環境の最適制御〔I〕

最適公害制御モデル

抄録

In this paper, we have developed and refined one type of the optimal control model which will be intended to control, by means of the allocations of the production factor of ‘capital’, the trade-off type of the stock of pollution in which the substitutability between consumption and the stock of pollution is permitted; and several very interesting analytical results have been obtained.
Our model is formulated to maximize the functional (12) subject to the capital stock constraint (1), the production function (3), (5), the pollutional flow-discharge function (7), the accumulation-of-pollution equation (9), and the initial condition of the stock of pollution (11-2), as follows:
Judging from the viewpoint of controlling optimally the stock of pollution, it has become much worth consideration how levels the exogenously given total of capital stock _??_ is to be. There exists a critical level (i.e., X) in the range of _??_. Depending whether the current total of capital stock _??_ may be greater than, less than, or equal to the above-mentioned X, the prescription of the optimal control of the stock of pollution will be expected to diverge in many branches of it.
The same thing will, of course, be said for the historically given initial level of the stock of pollution also.
In such a manner, the optimal control of the stock of pollution depending greatly upon the initial level of the given total of capttal stock and the initial level of the stock of pollution, and also depending how these levels are, the desirable policy of the optimal control of pollution has become to vary entirely, sothat it will be necessary to take these points into consideration in order that weshould intend to carry into effect something of the environmental policy for thestock of pollution. practically.