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Part II of this paper is to be published in:Papers, Regional Science Association, vol. 15, 1965.
See K. Arrow and G. Debreu, “Existence of an Equilibrium for a Competitive Economy,”Econometrica, vol. 22 no. 3. July 1954, pp. 265–290; and W. Isard and D. J. Ostroff, “Existence of a Competitive Interregional Equilibrium,”Papers and Proceedings of the Regional Science Association, vol. 4, 1958, pp. 49–76.
Since we have been interested primarily in the extension of the system to which the basic Arrow and Debreu analysis applies, we have not incorporated certain refinements of it in our proof. For such refinements, the reader is referred to, among others: G. Debreu, “New Concepts and Techniques for Equilibrium Analysis,”International Economic Review, vol. 3 no. 3, Sept. 1962, pp. 257–273; G. Debreu, “A Social Equilibrium Existence Theorem,”Proceedings of the National Academy of Sciences, vol. 38, 1952, pp. 886–893; Gerard Debreu,Theory of Value, New York, Wiley, 1959; L. W. McKenzie, “On the Existence of General Equilibrium for a Competitive Market,”Econometrica, vol. 27 no. 1, Jan. 1959, pp. 54–71; J. Trout Rader,Edgeworth Exchange and General Economic Equilibrium, Ph. D. Thesis, Yale University, 1954, mimeographed and, in part, printed inYale Economic Essays, vol. 4, no. 1, Spring, 1964, pp. 133–182.
For full discussion of this point, see: W. Isard and M. F. Dacey, “On the Projection of Economic Behavior in Regional Analysis, Parts I, II,”Journal of Regional Science, vol. 4 no. 1 and 2, respectively, Summer, Winter, 1962, pp. 1–34, 51–83.
We speak of the diverse labor skills which an individual may offer as all falling in the single commodity categorylabor. The analysis is unaffected when labor services (or other goods and services) are categorized as more than one commodity.
APPENDIX I is not published with this paper. It has been published as: W. Isard and T. H. Tung, “Selected Non-Economic Commodities: Definitions, and Speculations on Supply and Demand, Measurement and Utility,”Papers, Regional Science Association, vol. 13, 1964.
However, see footnote 42, p. 32, below for an alternative approach to this conceptual problem.
That is, it is assumed that all consumption, production and other activity in each region takes place at a single point at which all individuals of the region reside. Thus, the continuous space of reality can only be approximated by the postulate of afinite number of regions, no matter how large this finite number may be.
For definition, see: Section 1.2.5., below.
That there are the same number of organizations (and later individuals and exporters) in each region is inessential to the analysis. This convention nowhere affects the analysis and is employed merely to simplify notation. It is consistent with different numbers of actual organizations in the several regions since we may always define and introduce into the system non-existent units which consume and produce zero quantities of all commodities.
APPENDIX II is not printed with this manuscript. It will be forthcoming as: W. Isard, “Parsons and Types of Individuals and Organizational Acts.”
In the discussion to follow we shall in general have in mind the organizations of reality which are by and large hybrids of two or more of the four types of organizations, each type characteristic of one of Parsons' four subsystems. See the discussion of APPENDIX II. Thus we may speak of an organization whose input-outcome vector is dominated by the firstl commodities and thus tends to be an economic-type organization. Yet, it may produce certain commodities asc-sociality,c-solidarity, andc-respect to use as intermediate goods in current production, thereby to raise morale and provide other incentives to achieve higher worker productivity. Or we may speak of an organization whose dominant outcomes arec-skill andc-enlightenment. This organization, tending to be educational (pattern-maintenance) in character, may perform research services for the government and industry, and may run enterprises for pure economic profit, thereby to accumulate funds (e.g. endowment) for long-run investment in the production ofc-enlightenment. Here, such strage items as steel ingot, magnesium, chemicals, steel scrap may be involved as inputs in its input-outcome plan. The conceptual framework is, of course, designed to treat any organization, whatever its character, in the same general way and therefore does not need to differentiate among organizations.
From the standpoint of the development of a general equilibrium framework, it is desirable as far as possible to disaggregate by commodity thec-sanctions of society in order to identify their differential effects upon different commodity-producing and commodity-consuming activities.
