At the end of the 1930’s Kantorovich was faced by a concrete planning problem – how to combine the available productive resources in factory in such a way that production was maximized. He solved this problem by inventing a new type of analysis, later called linear programming. This is a technique for finding the maximum value of a linear function under constraints consisting of linear inequalities. A characteristic feature of this technique is that the calculations give as by-products some expressions, called shadow prices, which possess certain qualities that make them useful as accounting prices.
- Speech given in 1975 Nobel lecture
- optimization models and their use in the control of the economy for the purpose of the best use of resources for gaining the best results.
- October Revolution. Then for the first time in history all main means of production passed into the possession of the people and there arose the need for the centralized and unified control of the economy of the vast country.
- The specific and peculiar problems
- The main purpose of economic theory changed from observation to control. Needed detailed planning. Since planning at such scale appeared for the first time, the solution needed to be found afresh
- Not just for the national economy but for enterprises and projects as well. Goals and Objectives. Precise accounting methods needed
- And then, the thing about indices. The way price, rent, interest exists in capitalist economy, in a centrally planned economy, its significance and existence itself gets questioned
- Together with material flows and funds in capitalist economies there are also studied and directly observed such important economic indices as prices, rents, interest rate in their static and dynamic properties. The indices mentioned serve as the background for all economic calculations, for aggregation, for the construction of the synthetic indices. It became clear that a, consistently planned economy cannot do without indices characterizing the analogous aspects. They could not be observed here and were given as normatives. The problem of their calculation was however not restricted only by technical aspects of calculation and statistics. It is important that in the new conditions similar indices received a quite different sense and significance, and some problems as to their nature, role and structure arose. For example, it was unclear and open to discussion whether a land rent should exist in a society where land is in the possession of the people or whether such an index as the interest rate has a right to exist.
- Centralization upto a level. Some control left for lower levels.
- The problem is to construct a system of information, accounting, economic indices and stimuli which permit local decision-making organs to valuate the advantage of their decisions from the point of view of the whole economy. In other words to make profitable for them the decisions profitable for the system, give a possibility to check the validity of the work of local organs activity also from the point of view of the whole economy.
- Question of the most efficient structural form of the control organisation.
- The problem of prediction and control in large shifts of weights of different branches of economy, of rapid changes in tech development.
- I mean the problems of prediction and control in conditions of large shifts in the weights of different branches, of the rapid changes in production and technology, national economy. The problems of estimating technical innovations and the general effect of technical progress. The problems of ecology connected with the deep changes of the natural environment under the influence of human activity, the prospects of exhausting the natural resources. The prediction of social changes and their influence on the economy. The changes in presence of contemporary computational technique, means of communication, managerial devices and so on.
- These problems exist in capitalist countries too, but the control problem was different level and peculiar. Since nothing existed at scale of this nature, "The economic theory of Karl Marx became the methodological background of the new created Soviet economic science and of the new control system."
- I just wish to point out that the system of planning organs was created on the initiative of the founder of our state V. Lenin and simultaneously on the same initiative a system of economic accounting (hozraschet) was introduced which gave a certain financial form of balance and control of separate economic activities.
- Although it worked well, there were inefficiencies/ possibilities of further improvements hence qualitative mathematical methods
- The new methods: The optimizing approach is here a matter of prime importance. The treatment of the economy as a single system, to be controlled toward a consistent goal, allowed the efficient systematization of enormous information material, its deep analysis for valid decision-making. It is interesting that many inferences remain valid even in cases when this consistent goal could not be formulated, either for the reason that it was not quite clear or for the reason that it was made up of multiple goals, each of which to be taken into account. For the present the multi-product linear optimizing models seems to be mostly used. I suppose that now it is spread in economic science not less than for instance Lagrange equations of motion in mechanics.
- It is well-known that the choice of optimal program i.e. of the set of intensities of these activities under some resource and plan restriction gives us a problem to maximize a linear function of many variables satisfying some linear restrictions.
- Properties which allow for wide and varied use:
- Universality and flexibility - For many branches of economy and levels of control. Additionally, in complex situations, becomes a take-off point for generalizations. It is possible to consider a series of models where necessary conditions and restrictions are introduced step-by-step while the needed descriptive precision is not reached.
- Simplicity - simple linear algebra
- Efficient Computability. Simplex method. Algorithms for computers - 1975 - nowadays modern variants of the methods on modern computers can rapidly resolve problems with hundreds and thousands of restrictions, with tens and hundreds of thousands of variables
- Qualitative analysis, indices. Together with the optimal planning solution the model gives valuable devices of qualitative analysis of concrete tasks and of the whole problem. This possibility is given by a system of indices for activities and limiting factors which is found simultaneously with the optimal solution and is in accordance with it.
- Concordance of the means with the problems - Both in capitalist economies and socialist economies. He feels the spirit corresponds closer to the problem of socialist economies. (I though wonder that efficiency and maximisation is a very capitalist objective as well)
- A problem that needs to be pointed out especially is that of decentralized decisions. The investigation of a two-level model complex leads us to the conclusion that in principle the decentralization of decisions with observance of the total object of the complex is possible by the means of a correct construction of objects in local models.
- Difficulties Difficulties arise both from the specific features of the object under investigation and from defects in the researches and their practical realization.
- It is especially important to test the influence of the difference between the model and reality on the obtained result and to correct the result or the model itself. This part of work is not often observed.
- Complication in the correct choice of the objective function.
- A solution of newly appearing economic problems, and in particular those connected with the scientific-technical revolution often cannot be based on existing methods but needs new ideas and approaches. Such one is the problem of the protection of nature.
- Accounting method is just one part. Control strucutre as well.
- Education of people. psychological barrier, to shift from many-years-used routines to new ones.
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