Exact measures of income in a hyperbolic economy

Abstract

For a closed economy with human-made capital, non-renewable resource depletion and (possibly) exogenous, hyperbolic technical progress as explicit-form inputs to a production function, there is a feasible development path that is ‘as if’ optimal with respect to hyperbolic utility discounting. On this path, typically, welfare-equivalent income > wealth-equivalent income > Sefton-Weale income > net national product, with possibly dramatic differences among these measures; and sustainable income can be greater than, equal to, or less than NNP. For low enough discounting, growing consumption is optimal even when technical progress is zero. A particular discount rate makes all income measures and consumption constant and (except net national product) equal; and zero technical progress then gives the Solow (1974) maximin as a special case. The optimal path is time-consistent because of the way the utility discount rate is chosen to depend on the economy's stocks, and hence on absolute time.