For purposes of this manuscript we assume that society can bestow upon and exact from individuals and organizations unlimited quantities ofc-sanctions. Analysis of the process by which society acquires the authority to levy both positive and negative amounts ofc-sanctions, and of the forces governing the extent of this authority involves dynamic considerations of the cultural subsystem which is beyond the static framework employed in this manuscript.
Rigorously speaking, social sanctions should be subdivided into two parts. One part would represent social sanctions which are priced and converted by society into a money payment (a money subsidy). The second part would represent social sanctions which are valued by a nontangible price and thus would take on a nontangible value (i.e. value not easily stated in terms of a currency). Since in our conception the latter by far dominates the former, we shall assume that all social sanctions when priced yield a nontangible value.
To facilitate his understanding of the conceptual framework, the reader may adopt a convention. He may assume that all nontangible income is spent onc-respect (commodityl+3), i.e., is held in terms of stocks of this commodity. Then implied net returns, hereafter to be designatedi-net returns, would be in terms of value ofc-respect. Or, since the commodityc-respect can be exchanged on each organizational market forc-rectitude,c-affection,c-power, and other commodities, this convention can easily be discarded for other conventions which specify that social sanctions and nontangible income be held in the form of stocks of some other commodity or commodities.
Since we wish to assign to money the same price in each region of a system using the same currency—as exists in reality—we later set the weight and thusc-transfer cost of money at zero. However, in reality, even with the clearing house mechanism among financial institutions—which in part exists to avoid unnecessaryc-transfer of money through balancing out credits and debits on a multilateral basis, and through effecting shifts in the ownership of assets—there may be shipments of money from one region to another. The cost involved may be small, but not negligible—and yet may not interfere with money having the same value among the several regions of the system. Hence, we set an upper limit to the volume of shipment of money, to reflect to some extent the obstacle whichc-transfer cost of money actually imposes.
This part of the assumption may be relaxed since it is not essential for the proof. It is made to avoid cumbersome notation.
For discussion of the concept of transport input, see Walter Isard,Location and Space-Economy, Cambridge and New York, Technology Press and Wiley, 1956.
This particular convention is convenlent but inessential to the proof. Any other can be adopted, such as having the importer responsible for the provision of these services. Since there can be available on the local marketc-transfer services imported from other regions, the competitive mechanism to be detailed below actually determines which region produces thec-transfer services used.
The exporting unit operates under conditions of constant returns to scale.
If he cares, the reader may distinguish several transfer media—e.g. waterway, rail, truck, telephone, mail, radio—and correspondingc-transfer rates, ideal weights and distances. Such introduction of reality is possible, but only with more complicated notation. The competitive mechanism developed below will select from among the several possible media in the performance of any particular export.
According to Parsons, a role is “the structured, i.e., normatively regulated, participation of a person in a concrete process of social interaction with specified, concrete role-partners. The system of such interaction of a plurality of role-performers is, so far as it is normatively regulated in terms of common values and of norms sanctioned by these common values, a collectivity. Performing a role within a collectivity defines the category ofmembership, i.e., the assumption of obligations of performance in that concrete interaction system. Obligations correlatively imply rights.” See: Talcott Parsons, et al,Theories of Society, New York, The Free Press of Glencoe, 1961, vol. I, p. 42.
Again, outcomes with negative values, because of these negative values, are analogous to inputs.
All contributions of economic goods to organizations must go through the economic market.
Ifi ofJ receives income from rights of ownership and membership, he may still be a subsistence farmer, such income being kept as a hoard of money.
One might argue that another technical constraint is that the individual's consumption must exceed a minimum subsistence level, for the notion of an equilibrium is incompatible with a situation in which participants are leaving the social system. In our framework, however, it is utility considerations and not technical constraints which ensure that all individuals can subsist when the system is in equilibrium.
This relationship embodies the essence of exchange, namely, that equal values be involved. Thus, for example, when an individual accepts from an educational organization a wage rate lower than that which prevails on the market of his region, he is in effect (a) receiving other goods in addition to money which exactly balances the deficiency in the wage rate, or (b) making a money contribution to the organization which is equal to the difference between the market rate and the rate which he accepts, and for which he must receive other commodities in exchange, or (c) some combination of (a) and (b).
