On the Dynamic Properties of the Labor-Surplus Economy

The dynamic properties of the optimal growth model are examined, based on a one good and two factor-labor and capital--model with a labor-surplus economy due to a fixed wage rate. If the average capital productivity is higher than the time discount rate which is assumed to be larger than the population growth rate, then the economy reaches the full employment stationary state in a finite amount of time. If both are equal, then the economy stays in the initial state forever. If the average capital productivity is less than the population growth rate due to a high and fixed wage rate, then the economy is in the poverty trap where both per capita capital and per capita consumption shrink to zero. If the average productivity is higher than population growth rate but lower than time discount rate, there can exist two different paths – one to stationary state and the other on the poverty trap – depending on the initial values of per capita capital if the elasticity of marginal felicity is less than one. Therefore the only way to get out of the poverty trap is to increase average capital productivity above the time discount rate indirectly by increasing labor productivity by means of a big push or imports of technology and/or by increasing per capita capital through imports of capital. Tadashi Inoue, Faculty of Economic Science, Hiroshima Shudo University 1-1-1 Ozukahigashi, Asaminami-ku, Hiroshima 731-3166, Japan e-mail; [email protected]