Prospects for utility and production in an economy with finite resources

The authors analyse per capita utility in a growing economy which has two exhaustible natural resorces. Per capita industrial output (X) and the remaining environmental resource (R). X is a Cobb—Douglas function of a growing labour force, capital, and the natural resources. The model predicts depletion of R when the elasticity of substitution (σ) is greater than unity. When σ is less than unity, per capita X continous to rise, but the rate of increase in utility becomes quite small. Only when σ is unity, do both per capita X and utility increase markedly through time.