The aggregated excess demand function and other aggregation procedures

Summary Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn2 commodities to all of the 2 ⁿ –(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k2 candidates over a space of n2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 ⁿ –1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this anything can happen conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.I am pleased to acknowledge conversations with L. Hurwicz, A. Mas-Colell and C. Simon about this material. In particular, I want to thank J. Jordan for his several helpful suggestions. Also, I benefited from comments made at meetings and seminars where these results were presented; this includes a June, 1990, conference in Stockholm, Sweden. Some stylistic suggestions were made by Arvid and Padon Kalinen. This research was supported, in part, by NSF Grant IRI-8803505.     

An appreciation of our referees

Editorial

An appreciation of our referees     

Operational Research and the environment

The discipline of Operational Research (OR) is primarily concerned with improving the effectiveness and efficiency of decision processes. These processes take place everywhere in society: industry, banking, agriculture, government, politics. Frequent use of mathematical optimization models is typical of OR. Since the early '80s these models are increasingly packaged in a user-friendly way, as Decision Support Systems. In the following we will illustrate how OR can be used to describe and solve a number of environmental problems.     

On modeling incentive systems which utilize pollution charges for pollution abatement

This paper examines a scheme of economic incentives for environmental protection, in which spatially differentiated pollution taxes are in use in compensating the pollution abatement costs. A simple mathematical model is described which determines an incentive system that encourages polluters to reduce the discharges to an acceptable level of ambient quality standards in a cost-effective manner. It is shown that the vector of pollution charges has to be proportional to the marginal abatement cost vector, but is smaller than the latter in magnitude. It is demonstrated that a necessary incentive effect may be achieved even if the total pollution charge is much lower (about three times) than the total abatement costs. It is also estimated how this charge incentive system reconciles conflicting criteria of cost-effectiveness and of equity. These conclusions are verified by numerical experiments with real data.     

Determinants of technical change: Empirical evidence from Switzerland

The purpose of this paper is to analyse both theoretically and empirically those factors which underlay the—empirically observable—inter-industry differences in technical progress. At the theoretical level economists agree more and more that technical progress can be explained at the industry level ey the following three factors: 1. the technological opportunities, 2. the appropriability conditions, meaning the ability to capture and protect the results of technical innovations, and 3. the market demand conditions.The basic theoretical model was tested with the help of two sets of Swiss data. One set was made available by Swiss Federal Office of Statistics and consists of quantitative information on R&D expenditures, R&D personnel, total employment and sales figures for 124 (4-digit SIC) industries for the year 1986. The second set was derived from a survey I carried out in the summer of 1988. 940 industry experts were approached: 358 of them, or 38 percent, covering 127 industries, completed the questionnaire. The items on the questionnaire were related to the two supply-side determinants of technical progress—items 1. and 2. above. For the empirical specification of the theoretical model, technical progress (as the dependent variable) was measured by three indicators: an output indicator, representing the introduction rate of innovations since 1970; two input indicators, share of R&D expenditures in sales and share of R&D personnel in total employment. All data were aggregated at the industry level (4-digit SIC). Three equations were estimated individually, using the OLS, GLS and Tobit methods.