A region, as considered by the regional scientist, is any area possessing homogeneity or interdependence of the phenomena being studied. These phenomena may be economic, geographic, political or social. The Montreal metropolitan area is a region exhibiting a high degree of interdependence among its many activities. Where there is such interdependence, a change in one segment of the regional structure will have repercussions on many others. As we shall see later such effects can be measured. This is a real advantage if one is interested, say, in the income, employment and other effects of a new steel-producing plant in the Montreal area.
Regional science differs significantly from another spatial discipline, geography, in its construction of mathematical models, and the testing of these models against empirical studies. The use of such models (which are simply algebraic expressions of some observed or hypothesized regularity in human behavior) is becoming increasingly important in the social sciences, as it has long been in the physical sciences.
The thesis that aggregate human behavior is amenable to mathematical formulation, and thus prediction, is the subject of considerable controversy. Indeed, though the evidence to support this contention is constantly growing, it must be admitted that the mathematical models, which purport to represent spatial activity, are disappointingly crude. It must be remembered, however, that the models are pioneering efforts, and that much study is being devoted to their improvement.
In a practical sense, then, regional science is the mathematical and statistical analysis of the various elements which spatially interact in an area, with a view to predicting the effects on these elements of a change in any of them. It is for this reason regional science may become in the future an invaluable tool for the businessman interested in expanding or relocating his firm. The techniques described below may take much of the guesswork out of decision-making.
The most useful tools being perfected by regional scientists are regional and interregional input-output analysis, linear programming, social accounting, and the gravity model.
Input-output analysis, now generally well-known among economists, was first developed to simulate the total production activity of a nation. The inputs refer to factors of production-such as raw materials and labor, while the output is the final product. The system envisages much interdependence with one industry's output being another's input, and vice versa. An input co-efficient is the amount of input (usually in dollars) required per unit of output. A change in any output will have direct and indirect effects throughout the economy, and these may be traced using a matrix of simultaneous equations. Applying this technique to a limited area, or region, such as a metropolitan area, may reveal complicated links hitherto ignored. If we use this method to estimate the impact of the new steel plant on the Montreal area, we can come up with an estimate of the new direct and indirect job opportunities. This information would also be useful to service industries, union leaders, and city planners. Input-output may also be used to estimate the increased income accruing to the area (which would interest local merchants), and the area demand for steel. linear programming
While input-output analysis is a technique for measuring the impact of change upon an economy, interregional linear programming is an optimizing technique; that is, given certain conditions, it can show, for example, how to minimize transportation costs or maximize profits. Like input-output, linear programming uses linear algebraic equations, but also introduces constraints such as fixed capacity and limited resources.
In this respect it is closer to reality, and the problem is set up to minimize or maximize some objective, subject to certain constraints. Linear programming is not peculiar to regional science, and is usually associated with operations research, but it is admirably suited to determining efficient shipment patterns between warehouses and customers, or between resources and factories. This approach to the allocation of basic industrial commodities among regions has been successfully applied to the coal, petroleum, and feed grain industries in the United States.
A rather valuable feature of interregional linear programming involves a mathematical "trick" called the dual of the linear program. Thus where the original or primal problem is concerned with allocation, the dual is a valuation problem. For example, if, as above, we are allocating resources among factories (which probably use different processes) in various regions, the dual is the problem of imputing the market value of the final good back to the resources used in producing that good. The dual may thus be used in cost accounting for indicating the amount of profit which may be assigned to a certain resource. In other words, it would indicate how much would be lost or gained by varying the resources, if such were possible. In the warehouse problem, the dual may be used determine the locational rent.
Regional and interregional social accounting is the application of national income accounting methods to regions. The businessman may wish to know the importance of his firm to the community in which it is located, and social accounts provide a very useful basis for such information. At the present time, income and product accounts are not a regular feature of municipal or metropolitan administration. Their, preparation, however, is no more tedious or expensive than a detailed economic base study. The latter method is concerned primarily with determining the size and composition of an area's export trade on the useful assumption that exports are the life blood of the region. (In this context "export" simply refers to goods moving to points outside the region, but not necessarily outside the country.)gravity model
The last concept being exploited by regional scientists is the gravity model. This rather esoteric idea is related to the Newtonian notion of the gravitational attraction of physical masses. For the latter, however, regional science substitutes masses of people. This idea did not originate with those who today consider themselves regional scientists; as a matter of fact it was a man of business who first commercially exploited the relationship of people and distance.
It appears to be an empirical fact that the percentage of people from an area patronizing an establishment falls off regularly with the distance of that area from the establishment. This is the idea in its pristine simplicity but, for practical application, many refinements are necessary. In addition, gravity models form the basis of inchoate techniques for predicting changes in population, income, and locational rent.
These, then, are the tools of regional science which seem to offer the most to the businessman. In addition to their rather obvious crudity, they have certain technical disadvantages. An important conceptual assumption of input-output analysis is that of linearity, which means that the input of a raw material per unit of output is fixed regardless of the amount produced. There are thus no economies of scale taken into consideration. Linear programming can improve on this state of affairs by incorporating constraints of various kinds, and by treating different levels of production as different processes.
From a practical standpoint two disadvantages loom large: the substantial amount of detailed statistical data required, and the complexity of the mathematical computations. The problem of data may occasion no headaches when a company is studying its own operations, yet even here cost accounting breakdowns may not be adequate. But when government data are used many omissions are encountered because of the rule against revealing information on individual companies, and failure to collect adequate highway shipment information. Nevertheless, from the data available (and shrewd guesswork) useful first approximations may be calculated.
The solution of large numbers of equations involves matrix algebra and electronic computers. The algebra is necessary to set up the problem, while the computer can solve it in a reasonable length of time. Some problems include so many unknowns and constraints that no existing machine can handle them!world wide concern
While the techniques described seem particularly relevant to business, they do not tell the whole story of regional science. To an impressive degree this new field reflects the growing world-wide concern for the fair sharing of the earth's resources, and their efficient use. While the applicability of these techniques to national planning may be uppermost in the minds of some, their most challenging ultimate role may lie in their incorporation into a general model which will be a realistic representation of our free enterprise system. The development of such a model would be an important milestone along a middle road between profligate capitalism and stultifying communism. Source: Canadian Business, Vol. 33, No. 11, November 1960.