Sensitivity analysis of optimal growth plans with exogenous capital stocks

Abstract

The sensitivity of optimal growth plans with respect to changes in the target capital stocks and to changes in the length of the planning horizon was first considered by Brock (1971) where he showed that consumption would increase and investment in production would decrease in all periods if the target (or final) stocks were decreased. These results have been extended to multisector models by Nermuth (1978) and to models with irreversible investment by Mitra (1983). Similar results for changes in initial capital stocks were also obtained by Mitra (1979). As the planning horizon becomes longer, then the optimal growth plans become less sensitive to the initial and final stocks and the focus of the model is on the long-run stability or insensitivity of optimal plans. Such turnpike results have been developed for general models, as in MacKenzie (1976) or Majumdar and Nermuth (1982). For the growth models discussed above, the initial and final capital stocks are exogenously determined and the available stock in each period is endogenously produced. We will consider an expanded growth model where available capital in each period includes stocks endogenously produced as well as exogenously supplied (or demanded) stocks. There are several situations in