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The model with prices

Economists have raised strong objections about the dire outcomes predicted by envionmentalists using systems dynamics models, such as that of the Club of Rome [Meadows , 1972]. One of their criticisms concerns the ability of market mechanisms to damp dangerous oscillations [Stiglitz, 1979,Cropper , 1979]. The argument is that when a resource becomes rare its concomitant price increase lowers its exploitation, or favors technologies less wasteful in resource usage.

Let us rewrite the production in monetary units as

 

where

 

in order to introduce a production in value which depends upon the production in fishes, instead of the previous expression which contained only a constant production coefficient, .

The differential equation for the resource, N, remains unchanged. (We use equation 3 from section 2 without the carrying capacity term). The only change occurs in the differential equation for the capital:

 

A simple monetary coefficient function is given by:

 

and the differential equation for the capital is then:

 

  
Figure 8: Plot of the production expressed in monetary units, , as a function of production, P, for the functions used in section 4. The solid line corresponds to "market" prices with coefficients b=2 and of the first model, equation 33. Note the plateau region which gives a constant income at large production. The dotted line corresponds to the second model with a minimum sustained price , with the same values for b and c, equation 39.

Figure 8 indicates a simple interpretation of the coefficients b and c in the fraction : b is a maximum production in value, obtained when the catch goes to infinity, and c is a characteristic scale on the production P. is the maximum price, which is obtained at zero production. We might consider that the above function reflects the situation where there is a strong decrease of prices with production since value production saturates at high production: there remains no incentive for producers to increase the catch in this regime. Under "normal" circumstances, the decrease of with P is probably less strong than in expression 33. Price dynamics under normal economic conditions are probably intermediate between the models of section 2 and 4.



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weisbuch
Fri Feb 7 13:18:37 GMT+0100 1997