Abstract
A two-sector model of per capita utility is developed. The sectors are industrial (characterized by a Cobb—Douglas production function with technological change), and environmental (output proportionate to the amount of resources set aside from industry). The growing population contains identical individuals with Cobb— Douglas utility functions; each shares both outputs equally. It is shown that without technological change per capita utility must eventually fall due to resource exhaustion, even without population growth. Technological change can maintain constant or growing per capita utility through time, with the required rate depending on parameters of both production and utility functions.
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