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Arrow-Debreu Model of General Equilibrium
Juřena, Filip ; Červinka, Michal (advisor) ; Adam, Tomáš (referee)
Arrow-Debreu Model of General Equilibrium Filip Juřena Abstract In this thesis, we deal with the Arrow-Debreu model of general equilibrium, which is an integrated model of production, exchange and consumption. At the beginning, we present and discuss the original assumptions of the Arrow-Debreu model, i.e. the assumptions introduced by Kenneth J. Arrow and Gerard Debreu in 1954. Under these assumptions, Arrow and Debreu proved the existence of a general equilibrium. As a part of the proof, Arrow and Debreu showed that the equilibria of their model are the same as the equilibria of an abstract economy, or a generalized Nash equilibrium problem (GNEP). We describe the GNEP and look at whether there is a connection which allows to apply results developed by researchers from other disciplines to the Arrow-Debreu model. A part of the thesis is dedicated to a two-factor, two-commodity, two-consumer model, which is based on the original assumptions of Arrow and Debreu. In order to find the solution, we use a method called applied general equilibrium modelling and a software called GAMS. We examine the impact of better technology and taxes on consumers and producers. We have brief remarks on applications of the model at the end.
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Arrow-Debreu Model of General Equilibrium
Juřena, Filip ; Červinka, Michal (advisor) ; Adam, Tomáš (referee)
Arrow-Debreu Model of General Equilibrium Filip Juřena Abstract In this thesis, we deal with the Arrow-Debreu model of general equilibrium, which is an integrated model of production, exchange and consumption. At the beginning, we present and discuss the original assumptions of the Arrow-Debreu model, i.e. the assumptions introduced by Kenneth J. Arrow and Gerard Debreu in 1954. Under these assumptions, Arrow and Debreu proved the existence of a general equilibrium. As a part of the proof, Arrow and Debreu showed that the equilibria of their model are the same as the equilibria of an abstract economy, or a generalized Nash equilibrium problem (GNEP). We describe the GNEP and look at whether there is a connection which allows to apply results developed by researchers from other disciplines to the Arrow-Debreu model. A part of the thesis is dedicated to a two-factor, two-commodity, two-consumer model, which is based on the original assumptions of Arrow and Debreu. In order to find the solution, we use a method called applied general equilibrium modelling and a software called GAMS. We examine the impact of better technology and taxes on consumers and producers. We have brief remarks on applications of the model at the end.
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