On the two sector growth model with adjustment costs of investment

Two types of growth models with adjustment cost of investment - Uzawa(1965)'s Penrose effect type and Eisner and Strotz (1963), Lukas (1967)'s et. al. type - are generalized into two sector model with capital intensive consumption good. Our approach is based on Abel and Blanchard (1983). First by constructing the competitive equilibrium which is composed of utility maximization over time of the representative consumer subject to the flow budget constraint, and the net cash flow maximization over time of the firm subject to the equation of motion capital, the equivalence between the competitive equilibrium and the social planner's optimum is shown. Then using the concavity of the value function (=maximized utility function), the global stability of the social planner's optimum is derived. In one sector model it is known that investment - capital ratio decreases as capital labor ratio increases, while per capita consumption increases as capital - labor ratio increases. These results remain robust in our two sector model.