Show that one step ahead forecast of the MRS is constant

Question

(Consumption under Certainty) Consider the representative household who is uncertain about its future income stream, {Y_t}   , at t=0, the representative household maximizes the following expected lifetime utility

Subject to A0 0 given and

 ,    0   (*)

Note that the household cannot choose the entire path of consumption at time 0 due to uncertainty. It can only choose C₀ and contingency plans for C_t , t , where the plans are contingent of the realization of  Y_t

Show that one step ahead forecast of the MRS ( E_tm_{t, t+1} ) is constant.

Summary

This question belongs to operations management, given future income stream and expected life time functions under certain conditions. You are required to understand the concept and answer the given questions.

Total Word Count 92