Please help with this question. I'm not completely sure if I have done this question correctly.

1. Consider a dynamic programing problem of: (col-4 )1-$ 1- + BEt [V (k', =')] + Ally - c- i]+ V (k, z) = max A? [y - zkan' -"] + X3K - (1 - 6) k - i]+ *4 [ 1 - n - e]+ AS [In =' - (1 - p) Inz - pln z + o'] where the maximization is with respect to {c, (, n, y, i, k'} and the A's. (a) Show that we will have an intratemporal and intertemporal Euler equations will have the form: MUe(t) MUc(t) M Pr(t ) = BE: {MU (t + 1) [MPk(t + 1) + (1-8)]} where the MU's are the marginal utilities and MP's are the marginal products. To do this, follow these steps: (i) write out the DP problem (Bellman's equation, states, and actions); (ii) find the FOC(s); (iii) find the Benveniste-Scheinkman Condition(s); and (iv) substitute out the value functions from the FOC(s) to find the Eulers and thus the optimality condition(s)