Dynamic programming
Example
Consumer saving problem:(^1) The planning period is Önitet= 1 , 2 ,.. .,T.
(^2) At every periodtthe consumer has wealthwt0 and consumption
ct0. The utility function for the consumer isu(c)=
p
c.
(^3) At everytthe set of feasible decisions areΦ(wt 1 )=[ 0 ,wt 1 ].
(^4) There is a production function
f(w,c)=(w c)( 1 +r)$k(w c)withr 0.
(^5) The consumer is maximizing the aggregate utility∑Tt= 0 u(ct).