Analysis of a Growth Model with a CES Production Function

The paper investigates a growth model with a production function of constant elasticity of substitution, which generalizes the Cobb–Douglas or Leontief functions. The investment indicators of the model are considered as control parameters chosen to maximize the utility functional. An infinite-horizon optimal control problem is formulated. A Hamiltonian function and a Hamiltonian system are constructed by applying the Pontryagin maximum principle. A qualitative analysis of the Hamiltonian system is provided. Next, the existence and uniqueness of a steady state in the system are proved, and an algorithm for its search based on solving a nonlinear equation in one special variable is given. The Hamiltonian system near the steady state is stabilized by applying a regulator that can be constructed due to the saddle-point character of the steady state. A numerical example is given that illustrates the obtained analytical results.