Heterogeneous capital and consumption goods in a structurally generalized Uzawa’s model

This paper proposes a growth model with heterogeneous capital and consumption goods and services. It structurally generalizes the Uzawa growth model by introducing heterogeneous capital and multiple consumption goods and services. We show the dynamic properties of the model and simulate the motion of the national economy with two capital goods and two services over time. We also examine effects of changes in preferences and technologies on the dynamic paths of the economy. The model with heterogeneous capital reveals different properties from those of the model with homogeneous capital. Our model shows the importance of introducing heterogeneous capital into the neoclassical growth theory. For instance, the comparative dynamic analysis shows that when the propensity to save is increased, the wealth per capita is increased initially but reduced in the long-term and the wage rate and national output level fall; the consumption levels of the two services fall even though the prices of the two services fall only slightly; the stock of the light capital good rises initially but falls in the long-term; the stock of the heavy capital good falls in association with rising in its price; the labor input of the heavy industrial sector fall and the labor inputs of the two service sectors rise while the labor input of the light industrial sector rises initially but falls in the long-term. Solow’s one-sector and Uzawa’s two-sector growth models cannot explain the structural changes with heterogeneous capital. Both Solow’s one-sector and Uzawa’s two-sector growth models show that a rise in the saving rate will increase the wealth per capita both in the short-term and in the long-term.