Kalaba, Robert E.; Tesfatsion, Leigh; Wang, J.-L.

Applied Mathematics and Computation Vol. 9 (1981): 227-234.

The complete system of ordinary differential equations developed by Kalaba and Tesfatsion (1981) for tracking solution branches of parameterized nonlinear systems is tested using several illustrative examples. One example is the standard Ramsey optimal growth model, for which analytical solutions can be obtained. For this example, the complete system is used to generate solutions c(rho) and k(rho) for the steady-state per-capita levels for consumption and capital as the time preference parameter rho varies from 0 to 0.50. Accuracy to four decimal places is obtained. This represents a stringent test of the method, since the derivative of k(rho) near rho=0 is on the order of -10^2 whereas the derivative of k(rho) near rho=0.50 is on the order of -10^0. Annotated pointers to related work can be accessed here: http://www.econ.iastate.edu/tesfatsi/nasahome.htm

JEL Classification: C6

Keywords: Comparative statics, solution tracking, ordinary differential equations, parameterized nonlinear systems, optimal growth