Marshall, Predoehl, Isard, Moses and Beyond: Locational Substitution


Related Pages:

Production, Substitution and Location: Historical Contributions & Statements:

Marshall, Alfred, Principles of Economics, Book V, Ch.IV, Paragraph 3: "At the beginning of his undertaking, and at every successive stage, the alert business man strives so to modify his arrangements as to obtain better results with a given expenditure, or equal results with a less expenditure. In other words, he ceaselessly applies the principle of substitution, with the purpose of increasing his profits; and, in so doing, he seldom fails to increase the total efficiency of work, the total power over nature which man derives from organization and knowledge. Every locality has incidents of its own which affect in various ways the methods of arrangement of every class of business that is carried on in it: and even in the same place and the same trade no two persons pursuing the same aims will adopt exactly the same routes..."

Hoover (1948, p.44) recognized the locational implications of complex production substitution patterns (incl. continuous substitution on the input side, the output side and between inputs and outputs) when he stated that "in many industries, also, it is possible and profitable to vary the proportions in which various products are turned out so as get more of those products which can be sold more profitably. Oil refineries, for instance, can vary their yields or various grades of refined products in response to changes in relative demand and price."

Moses' (1958) conclusions:
"If the production function is not homogeneous of the first degree there is no single optimum location (along the arc IJ). The optimum location varies with the level of output. Moreover, if continuous spatial, as well as factor, substitution is possible there will be a different optimum for every level of output. This being so, demand considerations should be introduced into the analysis..."

"....we have given emphasis to the inseparability of three problems:

  1. the optimum output
  2. the optimum combination of inputs
  3. the optimum location."
The crucial theoretical construct which Moses uses to arrive at this conclusion is the
spatial (or locational) iso-outlay line.

Walter Isard, General Theory, M.I.T.Press, 1969, p.106:

"Formal location theory may be viewed as treating an elaborate substitution problem (both in the large and the small) wherein is determined simultaneously for an organization the optimal location or set of locations and the optimum combination of inputs and outputs for these locations. Since prices of inputs and outputs vary with location, and since transport (transfer) and communication costs are involved especially when the sources of inputs, the sites of production and other activities, and markets do not coincide, the substitution problem breaks down into a number of partial substitution problems many of which have spatial aspects. There may be substitution between
  • transport inputs on one raw material or output and transport inputs on a second raw material or output,
  • transport outlays on one set of inputs and outputs and those on a second set of inputs and outputs,
  • between transport outlays and labor outlays,
  • or power outlays,
  • or capital outlays
  • or tax outlays
  • between transport outlays and production outlays in general,
  • between any two types or groups of production outlays,
  • between any one type or group of outlays and any type or group of revenues,
  • between types and groups of revenues,
  • and so forth.

Implied by such substitutions are different factor proportions, output mixes, and scales for each location or pattern of locations that may be considered. Optimization principles govern the paths of substitution."

Other Web Sites:

Production Functions by Elmer G. Wiens [10/02]


Beyers, William B. and Günter Krumme "Multiple Products..." (1974)

Dicken, Peter and Peter Lloyd. Location in Space: Theoretical Perspectives in Economic Geography. (3rd edition), 1990.

Emerson, David L., "Optimum Firm Location and the Theory of Production," Journal of Regional Science, 13(3), 1973, 335ff.

Hoover, Edgar. Location of Economic Activities. 1948, pp.44-5. ("Substitutability of Materials or Products")

Isard, Walter, "The Contributions of Predoehl to Location Theory and Regional Science," Jahrbuch fuer Sozialwissenschaft, 14(3), 1963, 22-8.

Isard, Walter. Location and Space Economy. 1956,

Isard, Walter Distance Inputs and the Space-Economy 1 Part I: The Conceptual Framework, Quarterly Journal of Economics, Vol. 65, No. 2. (May, 1951), pp. 181-198. ( JSTOR Online)

I. Empirical regularities and the distance factor, 181.--II. The need for and definition of distance inputs, 186.--III. Distance inputs contrasted with capital inputs: spatial roundaboutness and extent of production; space preference and discounting, 190.--IV. Transport rate: the price of a distance input, 195.--V. Distance inputs and the classification of factors, 197.

