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variable revenue analysis

  An approach to industrial location theory concerned with spatial variations in revenue. It concentrates on the demand side of the industrial location problem, as opposed to the cost side addressed in variable cost analysis.

Total revenue may be defined as the product of the quantity of goods sold and the price obtainable for them. Revenue in alternative locations is thus:

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where TRi is revenue that can be earned by a plant located at i, Qj is the quantity of goods that can be sold at market j and Pj is the price at j: summation is over all n markets. This expression is a first step to opening up the various determinants of revenue, operating through quantity sold and price charged respectively .

On the quantity (demand) side, sales expectations in any market j will be influenced by a number of variables. The most obvious is population: the more people the greater the demand, other things being equal. Among those other things (which seldom, if ever, are equal) are people\'s incomes and their tastes or preferences, which influence the propensity to consume. Demand generally rises with income but it can fall (which is the case for the so-called \'inferior goods\' that people tend to buy in smaller quantities as they become better off). Tastes may vary with income, but they are also subject to spatial variations in accordance with culture, custom and so on. Another influence on the local level of demand for a good is the availability and price of substitutes.

The other variable in the expression above — price — is discussed under pricing policies. There are various ways in which goods can be priced, and this choice will determine whether price varies from place to place and the pattern that such variations might take. As price falls, more of a good should be consumed, subject to limits on capacity to consume and on the ability of some goods to attract additional sales as price rises, e.g. goods where status is gained by the purchase of things that are expensive. Price and quantity are thus related to each other in determining volume of revenue.

market-area analysis forms an important component of the variable revenue approach. The revenue that a firm can earn may be proportional to the market size or areal extent of the territory over which control can be exerted (see hinterland). However, the same area may yield different levels of revenue, because of the operation of the variables described above relating to the nature of the local population and its demand characteristics.

The analysis of market areas is closely bound up with locational interdependence. The location of one unit of production is seen as dependent on the strategy of competitors, as they seek spatial monopoly or control over market areas. Specific analyses of how firms locate in competition with one another under variable revenue conditions include the Hotelling model and its extensions, which incorporate alternative assumptions as to the elasticity of demand. The variable revenue approach has arisen as much from the development of the theory of imperfect competition in economics as from the realization that the effect of the market on plant location goes further than the cost of distribution (as approached via the aggregate travel model).

The graphic device of the revenue surface portrays spatial variations in the revenue to be derived from the sale of a given volume of output, depicted as a three-dimensional surface with distance along the two horizontal axes and revenue in pecuniary units on the vertical (see figure illustrating variable cost analysis, where it is a spatial constant and thus depicted an a horizontal plane). A section through a revenue surface is a space revenue curve, i.e. a plot of the revenue to be earned from a given volume of sales, in one distance dimension. Revenue surfaces are extremely difficult to identify empirically, and the revenue likely to be earned from alternative locations is normally estimated less directly .

The variable revenue approach is prone to both conceptual and practical difficulties. Although cost variations among alternative locations need not be disregarded completely (for example, they can be built into delivered price from alternative suppliers), the reciprocal relationship of unit cost to price via economies of scale is extremely difficult to handle. If unit cost varies with volume of sales, and this is dependent on price which, in its turn, is influenced by unit costs, then the problem of the optimal location is impossible to resolve. This is why industrial location theory makes such stringent assumptions on either the cost or the demand side.

At a practical level the variable revenue approach is more difficult to apply than variable cost analysis, because it is hard to identify consumer demand schedules. Hence the adoption of alternatives, notably the market potential model. Further complications arise from the actual practice of decision-making under the conditions of uncertainty characterizing real market competition. The unpredictability of consumer behaviour in choosing which outlet to patronize is a further complication. (DMS)

Suggested Reading Smith, D.M. 1981: Industrial location: an economic geographical analysis, 2nd edn. New York: John Wiley. Smith, D.M. 1987: Neoclassical location theory. In W. Lever, ed., Industrial change in the United Kingdom. London: Longman, 23-37 .



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