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Register a new userThe Hamiltonian approach to the problem of derivation of production functions in economic growth theory
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We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we investigate some existing models and propose a new one as special cases of the general $n$-dimensional Lotka-Volterra system of eco-dynamics.
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We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
The COVID-19 pandemic has forced changes in production and especially in human interaction, with social distancing a standard prescription for slowing transmission of the disease. This paper examines the economic effects of social distancing at the aggregate level, weighing both the benefits and costs to prolonged distancing. Specifically we fashion a model of economic recovery when the productive capacity of factors of production is restricted by social distancing, building a system of equations where output growth and social distance changes are interdependent. The model attempts to show the complex interactions between output levels and social distancing, developing cycle paths for both variables. Ultimately, however, defying gravity via prolonged social distancing shows that a lower growth path is inevitable as a result.
Technological improvement is the most important cause of long-term economic growth, but the factors that drive it are still not fully understood. In standard growth models technology is treated in the aggregate, and a main goal has been to understand how growth depends on factors such as knowledge production. But an economy can also be viewed as a network, in which producers purchase goods, convert them to new goods, and sell them to households or other producers. Here we develop a simple theory that shows how the network properties of an economy can amplify the effects of technological improvements as they propagate along chains of production. A key property of an industry is its output multiplier, which can be understood as the average number of production steps required to make a good. The model predicts that the output multiplier of an industry predicts future changes in prices, and that the average output multiplier of a country predicts future economic growth. We test these predictions using data from the World Input Output Database and find results in good agreement with the model. The results show how purely structural properties of an economy, that have nothing to do with innovation or human creativity, can exert an important influence on long-term growth.
A transformative approach to addressing complex social-environmental problems warrants reexamining our most fundamental assumptions about sustainability and progress, including the entrenched imperative for limitless economic growth. Our global resource footprint has grown in lock-step with GDP since the industrial revolution, spawning the climate and ecological crises. Faith that technology will eventually decouple resource use from GDP growth is pervasive, despite there being practically no empirical evidence of decoupling in any country. We argue that complete long-term decoupling is, in fact, well-nigh impossible for fundamental physical, mathematical, logical, pragmatic and behavioural reasons. We suggest that a crucial first step toward a transformative education is to acknowledge this incompatibility, and provide examples of where and how our arguments may be incorporated in education. More broadly, we propose that foregrounding SDG 12 with a functional definition of sustainability, and educating and upskilling students to this end, must be a necessary minimum goal of any transformative approach to sustainability education. Our aim is to provide a conceptual scaffolding around which learning frameworks may be developed to make room for diverse alternative paths to truly sustainable social-ecological cultures.
This is part I of a book on KAM theory. We start from basic symplectic geometry, review Darboux-Weinstein theorems action angle coordinates and their global obstructions. Then we explain the content of Kolmogorovs invariant torus theorem and make it more general allowing discussion of arbitrary invariant Lagrangian varieties over general Poisson algebras. We include it into the general problem of normal forms and group actions. We explain the iteration method used by Kolmogorov by giving a finite dimensional analog. Part I explains in which context we apply the theory of Kolmogorov spaces which will form the core of Part II.
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