proportional to the number of opportunities at that destination, and inversely proportional to the number of intervening opportunities between the origin and the destination.
Stouffer’s formulation can be mathematically expressed as follows:
where Y is the expected number of migrants, ∆x is the number of opportunities at the destination, x is the number of intervening opportunities, and k is a constant. Stouffer modified his theory of migration and intervening opportunities in the mid-1950s and added the concept of competing migrants in his model. His modified theory of mobility was published in 1960. The revised model proposes that during a given time interval, the number of migrants from city 1 to city 2 is the direct function of the number of opportunities in city 2, and an inverse function of the number of opportunities intervening between city 1 and city 2, and the number of other migrants for the opportunities in city 2. Thus, the revised formulation would read as under (Galle and Taeuber, 1966:6):
where Y is the number of migrants moving from city 1 to city 2, Xi is the number of opportunities in city 2, X1 is the number of opportunities intervening between city 1 and city 2, Xc is the number of migrants competing for opportunities in city 2, and k is a constant.
It may be realized here that the volume of migration from one city to another is the function of as much the attraction of one city as the repulsion from the other. Hence, another component as a measure of disadvantages that push people from city 1 is introduced in the numerator. The final formulation may be expressed as under:
where Xo is the number of out-migrants from city 1; a, b and c are parameters to be determined empirically; and other notations are as before.
In Stouffer’s model the measure of ‘disadvantages’ or ‘push’ factors in city 1 (X0) is defined as the total out-migrants from the city. Likewise, the measure of number of opportunities in city 2 (X1) is defined as the total in-migrants in city 2, whereas the measure of intervening opportunities between city 1 and city 2 (X2) is defined as the total number of in-migrants in a circle centred mid-way between city 1 and city 2, and having a diameter equal to the distance between the two cities. And, finally, the measure of competing migrants (Xc) is defined as the total number of out-migrants from a circle centred on city 2 with the distance between the two cities as its radius.