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Optimal consumption and investment in the economy with infinite number of consumption goods
Optimal Control Theory and Static Opimization. The performance of the economy is ekonkmia by current value of the total utility in some planning horizon.
Decisions on capital allocation determine the stocks of fixed capital productive capacities of the firms. The features which differentiate individual equilibria are the structure of fixed capital and the structure of ownership of the firms by capitalists. Next it is shown that a set of a continuum of equilibria exists, each of which characterized by the same matemaytczna interest rate and the same balanced growth rate.
Mathematical Analysis /
Diffusions, Markov processes and martingales, volume 1. A mathematical theory of marematyczna. In the article we present some extension for the classical problem of dynamic investment optimization.
Wydawnictwo Akademii Ekonomicznej w Poznaniu, Pozna, Cambrige University Press, Cambridge, We take the neoclassical model of growth with one product and many consumption goods.
ekonomia matematyczna emil panek pdf – PDF Files
Intriligator, North-Holland Publishing Company The instantaneous social utility of consumption is measured as the integral of individual utilities of the consumption goods. Cambridge University Press, Cambridge, A long-run classical equilibrium of the model is defined as a process of homothetic growth with equal profit rates.
Princeton University Press, Princeton, We show that the problem of choosing optimal consumption paths for each good can be decomposed into 1 problem of choosing optimal aggregate consumption, which can be solved using standard methods of optimal control theory, 2 problem of distribution aggregate consumption into consumption of specific goods. The number of consumption goods can be infinite and the consumption bundle is defined on some abstract, measurable space.
An Introduction to the Theory and Its Applications.
All papers reproduced by permission. McGraw-Hill, New York, Deterministic and stochastic optimal control. Firms themselves decide on prices and production levels capacity utilization on the basis of the stocks of unsold commodities.
Springer-Verlag, Nowy Jork, Handbook of Mathematical Economics, ekonommia. According to the classical theory, capitalists allocate their capital in the firms in response to profitability differentials. The model describes an economy in which n firms are owned by m capitalists.
The purpose of the paper is to build and investigate a decentralized dynamic model of classical inspiration thought of as an alternative to the neoclassical walrasian general equilibrium models. Every single agent firm or capitalist takes his decisions autonomously, generally in disequilibrium. Optimal consumption and investment in the economy with infinite number of consumption goods.
Economic Journal, 38, Springer- Verlag, Nowy Jork, Reproduction and distribution subject to the approval of the copyright owners.
Dover Publications, New York, The process of transforming product into consumption goods is described by another measure.