One Dynamic Input-Output Mode

This paper researches the existent problem of the stable increase solution for one dynamic input-output model that the time lag is one.Leontief first gives out the dynamic input-output model, but he don't solve its stable increase solution, which makes its application limited. Hua-luogeng researches the homogeneous input-output model, and gets the stable solution. This paper is mainly the dynamic input-output model that the time lag is one, which is base on the above models. After studying, we consider stochastic factor step by step in it, namely when consumption coefficient matrix is stochastic (when investment matrix is stochastic, it is almost same. So we don't research it), and they are both stochastic, then we research the stable increase solution. We utilize the means of the modern stochastic analysis and Markov process, that the stochastic dynamic input-output model don not exist the stable solution is proved. Namely, economic system must is adjusted constantly. The probability that the collapse time of the economic system is o is one.