On the solutions of natural resource-based economy

We derive closed-form solutions of two-sector renewable natural resource-based economic growth model using the partial Hamiltonian approach. The partial Hamiltonian approach provides the first integrals of the model under consideration. These first integrals are used to derive two different closed-form solutions when the elasticity of output is equal to the inverse of the elasticity of intertemporal substitution. We also compute the closed-form solution for the first integral obtained with a constraint on the parameter. We then analyze the balanced growth path and show that all the closed-form solutions converge to the same constant growth rate. The closed-form solution constructed with the aid of the partial Hamiltonian approach is cost-effective and straightforward to deduce optimal growth path.