minimum. This is an application of the principle of median location Naturally, a number of objections might be made to this procedure. One of the most obvious is that it is illogical to assume that our producer's sales pattern is independent of its location. It would be more reasonable to assume that the producer would have a smaller share of the total sales in markets more remote from its location, reflecting higher transport charges and other aspects of competitive disadvantage around this difficulty would be to decide that the producer is really primarily interested in marke possibilities only within, say, a radius of 400 miles, or only within the range of overnight truck delivery. It could then demarcate such areas around various points and select as its location the center of the area having the largest market volume A somewhat more sophisticated procedure would be to apply a systematic distance discount in the evaluation of markets by calculating what is called an index of market access potential for each of a number of possible locations. Thus to compute the potential index Pi for any specific production location(i), the producer would divide the sales volume of each market ()by the distance Dij from(i) to ()and then add up all the resulting quotients. Such potential measures have been widely used, with the distance (or transport costs, if ascertainable) commonly raised to some power such as the square. If the square of the distance is used, the potential formula becomes P (where M is market size and D is distance); and any given market has the same effect on the index as a market four times as big but twice as far away. In any ease, when the potential index P has been calculated for various possible locations, the location having the largest P can then be rated best with respect to access to the particular set of markets involved This measure of"potential, " in which each source of attraction has its value"discounted for distance, "is also generically known as a gravity formula or model-particularly when the attractive value is deflated by the square of distance over which the attraction operates. The reference to gravity reflects analogy to Newton' s law of gravitation(bodies attract one another in proportion to their masses and inversely in proportion to the square of the distance between them). William J. Reilly in 1929 proclaimed the Law of Retail gravitation on the basis of an observed rough conformity to this principle in the case of retail trading areas(a subject to be examined in more detail in Chapter 8), and John Q. Stewart and a host of others subsequently discovered gravity-type relationships in a wide variety of economic and social distributions. Gravity and potential measures have in fact been applied to almost every important measurable type of human interaction involving distance, and numerous variants of the basic formula have been devised. some of which we shall have occasion to examine later 19 All the shortcut methods described here have been widely used. Though they have been explained here in terms of the measurement of access to markets, or output access of potential locations, they are equally applicable to assessment of the input access potential of locations, when a unit is drawing on more than one source of the same transferable input. The measures can apply also to cases involving the transfer of services rather than goods-for example, measuring the job-access potential of various residence locations where a choice of job opportunities is desirable, or measuring the labor-supply access potential of altemative locations for an employer But at best, when a unit can serve many markets and/or draw from many input sources, the appraisal of alternative locations in terms of access is a complex matter. There is likely to be little opportunity to use the simple devices discussed earlier in this chapter, such as the balancing off of relative input and output weights, except perhaps as a means of initially narrowing down the range of locational alternatives. In such cases, the maps of cost and revenue prospects will show complex contours rather than simple ones as in the examples discussed earlier; and the evaluation of prospects at different locations will have to approach more nearly an explicit calculation of the expected costs, revenues, and profits at various possible levels of output at each of a large set of locations ine For most types of locational decision units, an exhaustive point-by-point approach in which theory and analysis abdicate in favor of pure empiricism would be so expensive as to outweigh any gain from finally determining the ideal spot. So there will al ways be a vigorous demand for usable shortcuts, ways of narrowing down the range of location choice, and better analytical techniques. The challenge to regional economists is to provide techniques better than hunch or inertia and cheaper than exhaustive canvassing of locations 2.9 SUMMARY This chapter deals with location at the level of the"location unit"as exemplified by a household, business establishment school, or police station. Location in terms of larger aggregates such as multiestablishment firms or public agencies, industries cities, and regions is taken up in later chapters. A single decision unit(for instance, a firm) can embrace one or more location Prospective income is a major determinant of location preference, but even in the ease of business corporations in which he profit motive is paramount there are other significant considerations, including security, amenity, and the manifold politica and social aims of public and institutional policy. Uncertainties, risks, and the costs of decision making and moving contribute to locational inertia and often to concentration The basis for locational preferences can be expressed generally in terms of a limited set of location factors involving both affecting a specific decision or type of location unit Location factors themselves have characteristic spatial patterns of advantage. Some factors, such as rent, may be relevant chiefly in comparing locations on a microspatial (small area)basis; other factors may emerge as important for macrospatial mparisons, involving locations far apart. Some location factors are primarily related to concentration: They may be most favorable in, say, large cities or dusters of activity or, alternatively, in small towns or rural locations. Other location factors involve transfer of input or output, so that locational advantage varies systematically according to distance. Other location14 minimum. This is an application of the principle of median location. Naturally, a number of objections might be made to this procedure. One of the most obvious