Lecture 23: Sustainability
Sustainability in Economics
• In economics, an economy is “sustainable” if future generations will
be able to enjoy the same standard of living as the current
generation.
• Work by Hartwick (1977), a Queen’s natural resource economist,
and others has identified a necessary condition for economic
sustainability: that a nation’s capital be kept intact. “Capital” here
refers not only to physical capital but to any stock from which
services flow.
• The intuition behind keeping capital intact is that, in order to have a
constant stream of income into the future, you need to have a
constant amount of wealth from which to earn income. If you want
to keep drawing interest out of your bank account, you must not dig
into the principal.
• If population grows, national wealth or national capital must
actually increase so that the capital:labour ratio is kept intact.
The Basic Model
• In the 1960s and beyond, economic growth was a hot topic, and
economists used a highly simplified model of the economy, based
on the aggregate production function Y = GDP = F(K,L).
This is called the neoclassical production function.
 All inputs are essential
 Even at very high prices, all inputs will be used
 Inputs can drop very low; there is no threshold level of input
necessary (Daly criticizes)
 All inputs are substitutable to some degree. (Daly criticizes)
 Inputs engage multiplicatively: synergies
 Constant Returns to Scale.
• In these growth models, part of Y is eaten, and the part not
consumed is invested in K. So we have another equation: I = Y –
C.
• Robert Solow (1974) used Y = F(K,L,R), where R is an exhaustible
resource like oil. S is the total stock of oil, and S falls every year by
amount R(t).
• Solow showed that, if there were no population growth, and
if there were no depreciation of K, then
a constant level of consumption (or consumption per person) could be
sustained indefinitely.
• John Hartwick (1977) showed what was going on in the math. The
amount being invested (not consumed) is equal to the “rents” from
resource extraction.
• “Hotelling rent” is the difference between the price of the marginal
ton of oil extracted, and its marginal extraction cost.
• Hartwick has shown that if I = Hotelling rent * R = total Hotelling rent
(THR), then the value of K + R is being held intact, and consumption
is sustainable. S ↓ K↑
• This is known as “Hartwick’s Rule
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• Hartwick showed that, if resource rents were reinvested in physical
capital according to Hartwick’s rule, consumption could be
sustained.
• As recently as this year, it has been shown that, if more than
resource rents were reinvested in physical capital, consumption
could grow. In fact, for every extra amount reinvested implies a level
of population growth that would be manageable at a constant per
capita consumption level. The population growth is not geometric,
however. It is quasi-geometric. N(t) = {a + b(t) }
• Unfortunately, to get their sustainability result, the math still requires
that there be no physical depreciation of capital, which is completely
unrealistic.
• However, if there is enough exogenous technical change, then
physical depreciation of capital is not a problem.
• Of course, if there is enough exogenous technical change, you don’t
even need to invest resource rents.
Different kinds of capital
1)
2)
3)
4)
Physical capital. Declines due to depreciation and due to shallowing
(when population grows). Neither is a problem so long as a sufficient
amount is saved. Output per worker can be kept intact. However, if the
population growth rate increases, more must be saved, so consumption
per worker falls.
Exhaustible Resources. The stock of an exhaustible resource like oil
declines as it is used. Output per worker can be maintained if THR is
invested. If more than THR is invested, arithmetic population growth can
be tolerated. If either depreciation occurs or population growth occurs at
a constant rate, output per worker cannot be maintained.
Renewable Resources. Renewable resources can be harvested
sustainably. The optimal amount to harvest each year depends on
demand, supply, the interest rate, and the biological growth rate of the
resource. However, renewable resources are often over-harvested for
lack of oversight and ownership. We may also be ignorant of some of the
biological factors needed to determine the biological growth rate. As the
population grows, demand will grow, and the maximum sustainable yield
will be reached. At that point we may have to make up for declining
harvest-per-person by investing in physical capital à la Hartwick’s rule.
