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This saving rule extends the Hartwick rule to an open economy. The first term says that the
nation saves the marginal resource rents valued at the world resource price minus marginal
extraction costs, so depletion of natural resource reserves must be compensated by increases
in foreign assets. The second term is the ‘anticipation of better times’ term. It says that the
nation saves less if it expects the world interest rate (provided A>K) or the price of its
resources to increase in the future. The country then saves less and postpones extraction. The
nation also saves less if it expects positive technical progress in future oil extraction
technology. A special case arises if extraction costs are zero and the world price of resources
follows the Hotelling rule, because then the depletion rate is given by E / E = -ε(r - π*) and
the max-min saving rule becomes A = Q(1 -1 / ε)E - π* QS. Saving marginal resource rents
minus imputed interest on the value of natural resource reserves thus sustains a constant level
of consumption. Countries with abundant reserves of exhaustible resources should thus run a
current account deficit if resource rents fall short of the imputed rent on the value of resource
reserves. Genuine saving is thus negative, i.e., A + Q(1 - ε 1 )S = -∏QS < 0.
Since the country saves less than its marginal resource rents and postpones extraction
of exhaustible resources if it expects extraction technology to continually improve or the price
it can fetch for its resources to continually increase in the future (cf., Asheim, 1986; Vincent
et al., 1997; van der Ploeg, 2010a)18, it is a priori unclear whether observed negative genuine
saving for resource-rich economies are due to poor institutions, badly functioning capital
markets, corruption or mismanagement or due to anticipation of better times. It is optimal for
a country with substantial oil reserves to save less than a country with almost no reserves,
because it makes sense to sell more of its reserves in the future when the price of oil is higher.
The Hartwick rule in the global economy
To examine the Hartwick rule for the global economy, consider a world consisting of natural
resource (say, oil) exporters and oil importers. With free international trade in oil and goods,
perfect capital mobility, zero labour mobility, no technical progress, no population growth
and identical technologies for both blocks, the max-min egalitarian outcome can be
characterized (Asheim, 1986, 1996). Factor intensities are determined by the world interest
rate and price of oil. The ratios of output, capital and resource use in oil-exporting economies
relative to those in oil-importing economies are then identical and equal to the ratio of the
labour force of oil-exporters relative to that of oil-importers.
18 Similar arguments can be applied to deforestation in a small open economy with a large endowment
of forest land and small endowment of agricultural land (Hartwick et al., 2001). The early phases of
clearing forest land are then governed by the high price of agriculture while later phases are driven by
profits from marketing timber from cleared land.