Profit rates equalization and balanced growth in a multi-sector model of classical competition

The article refers to the old issue of profit rates equalization, originated from the works of Smith and Ricardo. It is devoted to a dynamic, recursive model of classical competition in a growing economy. The economy is composed of n firms (sectors) producing n different goods. Decisions on prices and production are made in each period by firms managers who take production capacities, determined by fixed capital, as given. All firms are owned by one representative capital owner (a capitalist) who decides in each period on his consumption and investment funds and next distributes the investment fund among firms on the basis of their capital profitability differentials. The author presents proof of existence, uniqueness and stability of a long-run classical equilibrium, which is equivalent to a balanced, long-run growth of fixed capital, output and consumption with equal profit rates and zero inventories. (C) 2018 Elsevier B.V. All rights reserved.