URBAN INCOME AND RENEWABLE RESOURCE DEGRADATION IN RURAL
AGRICULTURE



Perrings (1989,1991), Clark (1991), and Ciriacy-Wantrup (1963),
have argued that low income causes high discount rates.  If this
is correct, it may explain the widely shared observation that
very poor regions seem to degrade renewable resource stocks far
below economically optimal levels (Chapman 1990, Moyo 1991, and
others).  Perrings' 1991 review article is an excellent summary
of our current knowledge.

A typical picture would show a commercial pasture or forest with
an apparently healthy level of forest trees or pasture grass. 
This would adjoin a communal area with no visible grass, much
barren ground, few trees or bushes, and goats replacing cattle as
the primary grazing stock.

In the communal area, cash income would typically be received
from relatives working in mines, factories, and urban areas at
low wages.  Many residents of communal areas or "homelands" would
be residing there after failing to find steady employment
elsewhere.

In this situation, credit markets may be organized for barter as
well as currency, and time preference rates and interest rates
may be very high.


Figure 1. Renewable Resource Biological Growth


Consider figure 1, representing the biological growth function. 
The horizontal axis M represents biomass, and K represents the
biological carrying capacity maximum.  H, the vertical axis,
shows the amount that can be harvested annually on a sustainable
basis for any given stock level M.  Beyond K, crowding and
disease increase mortality and bring net harvesting H to negative
values.

Hmsy is the conventional maximum sustainable yield harvest level.

Note that every H on the curve is sustainable, but Hmsy is
maximum.  In figure 1, the shaded ellipse represents a typical
low level of biomass and harvest in a poor rural area.

Whether a forest, pasture, wildlife, or fishery, figure 1
represents a degraded resource with limited output.  Stock level
M is close to the origin, or extinction of the resource.

An important point to make here is that this can be economically
optimal for poor rural areas, and that moving biomass and harvest
levels to the right requires higher incomes and lower discount
rates.

The basic relationship is expressed in equation 1 and figure 1. 
The discount rate is i, and the biological growth rate is r.  Mec
is the economic optimum biomass level.  K represents the maximum
total amount of biomass, K/2 is the biomass level with maximum
harvestable, sustainable yield, which is Hmsy in the figure. 
Note, in the equation, that if the interest rate is O, the
economic optimum biomass Mec becomes the same Mmsy as provides
the maximum sustainable yield.  Equation 1 is derived in the
Appendix.



Equation 1

           K    r-i
     Mec = -- * ---
           2    r

The resource degradation illustrated here does not depend on
excessive private use of a common resource.  Figure 1 in fact
assumes that the biomass is managed as private property, and, if
communally owned, is managed for maximum profit.

Consider a numerical illustration: a small watershed of 500
hectares with a maximum wood (or pasture) biomass of 7500 tons
("i.e.," K = 7500, or 15 tons per hectare).  The biological
growth rate before crowding is 0.5, and the rural interest rate
is 0.4.  The maximum sustainable yield would be a Hmsy of 937.5
tons annually at a biomass stock level Mmsy of 3750 tons.

With these values, the economically optimal vegetation level
(Mec) is a lower 750 tons.  The economically optimal harvest Hec
is 337.5 tons annually, much lower than the Hmsy above [note 1].

[Note 1. These figures follow from the growth function: 
         F(M) = rM - rM**2/K]

This follows from received economic theory (especially Clark,
1976 and 1990).  It has particular relevance to rural areas in
Southern Africa.  If it is correct that i is inversely related to
income and wages, then it is obvious that protecting rural
resources requires higher incomes.  Unfortunately, the current
reality in Southern Africa is population growth in excess of
growth in national income.  Thus, for most people in Southern
Africa, incomes are declining.

It bears repeating that this analysis does not invoke common
property assumptions: here, resource degradation is economically
logical where the resource is properly managed for long run
profit.

The same logic applies to a change of owners who face different
interest rates.  Imagine one owner is an owner-manager in the US,
with no debt.  This owner sells to a heavily debt-leveraged
buyer.  The new owner, with a much higher time discount rate,
will manage harvesting levels very differently than did the first
owner.

In equation 1, note that if i rises to or above r, then Mec = O:
extinction is optimal.

Climate change or drought in Southern Africa would manifest
itself through higher temperatures and lower precipitation.  This
would collapse both biological growth (r) and carrying capacity
(K) in figure 1.

If climate change in Southern Africa occurs in a macro-economic
setting of low wages, high unemployment, and high and rising
discount rates, then it may become even more frequent for i to
exceed r, exacerbating an already severe problem.

In 1991 and 1992, much of Southern Africa experienced continuing
unusual drought.  There is, of course, no empirical evidence that
this is a result of global climate change, but this is the kind
of consequence that may be anticipated.