3. (20 points) Consider a representative consumer at time t seeking to maximize the sum of discounted lifetime utility from t on, 00 E 351603\") 3:0 subject to the innite sequence of ow budget constraints Ptct + Stat = Stati2 + Dtati2 + Yta where the notation is as in class: at is holdings of a real asset (a \"stock\") at the end of period 15, St is its nominal price in t, Dt is the nominal dividend that each units of assets carried into t from period t 2 pays out, K is nominal income in t, ct is consumption in t, and Pt is the nominal price of each unit of consumption in t. Note well how the budget constraint is written: it is assets accumulated in period t 2 that pay off in period tthus, in this model, stocks must be held for two periods, rather than being able to be traded every period. Construct the Lagrangian to compute the stock price St in period :5. Explain intuitively how and why the stock price differs from that in the model studied in class, in which all shares can be traded every period