A Random Dynamic Input-output Model With Consumption

The dynamic input-output model had been put forwarded by W.Leontief. Since the problem of its balanced solution has not been solved, its application is very limited. Consider the randomness of economic development, in this paper, we study a random dynamic input-output model with consumption, and get the conclusion that the economic balanced growth solution for this model does not exit.First, we consider a dynamic input-output model with deterministic consumption vector S (t ), random consumption coefficient matrix and random investment coefficient matrix which the time lag is one. It has been proved that the economic balanced growth solution for this model does not exit, i.e., the probability that the collapse time of economic system is∞is zero. Thus, we prove the fact that economic system must be adjusted constantly.Next, in order to let input-output model be more practical, we randomize the consumption vector based on the above model. A dynamic input-output model with random consumption vector S (t ,ω), random consumption coefficient matrix and random investment coefficient matrix which the time lag is one has been discussed. By means of modern stochastic analysis and Markov process, it has been proved that the random dynamic input-output model does not have a balanced growth solution. In view of this, we show the defect of planned economy and the economic system must be adjusted constantly.