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The equilibrium
resource size  increases with the renewal rate of the resource r, the 
capital depreciation rate
 increases with the renewal rate of the resource r, the 
capital depreciation rate  , and decreases 
with the rate of production
, and decreases 
with the rate of production  , 
the efficiency of the harvesting
, 
the efficiency of the harvesting  and the amount of people involved
in the harvest, L (equation 5). The fact that the equilibrium
capital
 and the amount of people involved
in the harvest, L (equation 5). The fact that the equilibrium
capital  is inversely proportional to L simply reflects
the replacement of capital by labour in the Cobb-Douglas expression
1.
 is inversely proportional to L simply reflects
the replacement of capital by labour in the Cobb-Douglas expression
1.  also increases with r and decreases with
 also increases with r and decreases with  .
.
 is small, giving rise to oscillations,
 whenever resource renewal is fast with 
respect to capital depreciation, which is probably the case 
for most fisheries. The resource renewal rate for most species of fish
is of the order of a few years, while boats last for a couple of decades at least (major pieces of fishing gear typically last for seven years).
 The situation for forest exploitation might be the
opposite, with
 is small, giving rise to oscillations,
 whenever resource renewal is fast with 
respect to capital depreciation, which is probably the case 
for most fisheries. The resource renewal rate for most species of fish
is of the order of a few years, while boats last for a couple of decades at least (major pieces of fishing gear typically last for seven years).
 The situation for forest exploitation might be the
opposite, with  and no oscillations and a fast decay
towards equilibrium.
 and no oscillations and a fast decay
towards equilibrium.
 An important result is that
 is independent of the production coefficients
 is independent of the production coefficients
 and
 and  :
:  can be increased by
 technological or marketing
improvements that decrease the quantity of a natural
resource used in a given product. This would not change the oscillatory 
nature of the solutions. In the case of forest exploitation
such an improvement might be using less wood for a given piece of furniture
or making use of a larger proportion of each tree; for fisheries
it might be practices enabling the industry to use a larger fraction 
of the catch by marketing surimi or flour for cattle breeding.
On the other hand, such practices can improve the situation by increasing
the equilibrium resource size, which is a good 
defense against natural or artificial hazards which could suddenly
deplete the resource  below the threshold level necessary for reproduction.
 can be increased by
 technological or marketing
improvements that decrease the quantity of a natural
resource used in a given product. This would not change the oscillatory 
nature of the solutions. In the case of forest exploitation
such an improvement might be using less wood for a given piece of furniture
or making use of a larger proportion of each tree; for fisheries
it might be practices enabling the industry to use a larger fraction 
of the catch by marketing surimi or flour for cattle breeding.
On the other hand, such practices can improve the situation by increasing
the equilibrium resource size, which is a good 
defense against natural or artificial hazards which could suddenly
deplete the resource  below the threshold level necessary for reproduction.
 
 
    
   