(forward by Herbert E. Scarf) “Tjalling C. Koopmans was awarded the 1975 Nobel Prize for his work on the theory of optimal utilization of resources. This collection represents Koopmans’ work over the past 15 years on such topics as the representation of preference orderings, the computation of an optimal stationary capital stock, the comparison of economic systems, optimal growth theory, and models of energy and other exhaustible resources.”
“During the last half-century, economic theory and econometrics have undergone a vital transformation. Forma1 mathematical models have become the major vehicle for the presentation of economic ideas-ideas which can then be examined with the logical precision and special methods of argument made available by the language of mathematics. Tjalling C. Koopmans was, and is, one of the leaders of this intellectual revolution.”
“As many of the articles in this volume indicate, Tjalling Koopmans has a remarkable ability to attract a variety of collaborators to his professional ventures. He is gregarious, bold, inquisitive, and capable of initiating and maintaining fruitful relationships with economists, mathematicians, engineers, and scientists from all parts of the world. His qualities of leadership and intellectual involvement have been displayed during his long association with the Cowles Commission and the Cowles Foundation for Research in Economics. For many years, younger scholars have been guided by him in the choice of research topics and the methods of written and spoken ex- position, and visitors have been reminded that the requirements of clarity and logical coherence were never to be discarded when entering the seminar room.”
“Leaders of a scientific revolution combine judgment, intellectual penetration, and personal force. The articles in this volume testify to the presence of these qualities in one of the most distinguished economists of our time.” — Herbert E. Scarf
Contents: Note on a Social System Composed of Hierarchies with Overlapping Personnel; Maximizing Stationary Utility in a Constant Technology; On the Description and Comparison of Economic Systems; Representation of Preference Orderings with Independent Components of Consumption; Representation of Preference Orderings over Time; Some Observations on ‘Optimal’ Economic Growth and Exhaustible Resources; On the Definition and Computation of a Capital Stock Invariant under Optimization; Is the Theory of Competitive Equilibrium With It? Proof for a Case where Discounting Advances the Doomsday; Concepts of Optimality and Their Uses; Examples of Production Relations Based on Microdata; Economics Among the Sciences; Alternative Futures With or Without Constraints on the Energy Technology Mix; The Transition from Exhaustible to Renewable or Inexhaustible Resources; and Additively Decomposed Quasiconvex Functions.