Frank Albert Fetter, The Economic Law of Market Areas (1924)

Frank Albert Fetter’s theoretical journal article examines how competing markets divide geographical territory when buyers compare prices inclusive of transportation costs. Its central move is to turn a familiar proposition about price differences between trading centers into a precise account of the boundary between their customer districts. Fetter treats the designation “law” cautiously: the proposed relationship does not have the status of a physical law, but mathematical formulation can clarify economic relationships otherwise obscured by vague accounts of competition. The article proceeds from definitions and earlier treatments of market limits to a geometrical deduction, a diagram of changing market areas, and qualifications concerning actual freight systems.

Fetter distinguishes selling markets, from which goods move outward to consumers, from buying markets, toward which dispersed producers send their output. He develops the argument principally for selling markets under competitive conditions, restricting it to standardized, homogeneous commodities. This restriction matters: differentiated goods can attract socially or economically distinct purchasers scattered across noncontiguous territories, making geographical proximity an insufficient explanation of market membership. For homogeneous goods, however, the relevant comparison is between delivered costs.

Two competing centers cannot ordinarily sustain a price difference greater than the cost of shipping between them: the cheaper center would displace its rival. Transportation thus gives each market a local advantage analogous to a protective tariff. Yet this familiar limit on prices does not establish how the territory between and around the centers is divided. Fetter credits J. B. and J. M. Clark with identifying a meeting point along the direct route between markets, while criticizing their hesitation to accept a definite boundary rather than a zone of indifference. His own earlier analysis also remained confined to that single line. The new problem is to determine the boundary’s shape on a surface map.

The location is on the boundary, or point of indifference, in respect to two markets when the sum of base prices and freights is exactly equal.

This equality supplies the organizing principle. A purchaser on the boundary pays the same delivered cost from either center; purchasers on either side obtain a lower delivered cost from one of them. If freight charges are proportional to distance and shipments follow straight routes, equal delivered costs imply a constant difference between distances to the two centers. Those centers become the foci of a hyperbola. Fetter states the resulting law explicitly:

The boundary line between the territories tributary to two geographically competing markets for like goods is a hyperbolic curve. At each point on this line the difference between freights from the two markets is just equal to the difference between the market prices, whereas on either side of this line the freight difference and the price difference are unequal. The relation of prices in the two markets determines the location of the boundary line: the lower the relative price the larger the tributary area.

The law makes market territory endogenous to relative prices rather than a district fixed in advance. Equal base prices yield a straight perpendicular bisector between the centers. Unequal prices bend the boundary around the higher-priced market, reducing its territory. At the limiting differential—the entire freight charge between the centers—the higher-priced market’s district contracts to a line extending away from its competitor. Absolute price movements matter only insofar as they alter the differential. Higher freight rates, meanwhile, strengthen local protection: they permit the higher-priced center either to serve a larger territory at the existing differential or to retain its territory at a larger differential.

The diagram connects this geometry to supply and demand. With one market’s price fixed at 100 and freight between centers at 10, successive curves mark the territory available to the other center at different prices. As its supply expands and its price falls, that center both stimulates demand within its existing district and acquires customers previously served by its rival. Market boundaries therefore express adjustments in competitive demand and supply, not merely distances on a map.

This deduction also challenges statistical arguments built on arbitrary geographical divisions. Fetter describes an unnamed practical case in which shipment balances were calculated across a roughly perpendicular straight boundary. A district’s apparent shortage was then used to argue that its central market price must cover the other center’s price plus the full freight between them. But deliveries into a district need not reach its central market, and the district’s assumed boundary may already misrepresent the competitive allocation of customers.

The outcome of this balance sheet of shipments is quite dependent upon the line of division chosen, both as to the point at which it intersects the line of shortest distance and even more as to its shape and direction at either side of the intersection.

The methodological consequence is that territorial statistics cannot establish a pricing argument without a defensible account of the territory itself. For buying markets, the direction of the price advantage reverses: a higher buying price attracts producers from a wider area because their choice depends on receipts net of freight.

Fetter closes by limiting the claim’s empirical reach.

It is merely in the nature of a first approximation to the solution of the various practical problems that may arise.

Tapering rates, indirect routes, water transport, and topographical obstacles distort the geographical curves. Equality of delivered costs remains the governing relationship, but actual maps need not display ideal hyperbolas. Fetter mentions inductive verification without presenting it here. The article’s contribution is consequently a theoretical clarification with implications for industrial pricing, antitrust and price regulation, tariffs, and marketing: spatial competition must be analyzed through relative prices and transportation costs together, rather than through administratively convenient districts or the expectation that every seller should compete everywhere.