Mathematical Economics  - PhDEcon (2017-18)

Course webpage at Sigarra

1 - Differential Equations and Difference Equations

Problem set

Some sources:

A model of stock prices (De La Fuente, 2000, pp. 503-513).

The Solow model of economic growth (Solow, 1956; De La Fuente, 2000, pp. 518-527; Gandolfo, 1997, pp. 175-184).

Core-periphery dynamics (Fujita et al., 2001, pp. 34-41)

A dynamic IS-LM model (De La Fuente, 2000, pp. 494-503).

An overlapping generations model of economic growth (Diamond, 1965; De La Fuente, 2000, pp. 527-537).   

The multiplier-accelerator model (Samuelson, 1939; Gandolfo, 1997, pp. 71-81).

   Bibliography:

De La Fuente, Angel (2000): "Mathematical Methods and Models for Economists", Cambridge University Press.

Gandolfo, Giancarlo (1997): "Economic Dynamics", 3rd edition, Springer.

Chiang, Alpha C. and Kevin Wainwright (2005): "Mathematical Economics", 4th edition, McGraw-Hill.

Zhang, Wei-Bin (2005): "Differential Equations, Bifurcations, and Chaos in Economics", World Scientific, ISBN: 981-256-333-4.

Zhang, Wei-Bin (2006): "Discrete Dynamical Systems, Bifurcations and Chaos in Economics", Elsevier, ISBN: 978-0-444-52197-2.

Other bibliography:

Diamond, Peter (1965): "National Debt in a Neoclassical Growth Model", American Economic Review, 55 (5), pp. 1126-1150.

Fujita, Masahita, Paul Krugman and Anthony J. Venables (2001): "The Spatial Economy", MIT Press.

Machlup, Fritz (1959): "Statics and Dynamics: Kaleidoscopic Words", Southern Economic Journal, 26 (2), pp. 91-110 [reprinted in "Economic Semantics", 2^nd edition, Transaction Publishers].

Samuelson, Paul (1939): "Interactions between the Multiplier Analysis and the Principle of Acceleration", Review of Economic Studies, 21 (2), pp. 75-78.

Solow, Robert (1956): "A Contribution to the Theory of Economic Growth", Quarterly Journal of Economics, 70 (1), pp. 65-94.

Solving linear differential equations

Some economic applications of differential equations

2 - Optimal Control and Dynamic Programming

Introduction to Dynamic Programming (slides)

Optimal Control - Problem set

Dynamic Programming - Problem set

Bibliography:

Chiang, Alpha C. (1992): "Elements of Dynamic Optimization", 1^st edition, McGraw-Hill.       

Stokey, Nancy L. and Robert E. Lucas, with Edward C. Prescott (1989): "Recursive Methods in Economic Dynamics", Harvard University Press.

De La Fuente, Angel (2000): "Mathematical Methods and Models for Economists", Cambridge University Press.

Other bibliography:

Borges, Ana P. and João Correia-da-Silva (2011): "Using cost observation to regulate a manager who has a preference for empire building", The Manchester School, 79 (1), pp. 29-44.

Cass, David (1965): "Optimum growth in an aggregative model of capital accumulation", Review of Economic Studies, 32 (3), pp. 233-240.

Hotelling, Harold (1931): "The economics of exhaustible resources", Journal of Political Economy, 39 (2), pp. 137-175.

Laffont, Jean-Jacques, and Jean Tirole (1986): "Using Cost Observation to Regulate Firms", Journal of Political Economy, 94 (3), pp. 614-641. 

See also:

The growth model of Ramsey-Cass-Koopmans (De La Fuente, 2000, pp. 622-629).

Para saber mais:

        Prémio Nobel da Economia