Choice of Technique in a Continuous Time Infinite Horizon Optimal Growth Model

摘要

We consider the choice of technique in a continuous time infinite horizon optimal growth model. There are n+2 goods, output, labor and machines M(1),M(2), ..., Mn. We can convert one unit of labor to q units of output or r(i) units of M(i), for each i. Also, we can convert one unit of labor and one unit of M(i) to q(i) units of output. We prove under some sufficient and necessary conditions that we never build any machines for the general concave utility function. If the condition is not met, we build one machine from beginning to end when the utility function is linear; when the utility function is nonlinear life gets complicated. In the one machine case, we give a general algorithm to solve it. In the many machines case, we prove an asymptotic result (as t approaches infinity, the behavior is similar to that of the linear case) and give examples showing that a simple characterization of the optimal solution is difficult. (Author)