Appendix on Dynamic Optimisation
Angus Chu
Chapter 17 in Advanced Macroeconomics:An Introduction for Undergraduates, 2020, pp 139-141 from World Scientific Publishing Co. Pte. Ltd.
Abstract:
In this appendix, we demonstrate how to use a mathematical tool known as the Hamiltonian (named after William Rowan Hamilton) to solve dynamic optimisation problems in continuous time. We use the Ramsey model as an example. The household’s lifetime utility function is given byU=∫0∞e−ρtu(Ct)dt, (17.1)where u(Ct) is a differentiable, strictly increasing and concave function in Ct, which denotes consumption. The parameter ρ > 0 is the subjective discount rate. The household maximises utility in (17.1) subject to the following capital-accumulation equation:K˙t=F(Kt)−Ct, (17.2)where K˙t≡∂Kt/∂t denotes the change in the level of capital with respect to time t, and F(Kt) is a differentiable and concave production function in Kt net of capital depreciation…
Keywords: Macroeconomics; Dynamic General Equilibrium; Economic Growth; Endogenous Technological Change; Monetary Policy; Fiscal Policy; Business Cycles; Unemployment; Market Failure; The Neoclassical Growth Model; The Romer Model; The Schumpeterian Growth Model; The Solow Growth Model; The Ramsey Model; The New Keynesian Model (search for similar items in EconPapers)
JEL-codes: E6 E62 E66 F4 F43 O11 (search for similar items in EconPapers)
Date: 2020
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