The transition.

We consider two schemes for a multisectoral economy to reach a balanced growth in the absence of central planning. In our case, the economy is closed and consists of n sectors. The output vector x(t) ∈ R satisfies the inequality Y x(t) ≤ x(t − 1) at step t, t = 1, 2, . . ., where Y = {yij} is a technological matrix. As is shown in [1], if the matrix Y is indecomposable and primitive, then the economic system can have a balanced growth x(t) = γx(0) at all steps t ≥ 1 if and only if x(0) is the Frobenius vector of Y . In this case we have γ = 1/λY where λY is the Frobenius eigenvalue of Y . The balanced growth is also called a turnpike regime. Further, we consider the case when the vector x(0) is not Frobenius of Y and the system is decentralized. Let us introduce some notation. By yji(t) denote the volume of product j that may be used by sector i at step t, by xpi (t) denote the plan of output for sector i at step t (this plan must be fix by the sector before the start of step t) , by xi (t) denote the total demand for the product i that was produced at step t, by xi (t) denote the total sale of the product i produced at step t. Variables xi (t) and x p j (t + 1) are related as