Exact Measures of Income in Two Capital-Resource Economies
Pezzey
John C.V.
2001
Exact optimal paths are calculated for two closed, continuous-time
economies with explicit functional forms for utility from consumption, and for
production from human-made capital and a non-renewable resource. Features of
the first economy are non-linear utility, hyperbolic utility discounting and (possibly)
hyperbolic technical progress. In it: (a) welfare-equivalent income > wealthequivalent
income > Sefton-Weale income > Net National Product, confirming that
even if income is viewed only as a measure of prosperity, there is no point in
trying to define it uniquely; (b) the Solow (1974) constant consumption path is a
special case for a particular discount rate; (c) for a low enough discount rate,
sustained growth is optimal even when technical progress is zero. The second
economy has linear utility, a non-linear output split between consumption and
investment, and exponential technical progress. In it, (a) Weitzman’s (1997)
technological progress premium works only if an upwards correction factor is first
applied to the rate of progress in production, to convert it to a rate of progress in
Net National Product; (b) Hartwick’s rule has an unfamiliar form.
412