An Analytical Introduction to Dynamic Optimization: The Robinson Crusoe Economy

21 Pages Posted: 29 Jan 2008

See all articles by Dirk Bethmann

Dirk Bethmann

Korea University - Department of Economics

Date Written: January 28, 2008

Abstract

Dynamic optimization is an essential tool of modern macroeconomics. We suggest to teach this technique based on a simplified version of the Uzawa-Lucas model of endogenous growth. Using this model it is possible to present the key concepts of dynamic optimization without applying linearization techniques. Even though the model assumes a concave utility function and a neoclassical production technology, we will state the stable and the unstable solution branches in the phase diagram in closed-form. Saddle path behaviour and the role of transversality conditions can therefore be studied extensively without using complicated mathematical tools. We also show how homogeneity in the initial conditions, a property that applies to almost all macroeconomic models, can be used to introduce a simple numerical solution method.

Keywords: Closed-form solution, saddle path stability, homogeneity in initial conditions

JEL Classification: A23, C61, C63

Suggested Citation

Bethmann, Dirk, An Analytical Introduction to Dynamic Optimization: The Robinson Crusoe Economy (January 28, 2008). Available at SSRN: https://ssrn.com/abstract=1088082 or http://dx.doi.org/10.2139/ssrn.1088082

Dirk Bethmann (Contact Author)

Korea University - Department of Economics ( email )

1 Anam-dong 5 ka
Seoul, 136-701
Korea

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