Isard, Walter, Distance Inputs and the Space Economy Part II: The Locational Equilibrium of the Firm, Quarterly Journal of Economics, Vol. 65, No. 3. (Aug., 1951), pp. 373-399. ( JSTOR Online)

VI. Transport-oriented equilibrium under simplified conditions, 373.--VII. Transport-oriented equilibrium with realistic rate structures, 379.--VIII. Substitution between outlays and revenues and other forms of orientation, 390.--IX. Equilibrium with a real markets and material sources, 395.--X. Conclusions, 398

Isard, Walter. General Theory. 1969, p.106 ("Extension of Location Theory to Embrace the Spatial Pattern of Decision-Making Authority")

Marshall, Alfred. Principles of Economics, 8th edition, 1920, Reprinted 1959, Book V, Chapter IV, Paragraph/Section 3 pp.295f. ("The Principle of Substitution") [also here!]

Miller, Steven M. and Oscar W. Jensen, "Location and the Theory of Production: A Review, Summary, and Critique of Recent Contributions," Regional Science and Urban Economics 8, 2 (May 1978), 117-128.

Moses, Leon, "Location and the Theory of Production," Quarterly Journal of Economics 72(1958), 259-72.

Ponsard, Claude. History of Spatial Economic Theory.

  1. Substitution and Location (Predoehl), pp.34ff.
  2. Substitution between Transport Inputs (Isard), p.92
  3. Weber's Problem Generalized (Moses) p.103.

Predöhl, Andreas, "The Standortproblem in der Wirtschaftstheorie," Weltwirtschaftliches Archiv, 21 (1925), 294-331.

Predöhl, Andreas, The Theory of Location in its Relation to General Economics. Journ. of Political Econ. 36, 1928, 371-90. ( JSTOR-Online)

Sakashita, Noboru, "Production Function, Demand Function and Location Theory of the Firm," Papers, Regional Science Association, 20 (1968), pp.109-22.

Woodward, Robert S., "The Iso-Outlay Function and Variable Transport Costs," Journal of Regional Science, 13(3), 1973, pp.349-55.

Wright, W.David C., "Some Substitution Effects in the Location Decision of a Firm," Journ of Political Economy, July/Aug 1971, pp.903ff.


Isard's and Moses' Locational Triangle with (Substitution) Arc

[Transformation Curves]

Transformation Curves (at different scales of production)
Source: Beyers & Krumme, "Multiple Products..." (1974)

Mon Oct 28 08:22:03 PST 2002 - Here is another important place to find something about substitutiton:

Mon Oct 28 07:42:50 PST 2002 -

On Mon, 28 Oct 2002, you wrote:

> after reviewing my notes, the readings, and the website, there is still
one concept I am unsure space can be introduced into 
problems...I think it deals with Moses' iso-outlay line, but am not there somewhere I can look to help clarify. Should I worry
about this concept for the midterm?  Thanks.

Date: Mon, 28 Oct 2002 07:31:29 -0800 (PST)

Subject: Re: midterm question

Yes, Moses has expressed it most explicitly. Based on his elaboration, one
can generalize the substitution problem and include the output side and
other variables which may significantly interact with space-related costs.
On top of that, we suggested in class that space can come into play via
	a) different market conditions for inputs and outputs in space
(thereby affecting the price-relationships for inputs and outputs)
	b) access to different production technologies at different
locations leading to different families of isoquants (on the input side)
and transformation curves (on the output side).

The results would be (compare with Moses' formulation!) that the location
problem may not be solvable without also determining a host of other
variables; or that these other variables may become important
(interdependent) location factors.

These would be the pertinent pages:

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