les be and disadvan tages. till do not al of 10 cents put to him melt one ton of iron or our answer would se two locations indicative tions for thi rwout wage tabnsn s to refer to from a wider supply area, be very elastic Ajax's entry as a buyer would not drive the e economies of larger volume would be sufficient to make E ght that it would be better to operate on a reduced scale in Burton City. Similarly, some locations will offer a more elastic demand for the output than others, and here7 have been asked to rate them in relative importance, either by adjectives ("extremely important," "not very important," and so forth) or on some kind of simple point system. This primitive approach is unlikely to provide any insights that were not already available and may sometimes be positively misleading. In the first place, it provides no real basis for a quantitative evaluation of advantages and disadvan tages. If, for example, "taxes" are given an importance rating of 4 by some respondent, and "labor costs" a rating of 2, we still do not know whether a tax differential of 3 mills per dollar of assessed property valuation would offset a wage differential of 10 cents per man-hour. The respondent probably could have told us after a few minutes of figuring, but the question was not put to him or her in that way. A further shortcoming of the subjective rating method is that respondents are implicitly encouraged to overrate the importance of any location factors that may arouse their emotions or political slant, or if they feel that their response might have some favorable propaganda impact. It has been suggested, for example, that employers have often rated the tax factor more strongly in subjective-response surveys than would be supported by their actual locational choices. A more quantitative approach is often applied to the estimation of the strength of various location factors involving transferred inputs and output. For example, we might seek to determine whether a blast furnace is more strongly attracted toward coal mines or toward iron ore mines by comparing the total amounts spent on coal and on iron ore by a representative blast furnace in the course of a year, and such a figure is easily obtained. Unfortunately, this method could not be relied on to give a useful answer where the amounts are of similar orders of magnitude. We might use it to predict that a blast furnace would be more strongly attracted to either coal mines or iron ore mines than it would be to, say, the sources of supply of the lubricating oil for its machinery; but it may be assumed that we know that much without any special investigation. A little closer to the mark, perhaps, would be a comparison between the annual freight bills for bringing coal to blast furnaces5 and for bringing iron ore to those furnaces. But this comparison is obviously influenced by the different average distances involved for the two materials as well as by the relative quantities transported, so again it tells us little. We might instead simply compare tonnages and say that if it takes coke from two tons of coal to smelt one ton of iron ore, the choice of location for a blast furnace should weight nearness to coal mines twice as heavily as nearness to iron ore mines. Here we are getting closer to a really informative assessment (for these two location factors alone), although our answer would be biased if one of the two inputs travels at a higher transport cost per ton-mile than the other (a consideration to be discussed later in this chapter). It would appear that in order to assess the relative importance of various location factors for a specific kind of activity we need to know the relative quantities of its various inputs and outputs. If, for example, we want to know whether labor cost is a more potent location factor than the cost of electric power, we first need to know how many kilowatt-hours are required per man-hour. If this ratio is, say, 20, and if wages are 10 cents an hour higher in Greenville than in Brownsville, it would be worthwhile to pay up to ½ cent more per kilowatt-hour for power in Brownsville (assuming of course that these two locations are equal with respect to all other factors, including labor productivity). This kind of answer is what the locator of a plant would need; but it should be noted that it is not necessarily indicative of the degree to which we should expect to find this kind of activity attracted to cheap power as against cheap labor locations. Perhaps differentials of ½ cent per kilowatt-hour or more are frequently encountered among alternative locations for this industry, whereas wage differentials of as much as 10 cents an hour are rather rare for the kind of labor it uses. In such a case, the power cost differentials would show up more prominently as decisive locational determinants than would wage differentials. Thus we conclude that, for some purposes at least, we need to know something about the degree of spatial variability of the input prices corresponding to the location factors being weighed against one another. When we consider a location factor such as taxes, we encounter a further complication: There is no appropriate way to measure the quantity of public services that a business establishment or household is buying with its taxes or to establish a "unit price" for these services. The only way in which we can get a measure of locational sensitivity to tax rates is to refer to the actual range of rates at some set of alternative locations and translate these into estimates of what the tax bill per year or per unit of output would amount to at each location. This procedure has been followed in some actual industry studies, such as the one carried out by Alan K. Campbell for the New York Metropolitan Region Study.6 A major relevant problem is how to measure and allow for any differences in the quality of public services; this is related to tax burdens, although not in the close positive correspondence that one might be tempted to assume. Insight into still another problem of assessing relative strength of location factors comes from consideration of the implications of a differential in labor productivity. If wages are 10 percent higher in Harkinsville than in Parkston, but the workers in Harkinsville work 10 percent faster, the labor cost per unit of output will be the same in both places, and one might infer that neither place will have a net cost advantage over the other. In fact, however, the speedier Harkinsville workers will need roughly 10 percent less equipment, space, and the like than their slower counterparts in Parkston to turn out any given volume of output; so there will be quite a sizable saving in overhead costs in Harkinsville. This advantage, though resulting from a quality difference in production workers, will appear in cost accounts under the headings of investment amortization costs, plant heating and services, and perhaps also payroll of administrative personnel and other nonproduction workers. A somewhat different kind of identification problem arises when there are substantial economies or diseconomies of scale. Suppose we are trying to compare two locations for the Ajax Foundry, with respect to supply of the scrap metal it uses as a principal input. The going price of scrap metal is lower in Burton City than in Evansville; but only relatively small amounts are available at the lower price. If Ajax were to operate on a large scale in Burton City, it would have to bid higher to attract scrap from a wider supply area, whereas in Evansville scrap is generated in much larger volume and supply would be very elastic: Ajax's entry as a buyer would not drive the price up appreciably. In this case, Ajax must decide whether the economies of larger volume would be sufficient to make Evansville the better location or so slight that it would be better to operate on a reduced scale in Burton City. Similarly, some locations will offer a more elastic demand for the output than others, and here