چكيده انگليسي :
Keynesian systems with rigidity and exibility of prices and in ation de ation expectations Morteza Ghanbarzadeh chaleshtori @math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 37N40 91B24 91B25 91B55 91B64 34C23 Keywords Keynesian economics Bifurcations Business cycles Nonlinear analysis AbstractThis thesis is based on a paper by Hiroki Murakami 2014 In this thesis by utilizing the Poincar Bendixsontheory and the Hopf bifurcation theory we analyze both rigid price and exible price nonlinear dise quilibrium Keynesian macroeconomic systems prove the existence of a persistent business cycle andderive the conditions for global asymptotic stability of the equilibrium Consequently we nd that aHopf bifurcation occurs for a lower value of the quantity adjustment parameter in the exible pricesystem than in the rigid price one and that in ation expectation e ects may easily destabilize theeconomic system Furthermore we reveal that global asymptotic stability of the exible price systemis unlikely to be achieved This thesis is organized as follows In Chapter 1 Introduction and some economic schools introduced In Chapter 2 we will introduce some basic basic economic concepts and de nitions including ISLMmodel philips curve economic growth economic equilibrium some economic functions for our anal ysis and mathematical economic from keynes point of view In Chapter 3 we will introduce some basic mathematical de nitions and theorems necessary for ouranalysis in the following chapters including Hopf bifurcation theorem Routh Horwitz criterion Brock Scheinkman theorem Liu s criterion and Asada Yoshida s theorem In Chapter 4 we will consider a rigid price disequilibrium system In this system aggregate incomewill be assumed to move in response to the current economic conditions and capital stock will in crease or decrease as a result of ex post net investment capital formation while the money market
