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Keio Economic Society, Keio University
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  • Economics
  • Mathematics


The paper is an attempt to overcome some of the major difficulties inherent in the usual notion of the tatonnement process as applied to an economy with production. First, firms are not likely to adjust their production plans sensitively to price changes arising in the process which prohibits actual production and trade of commodities. Second, factors of production are not gross substitutes for each other under normal conditions so that the very basis of the Arrow-Block-Hurwicz theorem, fundamental in the stability analysis, is rather vacuous in the production model. Third, there is no place for money in the entire setting with the result that the issue of the stability of money equilibrium prices is made irrelevant. To get around these difficulties, the paper envisages an economic process extending over many inter-related periods with money functioning as a means of payment. A unit period of the short run economic activities, comparable to the Hicksian week, is supposed to consist of two sub-periods, the first devoted to production, and the second to consumption. The paper presents three distinct results. The first two results are concerned with the existence and global stability of the market equilibrium in each sub-period. In particular, the commodity market equilibrium is shown to be globally stable under conditions weaker than the gross substitutability with the indication that the explicit introduction of money as a means of payment adds to the stability. The last result is concerned with a simple process of firms' interperiodical price adjustment in terms of expectation. This process is shown, by the application of the Arrow-Block-Hurwicz theorem, to be globally stable under the weak gross substitutability only with respect to commodities.

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