Input Demand Functions Research Articles

Industrial Market Forecasting with Anticipations Data

A forecasting model for industrial markets is developed and illustrated that utilizes publicly available data on anticipated future capital spending and sales. The model is based upon input demand functions derived from a fixed coefficient production function. Since the proposed forecasting method is easy to implement and offers the prospect of reasonably accurate forecasts, it may serve not only as a principal forecast technique but also as a standard of performance against which more elaborate and costly procedures are judged.

On Part-Time Farming

Economic logic and empirical observation suggest that increasing numbers of part-time farms can have important implications for organization of agricultural production and development of rural areas. Production relationships on part-time farms may differ because:1) Farm operators working off the farm may organize resources and respond to price changes differently than full-time operators;2) Part-time operators may have different demand functions for production inputs, particularly land and labor, and3) Part-time operators may achieve different levels of efficiency than their full-time counterparts.

Competitive Firm and the Theory of Input Demand under Price Uncertainty

In this paper, we examine the behavior of the competitive firm faced with making input-hiring decisions under conditions of price uncertainty. Unlike Sandmo and Baron, among others, we show categorically that a marginal increase in uncertainty stimulates a decline in the firm's output, provided the absolute risk aversion is decreasing. Furthermore, the implications of a change in expected price remain unchanged, but those of a change in input price need not be the same as in the certainty case. Specifically, the input demand function is downward sloping only if the production function is well behaved.

THE DEMAND FOR INPUTS AND THE AGGREGATE SUPPLY FUNCTION FOR AGRICULTURE*

This paper presents a theoretical derivation of aggregate supply elasticities from the relevant input demand elasticities. By way of illustration, an estimate of the aggregate supply elasticity with respect to product price for United Kingdom agriculture is calculated. In addition, the paper investigates the supply function that is implied by input demand functions which contain a geometrically declining lag distribution. The paper concludes by suggesting that the indirect estimation of aggregate supply elasticities may well be preferable to direct estimation of the elasticities.

"Inferior Factors" and the Theories of Production and Input Demand

In a previous issue of this Journal,2 I provided an extension of the Allen-Mosak theory of jointly-derived input demand functions3 to cover imperfect competition in the commodity market. One result emerged. Specifically, I could not prove that commodity price alvays varies directly with input price. Further, I was unable to explain why it might not do so. I can now provide an explanation of this perverse behaviour. Indeed, it is possible to extend the analysis of the former paper, to explain precisely the conditions under which the peculiar price variation can occur, and to specify some of the characteristics of production functions that give rise to the phenomenon. Having found the key to this particular puzzle, it is possible to present several interesting extensions of the theories of production and of jointly-derived input demand functions. Before turning to the positive aspects of the paper, a negative result would seem to be worth a sentence or two. Proposition: in general, absolutely nothing can be said about the characteristics of derived input demand functions if there is imperfect competition in the input markets, i.e. if the price a firm pays for an input varies with its usage by the firm. No substantiation of this proposition is offered here, although the reason should be intuitively clear from the model presented below.4 In what follows a sketch of the basic model is first presented. The definition of an inferior of production is then introduced and analysed. In the bulk of the paper, Sections IV to VI, the concept of factor inferiority is used to analyse various aspects of the theories of production and input demand. Section VII is a very brief conclusion.

Production, Prices, and the Theory of Jointly-Derived Input Demand Functions

The theory of derived input demand has been examined intensively for the situation in which there is only one variable input. Only special cases, however, of the theory of jointly-derived input demand functions have been investigated. In 1938 both Mosak and Allen analysed related factor demands under the assumption of perfect competition in the commodity and factor markets.2 Somewhat later Samuelson studied the same problem without the assumption of perfect competition in the product market.3 However, he imposed a different restrictive condition, namely that the firm under consideration be confined to movements along a given production isoquant in response to changes in relative factor prices. The purpose of this article is to generalize the theory of jointlyderived input demands by removing some of the restrictive assumptions contained in earlier studies. In particular, the following assumptions are made: (a) product demand is a function of and varies inversely with product' price, the prices of related commodities remaining unchanged throughout ;4 (b) the firm in question is a perfect competitor in the factor market; and (c) there is a given production function whose first partial derivatives are positive and monotonically decreasing over the relevant range of input quantities. In the case of two variable inputs the results are quite clear and readily explicable in terms of well-known economic magnitudes. Section II is devoted to an exhaustive analysis of this special case. The general case is presented in Section III. The results, in some instances, are not as precise as in the two-factor model. Nonetheless, the general properties of jointly-derived input demand functions may be stated straightforwardly.