COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 754 "A Characterization of Globally Optimal Paths in the Non-Classical Growth Model" Rabah Amir May 1985 We show that the monotonicity property of optimal paths (or, equivalently, the uniform
boundedness of the marginal propensity of consumption by unity) is a necessary condition
for local (as well as for global) optimality, and is also sufficient for local optimality,
but not for global optimality. We also show that the well-known properties of the value
function -- continuity and monotonicity -- are sufficient (along with the above
conditions) to guarantee global optimality. In other words, if at any stock level, a local
non-global maximizer is selected, a discontinuity in the value function will be observed.
We suggest that the previous literature on this problem has not distinguished between
local and global maxima, and consequently has not attempted to derive conditions that
uniquely characterize global optimality. This is the major aim of this paper, and we hope
to have provided some insight towards a systematic approach to non-convex dynamic
optimization. |
