Analysis and balance survey of discrete input-output systems under random environment



Abstract: Under random environment, the balance survey is difficult in many fields, such as in the industrial structure, the economics, and the society. In this paper, we study the random dynamic input-output model with consumption, in which the time-delay is one; and analyze the existence of the balanced growth solution by the theory of Markov processes. We present a new criterion of the imbalanced survey, which is a positive right eigenvector of the expectation of a matrix associated with the input-output model. We also will prove that the collapse time is finite almost surely, which indicates that the random dynamic input-output model does not possess a balanced growth solution, and consequently, the economic system must be adjusted constantly.