Browsing by Subject "Bifurcations"

Now showing 1 - 4 of 4

Open Access
Essays on growth and macroeconomic dynamics
(2015-09) Özer, Mehmet
This dissertation is composed of four essays on economic growth and macro- economic dynamics. The first essay analyzes how the dynamic strategic in- teractions among agents a¤ect the long-run distribution of wealth in terms of catching up and the transitional dynamics. It is shown that incorporating the strategic behavior among agents leads to the wealth level of the initially poor and the rich households to be the same at the stationary state. Extending the model by incorporating relative wealth concern; the resulting equilibria depends the valuation of relative wealth concern by each individual and it is proved that under some plausible conditions the catching up occurs thanks to the strategic interaction in the form of open-loop. The stability of these two models are carried out for arbitrary number of people in the economy. In the second essay studies the e¤ects of above mentioned strategic interac- tion in Ramsey model with "Easterlin hypothesis". It is shown that strategic interaction among agents in the economy leads to a change not only in the distribution of wealth but also in the transitional dynamics substantially. The obtained complex dynamics is in the form of Hopf bifurcation which is one of the main tool to explain the economic fluctuations. Third essay of this thesis introduces Stone-Geary Preferences with an endoge- nous reference level of consumption in an Ak model in which reference level of consumption is an increasing function of the capital. It is shown that the result- ing equilibrium presents richer dynamics under such a Stone-Geary preferences. It is proved that endogenous reference level leads to global and local indetermi- nacy: economies starting with di¤erent initial conditions does not necessarily converge to the same steady state and also economies starting with the same initial conditions does not necessarily follow the same transition path. The aim of the fourth essay is to analyze the e¤ects of a pure public good that reduces the subsistence level of consumption on the long run equilibrium and the optimal tax rate. It is shown that although the steady state amount of public good is higher for the first best allocation, the subsistence level of consumption is the same with that of the second best equilibrium. On the other hand, the capital stock and the consumption of the private good are higher for the first best equilibria. Another important result of the essay is the "government revenue-tax rate" locus with a dynamic threshold which depends on the total factor productivity (TFP). The optimal amount of tax rate that maximizes the revenue of the government is an increasing function of the TFP and thus revenue maximizing tax rate varies across countries.
Open Access
Essays on nonlinear dynamics in optimal growth models
(2014) Yüksel, Mustafa Kerem
Economic models with time delay have long been considered in economic theory. It is considered that delay forces the economic system into persistent cycles which can be interpreted as intrinsic crises of the capitalist economy. The e§ect of delay on economic dynamics is analyzed by Hopf bifurcation according to the recent developments in economics and mathematics. Hopf bifurcation depends on the existence of a pair of pure imaginary eigenvalues of the Jacobian matrix evaluated at the steady state. However, recent studies are inconsistent in a determinate way to decide whether the optimal growth model with investment lags admits persistent cycles or not. In the second chapter of this thesis, the author tries to sharpen the analysis of one sector optimal growth model with one control and one state variables and time delay. We Örstly give a brief outline of the mathematical history and ëknow-howíof delays in economic models, as well as its interpretation, and then, we further the analysis set of the model of Asea and Zak (1999) and try to introduce of a new technique for the exposition of the eigenvalues of the characteristic equation of these type of models in a generalized framework. In the third chapter we introduce a new technique (see Louisell, 2001) to the study of economic models with delays and incorporate this technique to evaluate the cycleinducing e§ects of capital dependent population growth in economic models with time delay. We employ the Solow-Kalecki framework and show that the presence of capital dependent population growth induces cycles. Other than the introduction of a new technique into the area of economics, one particular contribution of this chapter is that the results clearly shows that delay is not su¢ cient in inducing cycles even in the most simple economic models. In the forth chapter, we show that Hopf bifurcation may emerge in an overlapping generations resource economy through a feedback mechanism between population and resource availability. In overlapping generations resource economy models, the cycle inducing factor is mainly the nonlinearity of the regeneration of the resources. On the contrary, we assume linear regeneration and yet, endogenize the population growth rate. We show that the interaction between instantenous population growth and regeneration rate triggers persistent cycles in the economy. In the Öfth chapter, we employ a continuous delay structure in the process of recruitment in the population growth in an optimal growth model and hence obtain cyclic solutions. We exploit Erlangian process in the population growth mechanism. As far as we know, the incorporation of Erlangian process in optimal growth models is handled in this chapter for the Örst time in economic literature. Through this mechanism, not only the population is considered as a function of per capita capital, or in other words, population growth is endogenized, but also the current level of population growth is linked with those of older generations. We Önd out that the interaction between the e§ect of older generationsífertility choices and the accumulation of capital induces cyclic behaviour in the economy. The sixth and the last chapter concludes with future research agenda. Overall, the thesis considers the e§ects of delay and endogenized population on the economies of interest (Solow, overlapping generations, optimal growth model) economically and tries to introduce the existing methods and develop new ones to investigate the e§ects of delay and endogenized population on the eigenvalues of the Jacobians that the drive the economies of interest at their steady states.
