Optimization in a Dynamic Leontief Model with Restricted Value Growth

The purpose of this paper is to develop a dynamic Leontief model of an msector economic system in which the production of all goods requires one time period and one primary factor, but no capital stocks of any good, and in which the total value of outputs from all sectors is required to grow at a specified rate in each period. The requirement of a fixed rate of total value growth is less restrictive than the familiar condition of balanced growth across all sectors, and it permits the definition and analysis of interesting finite-period optimization problems. Specific results of the paper include the following: (1) the proof that a value-added maximization problem with an unrestricted initial state will experience consumption in exactly one sector in each time period, and willyield an optimal value function which is linear in the variables that describe the terminal state of the system; (2) the development of an efficient Dantzig-Wolfe procedure for analysis of the total value-added maximization problem where both the initial and terminal states are specified; (3) the derivation of testable properties that will guarantee the attainability of a specified target state from a specified initial state of the system; (4) a formal comparison of some basic characteristics of total value growth and balanced value growth.