Consider the following seemingly small variation on part

(b) of Problem 8.16.

Choose an N, and define e ≡ 200/N. Now, assume that Y can take on only the values 0,e, 2e, 3e, ... , 200, each with probability 1/(N +1). Likewise, assume that C can only take on the values 0,e, 2e, 3e, ... , and find the Vn (X)’s only for X equal to 0,e, 2e, ... up to some upper bound B that you choose (and assume that Vn (X) = Vn (B) for X > B).

Show (analytically, not numerically) that value-function iteration using this numerical algorithm converges to V(X) = −∞ for all X. (Hint: If you get stuck, try it with N = 2, B = 300.)24