Optimal Economic Growth and Turnpike Theorems

This chapter is concerned with the long-term tendencies of paths of capital accumulation that maximize, in some sense, a utility sum for society over an unbounded time span. However, the structure of the problem is characteristic of all economizing over time whether on the social scale or the scale of the individual or the firm. The mathematical methods that are used are closely allied to the old mathematical discipline, calculus of variations. The chapter discusses that the utility function depends on time, as in the standard theory of the calculus of variations. Also the function to be maximized is the sum of utility functions for each period over the future. It is described as a separable utility function over the sequence of future capital stocks and corresponds to the integral of calculus of variations. As the consumption of one period influences the utility of later consumption, the separability assumption is not exact. The treatment of utility in a period as dependent on initial and terminal stocks is not a restriction because the usual assumptions that make utility depend on consumption and consumption on production and terminal stocks implies that an equivalent utility depending on capital stocks exists. The chapter also discusses that the primary sources of the optimal growth model are aggregate savings programs and capital accumulation programs for an economy, the theorems, and methods of the subject find applications in other areas with increasing frequency

Optimal Economic Growth and Turnpike Theorems

This chapter is concerned with the long-term tendencies of paths of capital accumulation that maximize, in some sense, a utility sum for society over an unbounded time span. However, the structure of the problem is characteristic of all economizing over time whether on the social scale or the scale of the individual or the firm. The mathematical methods that are used are closely allied to the old mathematical discipline, calculus of variations. The chapter discusses that the utility function depends on time, as in the standard theory of the calculus of variations. Also the function to be maximized is the sum of utility functions for each period over the future. It is described as a separable utility function over the sequence of future capital stocks and corresponds to the integral of calculus of variations. As the consumption of one period influences the utility of later consumption, the separability assumption is not exact. The treatment of utility in a period as dependent on initial and terminal stocks is not a restriction because the usual assumptions that make utility depend on consumption and consumption on production and terminal stocks implies that an equivalent utility depending on capital stocks exists. The chapter also discusses that the primary sources of the optimal growth model are aggregate savings programs and capital accumulation programs for an economy, the theorems, and methods of the subject find applications in other areas with increasing frequency

Measurement in Economics and Social Science

The paper discusses measurement, primarily in economics, from both analytical and historical perspectives. The historical section traces the commitment to ordinalism on the part of economic theorists from the doctrinal disputes between classical economics and marginalism, through the struggle of orthodox economics against socialism down to the cold-war alliance between mathematical social science and anti-communist ideology. In economics the commitment to ordinalism led to the separation of theory from the quantitative measures that are computed in practice: price and quantity indexes, consumer surplus and real national product. The commitment to ordinality entered political science, via Arrow’s ‘impossibility theorem’, effectively merging it with economics, and ensuring its sterility. How can a field that has as its central result the impossibility of democracy contribute to the design of democratic institutions? The analytical part of the paper deals with the quantitative measures mentioned above. I begin with the conceptual clarification that what these measures try to achieve is a restoration of the money metric that is lost when prices are variable. I conclude that there is only one measure that can be embedded in a satisfactory economic theory, free from unreasonable restrictions. It is the Törnqvist index as an approximation to its theoretical counterpart the Divisia index. The statistical agencies have at various times produced different measures for real national product and its components, as well as related concepts. I argue that all of these are flawed and that a single deflator should be used for the aggregate and the components. Ideally this should be a chained Törnqvist price index defined on aggregate consumption. The social sciences are split. The economic approach is abstract, focused on the assumption of rational and informed behavior, and tends to the political right. The sociological approach is empirical, stresses the non-rational aspects of human behavior and tends to the political left. I argue that the split is due to the fact that the empirical and theoretical traditions were never joined in the social sciences as they were in the natural sciences. I also argue that measurement can potentially help in healing this split

Medical Applications of Fast Field Cycling MRI

Non peer reviewedPublisher PD

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure