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We develop a partial Hamiltonian framework to obtain reductions andclosed-form solutions via first integrals of current value Hamiltonian systemsof ordinary differential equations (ODEs).  The approach is algorithmic and applies to many state and costate variablesof the current value Hamiltonian. However, we apply the method to models withone control, one state and one costate variable to illustrate itseffectiveness. The current value Hamiltonian systems arise in economic growththeory and other economic models. We explain our approach with the help of asimple illustrative example and then apply it to two widely used economicgrowth models: the Ramsey model with a constant relative risk aversion (CRRA)utility function and Cobb Douglas technology and a one-sector AK model ofendogenous growth are considered. We show that our newly developed systematicapproach can be used to deduce results given in the literature and also to findnew solutions.

A Partial Hamiltonian Approach for Current Value Hamiltonian Systems