is that it is illogical to assume that our producer's sales pattern is independent of its location. It would be more reasonable to assume that the producer would have a smaller share of the total sales in markets more remote from its location, reflecting higher transport charges and other aspects of competitive disadvantage. One way to get around this difficulty would be to decide that the producer is really primarily interested in market possibilities only within, say, a radius of 400 miles, or only within the range of overnight truck delivery. It could then demarcate such areas around various points and select as its location the center of the area having the largest market volume. A somewhat more sophisticated procedure would be to apply a systematic distance discount in the evaluation of markets by calculating what is called an index of market access potential for each of a number of possible locations. Thus to compute the potential index Pi for any specific production location (i), the producer would divide the sales volume of each market (j) by the distance Dij from (i) to (j) and then add up all the resulting quotients. Such potential measures have been widely used, with the distance (or transport costs, if ascertainable) commonly raised to some power such as the square. If the square of the distance is used, the potential formula becomes =  j Pi M j Dij ( / ) 2 (where M is market size and D is distance); and any given market has the same effect on the index as a market four times as big but twice as far away. In any ease, when the potential index P has been calculated for various possible locations, the location having the largest P can then be rated best with respect to access to the particular set of markets involved. This measure of "potential," in which each source of attraction has its value "discounted for distance," is also generically known as a gravity formula or model—particularly when the attractive value is deflated by the square of distance over which the attraction operates. The reference to gravity reflects analogy to Newton's law of gravitation (bodies attract one another in proportion to their masses and inversely in proportion to the square of the distance between them). William J. Reilly in 1929 proclaimed the Law of Retail Gravitation on the basis of an observed rough conformity to this principle in the case of retail trading areas (a subject to be examined in more detail in Chapter 8), and John Q. Stewart and a host of others subsequently discovered gravity-type relationships in a wide variety of economic and social distributions. Gravity and potential measures have in fact been applied to almost every important measurable type of human interaction involving distance, and numerous variants of the basic formula have been devised, some of which we shall have occasion to examine later.19 All the shortcut methods described here have been widely used. Though they have been explained here in terms of the measurement of access to markets, or output access of potential locations, they are equally applicable to assessment of the input access potential of locations, when a unit is drawing on more than one source of the same transferable input. The measures can apply also to cases involving the transfer of services rather than goods—for example, measuring the job-access potential of various residence locations where a choice of job opportunities is desirable, or measuring the labor-supply access potential of alternative locations for an employer. But at best, when a unit can serve many markets and/or draw from many input sources, the appraisal of alternative locations in terms of access is a complex matter. There is likely to be little opportunity to use the simple devices discussed earlier in this chapter, such as the balancing off of relative input and output weights, except perhaps as a means of initially narrowing down the range of locational alternatives. In such cases, the maps of cost and revenue prospects will show complex contours rather than simple ones as in the examples discussed earlier; and the evaluation of prospects at different locations will have to approach more nearly an explicit calculation of the expected costs, revenues, and profits at various possible levels of output at each of a large set of locations. For most types of locational decision units, an exhaustive point-by-point approach in which theory and analysis abdicate in favor of pure empiricism would be so expensive as to outweigh any gain from finally determining the ideal spot. So there will always be a vigorous demand for usable shortcuts, ways of narrowing down the range of location choice, and better analytical techniques. The challenge to regional economists is to provide techniques better than hunch or inertia and cheaper than exhaustive canvassing of locations. 2.9 SUMMARY This chapter deals with location at the level of the "location unit" as exemplified by a household, business establishment, school, or police station. Location in terms of larger aggregates such as multiestablishment firms or public agencies, industries, cities, and regions is taken up in later chapters. A single decision unit (for instance, a firm) can embrace one or more location units. Prospective income is a major determinant of location preference, but even in the ease of business corporations in which the profit motive is paramount there are other significant considerations, including security, amenity, and the manifold political and social aims of public and institutional policy. Uncertainties, risks, and the costs of decision making and moving contribute to locational inertia and often to concentration. The basis for locational preferences can be expressed generally in terms of a limited set of location factors involving both supply of locally produced and transferable inputs, and demand for transferable outputs satisfied both locally and at a distance; the inputs and outputs include intangibles. Various techniques exist for assessing the relative strength of location factors affecting a specific decision or type of location unit. Location factors themselves have characteristic spatial patterns of advantage. Some factors, such as rent, may be relevant chiefly in comparing locations on a microspatial (small area) basis; other factors may emerge as important for macrospatial comparisons, involving locations far apart. Some location factors are primarily related to concentration: They may be most favorable in, say, large cities or dusters of activity or, alternatively, in small towns or rural locations. Other location factors involve transfer of input or output, so that locational advantage varies systematically according to distance. Other location