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The Role of Impatience in Sustainable Growth

Posted November 4, 2013 | Categories: Hawaii's Environment, Blog, Project Environment

Sustaining economic growth requires appropriate husbandry of our natural capital resources (e.g. fish, trees, freshwater, and coral).  But how much conservation is optimal? According to proponents of "strong sustainability," natural capital should never be depleted. This is inconsistent with maximizing economic welfare however. In less developed economies, for example, depleting natural capital may be the best way for an economy to accumulate the produced capital (e.g. buildings, transportation infrastructure, and machinery) that is needed to increase the productivity of labor.

Depending on current resource stocks, optimal economic growth may require either drawing down or building up natural capital to its optimal steady state level. For non-renewable resources such as oil, this often means substituting more abundant resources (e.g. clean coal) and eventually transitioning to renewable resources such as solar energy.

In addition to balancing the uses of natural and produced capital, sustainable growth requires intergenerational equity. Simply put, this is the principle of non-discrimination against future generations. By adding the non-discrimination requirement to the problem of welfare maximization in an economy whose production is dependent upon both produced and natural capital, we get conditions for optimal and sustainable growth. As it turns out, the conditions are familiar to economists, albeit from different parts of economics. From growth theory, we have the Ramsey (1928) requirement that produced capital should be accumulated in each period until its marginal product falls to a multiple of the growth rate of consumption. In the long run, as consumption approaches its golden rule level, the target marginal product goes to zero. The same condition applies to natural capital. And from resource economics we have the extended Hotelling (1931) condition that the resource should be depleted (or accumulated) in each period until net marginal benefit of that resource -- typically the resource price minus its extraction or harvesting cost -- is equal to the marginal opportunity cost of harvest that is imposed on future generations.

This formulation contains a paradox however. If individuals are impatient, i.e. they prefer consumption now to equal consumption later, how can society impose the condition of intergenerational neutrality, i.e. require that consumption in different periods be weighted equally? This would seem to violate the condition of consumer sovereignty, i.e. the requirement that social welfare and justice should be based on individual preferences (as well as social weightings thereof). We resolve this paradox with a model of overlapping generations. This allows us to consider a representation of social justice that eschews intergenerational discrimination, while simultaneously allowing individuals to be impatient regarding their own welfare. The surprising result is that while individual impatience matters for the lifetime consumption plan of the individual, it does not matter for aggregate consumption. Optimal and sustainable growth in the aggregate is therefore still governed by the Ramsey and extended Hotelling conditions.

What does optimal and sustainable growth imply for the evaluation of environmental projects? In particular, the present values of global programs to mitigate global warming depend crucially on the project discount rate. Does intergenerational justice require that the project discount rate be zero? It does not. From principles first established by Irving Fisher around the turn of the 19th century, the project discount rate depends on the productivity of capital as well as the social rate of impatience. Even if individuals were not impatient, the inherent productivity of capital would still result in a positive interest rate. Nonetheless, intergenerational equity may indeed imply that the appropriate discount rate is small, especially if global warming and the rate of technological improvement limit growth in the very long run. Indeed Sir Nicolas Stern has suggested a rate of only 1.4% for discounting the benefits of climate mitigation.

What are the implications of intergenerational equity for the deficit and the national debt? From the Ramsey condition, deficits and debt are consistent with sustainable growth but only so long as they finance investments with positive present values. Since future generations don't vote in current elections, debt may be a politically-expedient device to transfer resources from the future to the present, even when doing so reduces the welfare of future generations more than it increases the welfare of current voters. Economists can stand against this and other perversions of democracy by rendering the intergenerational consequences of social profligacy more transparent.

-- Lee Endress, James Roumasset, and Christopher Wada


Endress, L., Pongkijvorasin, S., Roumasset, J., Wada, C.A., 2013. “Intergenerational Equity with Individual Impatience in a Model of Optimal and Sustainable Growth.” Resource and Energy Economics (forthcoming).

Endress, L., Zhou, T., Roumasset, J., 2005. “Sustainable growth with environmental spillovers.” Journal of Economic Behavior and Organization 58(4), 527-547.

Hotelling, H., 1931. “The economics of exhaustible resources.” The Journal of Political Economy 39, 137-175.

Ramsey, F.P., 1928. “A mathematical theory of saving.” Economic Journal 38(152), 543-559.



Note: This research extends earlier work by Endress et al. (2005) and is forthcoming in the peer-reviewed journal, Resource and Energy Economics (Endress et al., 2013). For more applications of economic principles to natural resource and environmental management problems, visit UHERO’s Project Environment (link to: http://www.uhero.hawaii.edu/45/project-environment).

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