Arrow and Debreu,op. cit. Since we have been interested primarily in the extension of the system to which the basic Arrow and Debreu analysis applies, we have not incorporated certain refinements of it in our proof. For such refinements, the reader is referred to, among others: G. Debreu, “New Concepts and Techniques for Equilibrium Analysis,”International Economic Review, vol. 3 no. 3, Sept. 1962, pp. 257–273;
Op. cit. Since we have been interested primarily in the extension of the system to which the basic Arrow and Debreu analysis applies, we have not incorporated certain refinements of it in our proof. For such refinements, the reader is referred to, among others: G. Debreu, “New Concepts and Techniques for Equilibrium Analysis,”International Economic Review, vol. 3 no. 3, Sept. 1962, pp. 269–270; andop. cit., ch. 4., respectively.
Observe that in his role of a one-man producer for profit, the individual receives a 100 percent share of profits of this operation.
We justify this assumption by claiming that a meaningful social system must be able to bring inflationary pressures to a halt at some level short of infinity.
In our fiction, we only allow him to change prices in small increments.
For further discussion, see: W. Isard, “General Interregional Equilibrium,”op. cit.; P. A. Samuelson, “Spatial Price Equilibrium and Linear Programming,”American Economic Review, vol. 42 no. 3, June 1952, pp 283–303.
In our conceptual framework, an alternative approach could be followed to yield different prices for a unit of the same non-economic commodity on the different organizational markets of a given region. In this approach, we hold to the classical condition that for any two non-economic commodities which are involved ini ofJ's exchanges at each of two organizational markets in a given region, the ratio of their marginal utilities must be equal to their equilibrium price ratioas perceived by i of J in each to the two markets. Hence, the equilibrium prices of each of the two non-economic commodities,as perceived by i of J, must be the same on both markets. However, recall that the concept of a non-tangible price with reference to a non-economic commodity signifies that there exists no common organized market for such a commodity. The unit of such a commodity is not defined in ways which are generally acceptable to a community at large for which an organized market could have relevance. Consequently, each individual may be taken to define a concrete outcome differently than other individuals in terms of units of non-economic commodities. Now, suppose all participants (including the fictitious organizational participant) perceive a given component of an outcome—say a handshake by the President of a university—as being associated with a specific non-economic commodity—sayc-respect. Suppose the organizational participant sets a value on that component based on the price he sets on the associated non-economic commodity (as he defines a unit of that commodity). Then, since each individual associates with the component (say the handshake) different amounts of the non-economic commodity (sayc-respect), he comes to associate with the value of that component a different price for the non-economic commodity. Hence, theunit price of a given non-economic commodity is in general different for each participant trading at a given organizational market. Hence, the equilibrium price for a non-economic commodity may vary from organizational market to organizational market, although the prices as perceived by the individual trading that commodity at several organizational markets in a given region are the same. Despite the fact that individuals trading at a given organizational market perceive different prices for a non-economic commodity, the operation of the market as described above is not affected. Whenever the organizational participant raises (lowers) the price on a non-economic commodity, he in effect raises (lowers) the price for all individuals and organizations trading at that market. He affects demand and supply in the manner already noted, and he continues to adjust the price of a commodity (as he defines it in the concrete situation) until supply and demand (in terms of his unit definition of the commodity) are equated, or until price falls to zero if supply persistently exceeds demand.
Proof of this theorem is to be developed in Part II to this paper, which is to be published in volume 15,Papers, Regional Science Association.
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They are greatly indebted to Tze H. Tung for constant assistance in the preparation of this manuscript and to Trout Rader, Tony Smith and Karl Vind for helpful criticisms; however, the authors alone are responsible for any shortcomings of the manuscript. The authors are grateful to the National Science Foundation for financial assistance.
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Isard, W., Isard, P. General social, political and economic equilibrium for a system of regions: Part I. Papers of the Regional Science Association 14, 1–33 (1965). https://doi.org/10.1007/BF01940898
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DOI: https://doi.org/10.1007/BF01940898