(see point 2 for results).
Environmental Capital. Pigouvian taxes – politically unpopular – can in
theory prevent the deterioration of environmental capital. However,
environmental capital typically does not grow. There is a finite amount of
clean water and air. To make up for environmental shallowing due to
population growth, Hartwick’s Rule-type investing will be needed. See
point 2 for results).
Is any nation using Hartwick’s Rule?
(you do not need to know this for exam).
Ref. Martin Skancke, Workshop on petroleum revenue management, 2006
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Alberta taxes private owners of mineral deposits, and collects “royalties” very similar to taxes from
those working Crown deposits. The royalties depend on price and volumje (gas & oil) or profits
(oil sands). From 1976-1983, 30% of government revenues from the energy sector were placed in
the Alberta Heritage Savings Trust Fund. That shrunk to 15%, then ceased in about 1988.
Recently, the Fund has been restructured, but I’m not aware of any dedication of energy sector
earnings to the fund. Recently, $400 was paid to each Albertan to represent their share of oil and
gas revenues from Crown land. This kind of payment is not scheduled or required by law.
Albertans are now considering a regular citizen’s dividend from moneys placed in the Fund.
According to the Norwegian Ministry of Finance, several oil-producing countries have some kind
of fund paid for by taxes on oil and gas revenues or a share of the government’s budget surplus.
Chile and Venezuela use the money to stabilize the government budget, which is very sensitive to
variations in oil and gas tax revenues. There are not necessarily any public savings over the long
run.
Alaska and Kuwait have savings funds which are separate from the government budget. Alaska
gives about half the interest earned on the fund back to the citizens in the form of a yearly cheque.
Kuwait, East Timor, and Norway have financing funds which pay for government deficits. Here it
is obvious when the net savings of the country are positive or negative.
According to the CIA World Factbook, Norway’s “Government Petroleum Fund” is currently
valued at $250 billion, which is equivalent to about 1 year’s GDP.
Norway uses part of its fund to buy foreign exchange so that Norway’s krone will not appreciate
too much due to demand for Norwegian oil and gas. When demand for your major export
commodity causes your currency to appreciate, your other export sectors are injured. This is
known as Dutch Disease.
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Hartwick’s rule is that resource rents must be reinvested in physical capital.
Ignoring the depreciation of physical capital for a moment, there must be
investment I > THR, else total capital is declining due to the running down of
the exhaustible resource. I – THR is called economic depreciation.
There is a similar number that can be calculated for countries which exceed
their optimal harvest of renewable resources.
Normally, statisticians collect data on GDP or GNP each year. They also
calculate NDP or NNP, which subtracts physical capital depreciation from
GDP or GNP.
Green NDP or NNP would go one step further and subtract economic
depreciation from NDP or NNP.
So we see that a nation’s capital base can be run-down (depreciated) or
built up (“savings”/investment).
A country may be investing a lot, but its resource base may be depreciating
even faster. An economy needs “genuine savings” in order to be
sustainable.
Genuine Savings
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Genuine Savings was calculated for various nations in a 2006 publication of
the United Nations titled “Where is the Wealth of Nations? Measuring Capial
for the 21st Century”.
Gross National Saving = (GNI – C – G ), where GNI is approximately equal to
GDP
minus the depreciation of physical capital = Net National Saving
Net National Saving
plus current spending on education
minus an approximation to Total Hotelling Rent
minus health and other damages from pollution (the authors included a charge
of $20 per ton for CO2 emissions)
= “Genuine Savings”
Genuine Savings, 2000, As % of GNP
USA, Canada
Australia
Denmark, Norway
Ireland
Romania
Kuwait, Saudi Arabia
Mexico, Bolivia
Haiti, Dominican Rep
Kenya
8.2, 12.7
4.3
14.8, 18.5
22.7
3.3
-12.9, -26.5
8.4, -0.6
26.1, 14.2
10.9