Treating the mathematical methods used in the economic dynamics, this book shows how they are utilised to build and analyse dynamical models. Accordingly, the focus is on the methods, and every new mathematical technique introduced is followed by its application to select economic models. The mathematical methods covered range from elementary linear difference and differential equations and simultaneous systems to the qualitative analysis of non-linear dynamical systems. Stability considerations are stressed throughout, including many advanced topics. Bifurcation theory and chaos theory are also dealt with. The reader is guided through a step-by-step analysis of each topic, be it a mathematical method or an economic model. This "user-friendly" feature is also present in the exercises.
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Firstorder Difference Equations
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2x2 systems absolute value adjustment analysis apply arbitrary constants assumed assumption asymptotically asymptotically stable behaviour chaos Chap characteristic equation characteristic roots comparative statics consider consumption convergence determined difference equation differential equation economic models equilibrium point equilibrium value examine example excess demand exchange rate exogenous first-order system flip bifurcation given growth model Hence homogeneous equation Hopf bifurcation Hopf bifurcation theorem income increase inequality initial conditions integral curves investment Jacobian Kaldor latent roots Liapunov Liapunov function limit cycle linear Lotka-Volterra equations mathematical matrix means method movement multiplier necessary and sufficient non-homogeneous equation non-linear normal form obtain optimal oscillations output parameter partial derivatives particular solution path period phase curve phase diagram polynomial positive problem production function qualitative rational expectations real roots saddle point satisfied second-order Sect singular point solution of Eq solve stabilisation policy Substituting system in normal theorem theory tion unknown function unstable variables vector zero