From Stock to Flow Capital Inputs for Agricultural Production Functions: A Microanalytic Approach

Abstract

CAPITAL is a multiperiodic input of production: it jointly supplies outputs with different time subscripts, and it contributes a major part of its services to future rather than to current production. While the distinction between current and future services may be unimportant for some purposes of analysis, production theory is exclusively concerned with the former. Only the current service flow of capital goods properly belongs as an input to the production function. The flow of capital services in a period of time, e.g., a year, would be approximated in a perfect market by the rental price of the capital assets per unit of time, times the units worked in a year. Unfortunately, data on work units performed by capital assets are notoriously scanty-to say nothing about the monetary evaluation of such services. Thus starts the search for an acceptable proxy, which satisfies the criterion of data availability, to be used as capital input. It mercifully turns out that for certain purposes a proxy is a perfect substitute for capital service flows as long as there is proportionality between the two concepts. In production functions of a multiplicative form, the Cobb-Douglas for instance, the constant term will absorb the proportionality and the elasticities of production will not be affected. However, the proportionality property, although implicitly assumed in most empirical studies, is very difficult to satisfy. The common practice in empirical research on the theory of production has been to measure capital inputs by a stock concept-be it gross or netted by a depreciation factor. Therefore, in the next section I examine the relationship that exists between service flows and the value of the stock of capital, before and after depreciation. The search for an acceptable proxy having failed, Section 3 of the paper is devoted to deriving the ideal service flow input itself from capital stock data that are readily available. In the final section, I provide the empirical vindication of the use of the capital service flow input in production functions. Microeconomic Greek agricultural data are used for this application.

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