Question $3(20$ pts$)$: Consider an $N$ period problem in which the

state space differs each period. That is$,$ the possible states in period $t$ are in $S_t$ for each $t=$

$1,2,$cdots,$N.$ Show how to reformulate the problem to fit the framework we discussed in class, that is$,$

there is a single state space $S.($In other words, how would you reformulate to create a single state

space $S).$