López (1994) and Selden and Song (1995) focus on the theoretical impact of
economic growth on environmental quality. Selden and Song (1995) re-examine the
model of Foster (1973) with minor modification. They provide theoretical insights that
embedded in Foster's (1973) model is the possibility of the inverted U-shape curve,
even if this need not occur in all cases. Treating environment as a factor of production
and the direct determinant of social welfare, López's (1994) theoretical study shows that
in the case of non-homothetic preferences the relationship between economic growth
and pollution depends on the elasticity of substitution between conventional factors of
production and pollution and on the relative degree of curvature of consumers' utility
(ie., the "relative risk-aversion" coefficient). According to López (1994), the lower the
elasticity of substitution and relative curvature coefficient, increases the more likely it is
that pollution increases with income. Under certain conditions,2
an inverted U-shaped
relationship between pollution and income is derived for the non-homothetic preference
case.3
However, Common (1995) points out that for some impacts, irreversible damage
may occur before the top of the inverted U-shaped curve is reached, and that the
relationship need not hold for all impacts