Do the same in terms of ht 1 so the choice variable is ht1

Question

This is a question about Bellman equation

a) F(N_t) = M_{t *} N_t^1/2 ( Technology)

Σ∞_{t=0 * B}^t U(C_t ) ( preferences)

M_{t+1 =} M_{t -} α N_t ( law of motion)

using Bellman equation, state planner's problem at t

b) Do the same in terms of H_{t +1} so the choice variable is H_t+1 and explain how to find steady state of M*