Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization

This contribution is concerned with efficient use of a resources if households are characterized by Stone-Geary preferences with a minimum subsistence level of consumption. We provide a closed form solution for the case of Cobb-Douglas production with constant returns to scale in reproducible capital and effective resource input. The model allows for exogenous technical change and depreciation of reproducible capital. The closed form solution exists in terms of the Gaussian hypergeometric function. For some constellations of the model parameters, the economy asymptotically approaches the generalized Hartwick's investment rule. We calibrate our model to analyze the existence of a solution and the dynamics for resource-rich low-income countries.