Existence of solutions to Hamiltonian dynamical systems of optimal growth
Publisher Summary This chapter discusses the existence of solutions to Hamiltonian dynamical systems of optimal growth. Cass and Shell have shown how a wide range of problems in the theory of economic dynamics may be formulated in terms of Hamiltonian dynamical systems. In particular, they have studied the system modeling consumption-optimal growth with discount rate p>0. The Hamiltonian function H(Q,k) is defined on the basis of certain assumptions about technology. It presents a set of conditions on the Hamiltonian function H(Q,k ) that are sufficient to guarantee that the system has a non-negative solution. These conditions include convexity-concavity and other properties that are consistent with or mimic the technological assumptions of Cass and Shell.