Hi, please list out the formulas where necessary , graphs where necessary , if the question doesnt require it, its fine not have it but please do put it down if it helps you to explain . If the answer is provided, its because I struggled to understand the answer, please dont just reproduce it, but rather explain it and list out the formulas used with explanations OF FORMULAS USED IN THE QUESTION , the procedure etc.Thank you!

Q7. A consumer lives for two periods. She maximises the lifetime utility function subject to a budget constraint (note: A, is initial wealth) U = In(C1) + 162 & Ci+ = A1+ Y1+ +r (a) What is the first-order condition for consumption in this case? In this case, marginal utility is d ct s d in(Ct) = , so the first order condition for consumption is 1/C (1/C2)/ (1 + p) -=1+r C2 1 +r C 1 1 +p (b) Use the first-order condition to substitute for C2 in the budget constraint, and solve for C1- Solving the first order condition for C2 we get C2 = 1 + P Substituting into the lifetime budget constraint, we get C1 - = A1 + Y+7 Y2 1 + p Itr It r ) / ( 1 + 7 ) (c) Set p = 0 and investigate how Y;, A,, Y?, and r affect C1. Interpret the results. (Note that the case of p = 0 corresponds to an incredibly patient consumer - one who does not subjectively discount the future at all) C = =( A, + Y , + 2) dy 1 2 ' dA1 do1 = 1; ac1 = -: If current income or wealth is higher, the consumer will consume half of it today and half of it will be saved in order to smooth consumption over time. dc1 dy2 -: If future income increases, the consumer will consume half of the present value of the increase in income today. dc1 _ _ 1 12 dr 2 (+r)?