Optimal endogenous growth with natural resources: Theory and evidence

Manh-Hung Nguyen et Phu Nguyen-Van


This paper considers an optimal endogenous growth model where production function is assumed to exhibit increasing returns to scale and two types of resource (renewable and nonrenewable) are imperfect substitutes. Natural resources, labors and physical capital are used in the final goods sector and in the accumulation of knowledge. Based on results in calculus of variations, a direct proof of existence of optimal solution is provided. Analytical solutions for the planner case, balanced growth paths and steady states are found for a specific CRRA utility and Cobb-Douglas production function. It is possible to have a long-run growth where both energy resources are used simultaneously along the equilibrium path. As the law of motion of the technological change is not concave reflecting the increasing return of scale so that the Arrow-Mangasarian sufficiency conditions do not apply, we provide directly a sufficient condition. Transitional dynamics to the steady state from the theoretical model are used to derive three convergence equations of output intensity growth rate, exhaustible resource growth rate and renewable resource growth rate, which are tested based on OECD data on production and energy consumption.


Endogenous optimal growth; transitional dynamics; renewable resource; nonrenewable resource;

Codes JEL

  • C61: Optimization Techniques • Programming Models • Dynamic Analysis
  • D51: Exchange and Production Economies
  • E13: Neoclassical


Manh-Hung Nguyen et Phu Nguyen-Van, « Growth and convergence in a model with renewable and non-renewable resources: existence, transitional dynamics, and empirical evidence », TSE Working Paper, n° 10-210, décembre 2010.


Manh-Hung Nguyen et Phu Nguyen-Van, « Optimal endogenous growth with natural resources: Theory and evidence », Macroeconomic Dynamics, décembre 2016, p. 2173–2209.

Publié dans

Macroeconomic Dynamics, décembre 2016, p. 2173–2209