TIME, INCOME AND WEALTH DISTRIBUTION AMONG HETEROGENEOUS HOUSEHOLDS IN A TWO-SECTOR MODEL WITH SECTOR-SPECIFIC EXTERNALITIES: A SYNTHESIS OF THE ARROW-DEBREU EQUILIBRIUM THEORY AND SOLOW-UZAWA GROWTH THEORY

This paper proposes a growth model of heterogeneous households with economic structure, endogenous labor supply, and sector-specific externalities. Following the economic structure of Uzawa’s two sector model, we consider the economic system with one capital goods sector and one consumer goods sector. Different from the traditional Uzawa model, we consider that capital goods are also used by households as consumer durables. The model is structurally general. For instance, if the economic system has only two sectors, then the Arrow-Debreu equilibrium theory can be considered as a special case of our model. Our model is an extension of the Solow-one sector and the Uzawa two sector model. As our model also includes labor supply and durable goods (housing) as endogenous variables, it is closely related with some other growth models in the literature. The model describes a dynamic interdependence among wealth accumulation, time distribution, and division of labor under perfect competition. We find different equations which are computational for simulating the dynamics. We simulate the model, plotting the motion, identifying the equilibrium point, and confirming stability. We also examine effects of changes in the externalities, the propensity to save, the human capital, and the population on the motion of the system.