Franklin M. Fisher

The Existence of Aggregate Production Functions

This paper discusses recent work on the existence of aggregate production functions in models in which capital goods are specific to firms and cannot be used interchangeably. It is found that this raises problems not only for capital aggregation but also for the existence of labor and output aggregates. Recent work on the question of using aggregate production functions as approximations is also discussed.

Returns to Scale in Research and Development: What Does the Schumpeterian Hypothesis Imply ?

Joseph Schumpeter argued that there are increasing returns in R & D both to size of R & D establishment and to firm size. This has been taken to imply that the combination of small firms into big ones would increase R & D output. Tests have been attempted in the literature looking at the relation between scale and R & D input. The present paper shows that these tests are inappropriate. Moreover, the stated conclusion as to R & D output does not follow from Schumpeters hypothesis. Indeed, it is very nearly true that none of these propositions can be derived from any other.

An econometric model of the world copper industry

This paper discusses a complete model of the world copper economy. Supply equations for primary copper are estimated for four principal producing countries and the rest of the world; demand equations are estimated for the United States, Europe, Japan, and the Rest-of-World. Scrap supply equations are estimated for the U.S. and non-U.S. sectors as are price adjustment equations. The model is closed with a net input equation for the United States and various identities. The two separate copper markets (U.S. and non-U.S.) are converted by inputs, the generally free London Metal Exchange and scrap markets, and the price-setting behavior of U.S. producers. The copper market is found to be characterized by low short-run but very high long-run price elasticities, making for considerable sensitivity to exogenous forces. The model, fitted to 1948-1969 data, is used for forecasting and simulation experiments. Generally, short-run forecasts are good and longer-run forecasts are not very satisfactory. Perhaps the most interesting finding of the simulation is the prediction that Chilean output would be very sluggish even in the absence of nationalization and that Chilean revenues would be substantially increased were the Chilean government to increase domestic mine production and to allow world prices to adjust accordingly.

On the Misuse of the Profits-Sales Ratio to Infer Monopoly Power

The common use of the profits-sales ratio as a measure of the Lerner index of monopoly power is flawed, even with the assumption of constant returns, because of problems connected with the valuation of capital. The size of the error is related to the cost of capital, the growth rate of the firm, the depreciation method used, and, most important, the shape of the stream of benefits resulting from an investment. Examples show that the error can be quite large; further, the error is likely to be systematically related to the variables used in regression studies.

Optimal water management and conflict resolution: The Middle East Water Project

[1] In many situations, actual water markets will not allocate water resources optimally, largely because of the perceived social value of water. It is possible, however, to build optimizing models which, taking account of demand as well as supply considerations, can substitute for actual markets. Such models can assist the formation of water policies, taking into account user-supplied values and constraints. They provide powerful tools for the system-wide cost-benefit analysis of infrastructure; this is illustrated by an analysis of the need for desalination in Israel and the cost and benefits of adding a conveyance line. Further, the use of such models can facilitate cooperation in water, yielding gains that can be considerably greater than the value of the disputed water itself. This can turn what appear to be zero-sum games into win-win situations. The Middle East Water Project has built such a model for the Israeli-Jordanian-Palestinian region. We find that the value of the water in dispute in the region is very small and the possible gains from cooperation are relatively large. Analysis of the scarcity value of water is a crucial feature.

Household Equivalence Scales and Interpersonal Comparisons

Recent papers have used household equivalence scales to construct measures of welfare inequality. This procedure rests on an often implicit value judgement, namely, that if, after adjustment for demographic characteristics, two households are on the same indifference curve, they are equally well off. That value judgement is not compelling, and there are situations in which it is ethically repugnant. This is particularly likely if tastes are functions of past experience and income.

Analyzing agricultural demand for water with an optimizing model

Abstract The paper introduces an optimizing linear model for analysing agricultural production under various water quantities, qualities, timing, prices and pricing policies. The model is designed to serve as a decision-making tool for planners of agricultural production on district and national levels. The output solutions provide the optimal mix of water-consuming activities to maximize the net income of the agricultural production of the districts and the water demands under various prices. It also provides the user with procedures to carry out ‘if–then’ sensitivity and scenario analyses and to generate optimal water demand curves. The paper presents the formulation of the model, indicating and analysing problems of linearity and scaling, the steps undertaken to examine and verify it, optimal water demand curves for eight districts in Israel (separately and as an integrated unit) and calculated estimates of water demand elasticity.

A Note on Estimation from a Cauchy Sample

Abstract A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.

An inter-seasonal agricultural water allocation system (SAWAS)

Abstract This paper introduces a linear programming optimization model for analyzing inter-seasonal allocation of irrigation water in quantities and qualities and their impact on agricultural production and income. The SAWAS model is a developed version of the Agricultural Sub-Model (AGSM). In this research, we stress water scarcity as a problem that arises when water is not found in proper quantity and quality at the appropriate place and time. The model is designed to serve as a decision-making tool for planners of agricultural production on both the district and the regional level. It generates an optimal mix of water-demanding activities that maximizes the net agricultural income of the districts and gives the water demands under various prices. It also provides the planner with tools to carry out ‘what-if’ experiments and to generate optimal water demand curves. A principal feature of SAWAS is the use of demand and the benefits from water together with costs and optimization within the agricultural sector to specify the optimal usage of different water qualities. Hence the agricultural planner can use the outputs of SAWAS in order to bridge the gap between the limited water resources and the increased agricultural production in an area that suffers from severe water scarcity. The paper applies the SAWAS model to the Jordan Valley in Jordan.

The Costs of Automobile Model Changes since 1949

T HIS paper reports estimates of the costs to the consumer of the changes in private automobile specifications that took place during the 1950s. Throughout we concentrate on the costs that would not have been expended if cars with the 19491 model lengths, weights, horsepowers, transmissions, and other specifications had been produced in every year. As there was technological change in the industry, we are thus assessing not the expenditure that would have been saved had the 1949 models themselves been continued, but rather the expenditure that would have been saved had such cars been continued but been built with the developing technology. We count as costs not only the costs to the automobile manufacturers themselves of special retooling for new models, but also the direct costs of producing larger, heavier, and more powerful cars,