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This volume contains a selection of Professor Uzawa's important contributions to mathematical economics. Subjects covered by these nineteen essays include consumption, production, equilibrium, capital, growth, planning, international trade, and the theory of social overhead capital. Written in the 1960s and early 1970s, the papers form a basis upon which economic theory has developed over the last twenty years. The collection includes some of Uzawa's classic contributions, such as 'Preference and Rational Choice in the Theory of Consumption' (presented at the First Stanford Symposium), 'Time Preference, the Consumption Function, and Optimum Asset Holdings', 'Neutral Inventions and the Stability of Growth Equilibrium', 'On a Two-Sector Model of Economic Growth', 'Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth', and 'On the Economics of Social Overhead Capital'. The collection will be useful not only in understanding the nature of the development in economic theory today, but also in reflecting upon the direction toward which economic theory will be advancing in the future

I feel greatly honoured to have been invited to participate in the inaugural conference of Environment and Development Economics. I should like first of all to congratulate Karl-Göran Mäler, Partha Dasgupta and Charles Perrings on the inauguration of the new journal and wish it to be successful in opening an entire new vista in economics.

AbstractMany problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maximands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.