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Estimating the quadratic almost ideal demand system and the effects of population ageing in the Czech Republic
Bílý, Michael ; Janský, Petr (advisor) ; Hájek, Jan (referee)
The aim of this thesis is to estimate the Quadratic Almost Ideal Demand System of non-durable goods on the Czech Republic Household Budget Survey data in two distinct models. Respective income, own and cross price elasticities are calculated and we interpret the resulting income, price and demographic characteristics of the household demand. The first model is used to estimate the effects of the 2015 Value Added Tax reform in the Czech Republic, which introduced 10% reduced rate on medication and books. We estimate how much the reform changes the consumption behaviour of households, the biggest changes are in the commodities of clothing, books, medications and household goods. The households are estimated to spend 1,049 billion CZK more on non-durable goods and the VAT revenue is estimated to decrease by 818 million CZK. The second model is used to predict the effects of the population ageing on the household demand. We do this in four scenarios to separate effects of the household composition change and to analyse the composed effects of increasing wealth and redistribution among the working and retired households. The population ageing has the highest impact on the commodities of food, fuel and light, transport and leisure services. The shift in composition affects the consumption mostly in the same...
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Transformations of ODEs into gradient systems in stationary points
Bílý, Michael ; Bárta, Tomáš (advisor) ; Spurný, Jiří (referee)
This bachelor thesis follows article by Bárta, Chill a Fašangová [1]. It is proven there that every ordinary differential equation with a strict Lyapunov function is in fact a gradient system for certain Riemannian metric on the set of all non-equilibrium points. We will try to determine necessary and sufficient conditions for this Riemannian metric to have continuous extension to isolated equilibrium point so that the ODE is gradient system on the whole domain. Powered by TCPDF (www.tcpdf.org)
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Maximum principles for elliptic systems of partial differential equations
Bílý, Michael ; Bulíček, Miroslav (advisor) ; Kaplický, Petr (referee)
We consider nonlinear elliptic Bellman systems which arise in the theory of stochastic differential games. The right hand sides of the equations (which are called Hamiltonians) may have quadratic growth with respect to the gradient of the unknowns. Under certain assumptions on Lagrangians (from which the Hamiltonians are derived), that are satisfied for many types of stochastic games, we establish the existence and uniqueness of a Nash point and develop structural conditions on the Hamiltonians. From these conditions we establish a certain version of maximum and minimum principle. This result is then used to establish the existence of a bound solution. 1
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Estimating the quadratic almost ideal demand system and the effects of population ageing in the Czech Republic
Bílý, Michael ; Janský, Petr (advisor) ; Hájek, Jan (referee)
The aim of this thesis is to estimate the Quadratic Almost Ideal Demand System of non-durable goods on the Czech Republic Household Budget Survey data in two distinct models. Respective income, own and cross price elasticities are calculated and we interpret the resulting income, price and demographic characteristics of the household demand. The first model is used to estimate the effects of the 2015 Value Added Tax reform in the Czech Republic, which introduced 10% reduced rate on medication and books. We estimate how much the reform changes the consumption behaviour of households, the biggest changes are in the commodities of clothing, books, medications and household goods. The households are estimated to spend 1,049 billion CZK more on non-durable goods and the VAT revenue is estimated to decrease by 818 million CZK. The second model is used to predict the effects of the population ageing on the household demand. We do this in four scenarios to separate effects of the household composition change and to analyse the composed effects of increasing wealth and redistribution among the working and retired households. The population ageing has the highest impact on the commodities of food, fuel and light, transport and leisure services. The shift in composition affects the consumption mostly in the same...
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Transformations of ODEs into gradient systems in stationary points
Bílý, Michael ; Bárta, Tomáš (advisor) ; Spurný, Jiří (referee)
This bachelor thesis follows article by Bárta, Chill a Fašangová [1]. It is proven there that every ordinary differential equation with a strict Lyapunov function is in fact a gradient system for certain Riemannian metric on the set of all non-equilibrium points. We will try to determine necessary and sufficient conditions for this Riemannian metric to have continuous extension to isolated equilibrium point so that the ODE is gradient system on the whole domain. Powered by TCPDF (www.tcpdf.org)
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