Open Access
Four essays on overlapping generations resource economies : optimality, sustainability and dynamics
(2012) Fazlıoğlu, Burcu
This dissertation is made up of four essays on overlapping generations resource economies. The Örst essay studies the e§ects of energy saving technological progress and substitution of renewable energy resources with non-renewable resources on natural resource depletion and long run growth. A growth model in two-period overlapping generations framework incorporating the presence of both resources and resource augmenting technological progress is developed. The e§ect of an increase in the intensity of the renewable resources in producing energy on long run growth is found to be positive. Although exhaustible resources are essential in production the economy can be sustained and the balanced growth path is optimal. In the second essay, the implications of assuming di§erent energy intensities for physical capital accumulation and the Önal good production is studied in an overlapping generations resource economy where energy is obtained from the extraction of the natural resources. Apart from the standard literature, physical capital accumulation is assumed to be relatively more energy-intensive than consumption. Multiple steady states, indeterminacy and bifurcations are obtained, without taking non-linearizing assumptions evident in the literature. For the non-renewable resources if the share of energy resources is low enough, local indeterminacy and hopf bifurcations may arise in the model. The aim of third essay is to analyze can costly resource extraction and di§erentiating energy intensities induce dynamics other than saddles in an overlapping generations resource economy. The capital accumulation sector is assumed to be more energy intensive. The energy input is extracted from the natural resources with some extraction costs. The main Önding of the essay is that both naturally evident assumptions contribute to the richness of the dynamics. Depending on the share of resources in capital accumulation dynamics other than saddle ñindeterminacy, áip and hopf bifurcationsñ can arise in the model for the non-zero steady state. In the fourth essay, a feedback mechanism between population and natural resource to a standard model of renewable resource based OLG economy is incorporated to check the stability of the dynamics. Multiple steady states and indeterminacy have been obtained even in the absence of logistic regeneration and independent of intertemporal elasticity of substitution. In particular, transcritical bifurcations may arise in the model varying the rate of constant regeneration with respect to population growth rate.
Open Access
Full electrostatic control of nanomechanical buckling
(American Physical Society, 2020) Erbil, Selçuk Oğuz; Hatipoğlu, Utku; Yanık, C.; Ghavami, Mahyar; Arı, Atakan B.; Yüksel, Mert; Hanay, Mehmet Selim
Buckling of mechanical structures results in bistable states with spatial separation, a feature desirable for sensing, shape configuration, and mechanical computation. Although different approaches have been developed to access buckling at microscopic scales, such as heating or prestressing beams, little attention has been paid so far to dynamically control all the parameters critical for the bifurcation—the compressive stress and the lateral force on the beam. Here, we develop an all-electrostatic architecture to control the compressive force, as well as the direction and amount of buckling, without significant heat generation on micro- or nanostructures. With this architecture, we demonstrated fundamental aspects of device function and dynamics. By applying voltages at any of the digital electronics standards, we have controlled the direction of buckling. Lateral deflections as large as 12% of the beam length were achieved. By modulating the compressive stress and lateral electrostatic force acting on the beam, we tuned the potential energy barrier between the postbifurcation stable states and characterized snap-through transitions between these states. The proposed architecture opens avenues for further studies in actuators, shape-shifting devices, thermodynamics of information, and dynamical chaos.