Browsing by Subject "Economic development--Mathematical models."

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Open Access
Bliss and growth: optimal policies under uncertainty
(1998) Voyvoda, Ebru
This thesis conducts a study on growth theory by analyzing how the results of the current optimal growth theory change when households are assumed to have bliss points in their consumption sets. For this purpose a discrete-time, one-sector, stochastic model of endogenous growth, adopting constant returns to scale technology and quadratic utility function, is constructed. The solution of the model through “value function iteration” shows the existence of qualitatively different equilibria, depending on the initial state of the economy. This result demonstrates that it is possible to combine “poverty traps” and “sustained growth” into a common analytical framework.
Open Access
Essays on endogenous time preference and strategic interaction
(2013) Turan, Agah Reha
This thesis includes three self contained essays on the existence and qualitative properties of equilibrium dynamics under endogenous time preference. In the Örst essay, we reconsider the optimal growth model proposed by Stern (2006). We prove the almost everywhere di§erentiability of the value function and uniqueness of the optimal path, which were left as open questions and show how a small perturbation to the price of future oriented capital qualitatively changes the equilibrium dynamics. Almost none of the studies on endogenous time preference consider the strategic interaction among the agents. In the second essay, by considering a strategic growth model with endogenous time preference, we provide the su¢ cient conditions of supermodularity for dynamic games with open-loop strategies and show that the stationary state Nash equilibria tend to be symmetric. We numerically show that the initially rich can pull the poor out of poverty trap even when sustaining a higher level of steady state capital stock for itself. Lastly, in the third essay, we consider the socially determined time preference which depends on the level of Ösh stock and characterize the basic Öshery model under this setup. We provide existence of collusive and open-loop Nash equilibria and compare the e¢ ciency and qualitative properties of them.
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
On the existence of Hopf cycles in optimal growth models with time delay
(2008) Yüksel, Mustafa Kerem
In this thesis, we analyzed the existence of cycles `a la Poincar´e-AndronovHopf in optimal growth models with time delay. The analysis builds upon a new method developed, which investigates the number of pure imaginary roots of the characteristic equation. The method was applied to the time-tobuild models of Asea and Zak (1999) and Winkler (2004).
Open Access
Threshold dynamics in one-sector optimal growth framework
(2014) Turan, Hamide Karahan
This thesis includes three self-contained essays on the threshold dynamics in onesector optimal growth models. In the Örst essay, we consider the preferences for wealth-habit in a one-sector optimal growth model. We show that the dynamics may encounter saddle-node bifurcations with respect to the parameters of the preferences. We analytically provide the monotone comparative statics and the continuity of the critical capital stock with respect to these parameters and the discount factor. In the second essay, we analyzed the joint dynamic implications of time-to-build lag in investment and non-convex technologies. We prove the existence of persistent cyclical dynamics even in one-sector optimal growth framework. Finally, in the third essay, considering time-to-build lag in non-classical optimal growth framework inducing threshold dynamics, we analyze the e§ects of an alternative information structure regarding the initial conditions on the equilibrium dynamics. In particular, we seek to understand the dependence of the cyclical dynamics on the information structure. In all essays, we also support the analytical solutions by numerical methods in order to better understand the underlying dynamics of the optimal path.