Macroeconomics need answers thx

Consider a representative consumer who lives for two periods: current and future. The consumer is assumed to have it units of time available each period, which can be allocated between leisure time and time spent working. The time constraint for the current periods is f + N 5 = h, Where I and N 5 are leisure time and working time in the current period, respectively, and h 2 i > 0. The time constraint for the future period is i; +N's = h, Where I: and N '5 denote leisure time and working time, respectively, and h 2 E' :2 0. The consumer derives utility from consumption and leisure Let C and Cr denote the consumer's current and future consumption, respectively. The preferences over consumption and leisure are dened by U(C, C', l, l\"), which satises all three properties specied in the textbook. The consumer's budget constraints are 0+8 0! w(hl]+7rT, w'(hi')+w'T'+(1+r)s, where S is savings; 7r and a" are the current and future dividend incomes; T and T' are the current and future lump-sum taxes; to and w' are the current and future wage rates, respectively; 1' is the real interest rate. The consumer chooses the current and future consumption and leisure to maximize their lifetime utility, taking the market wage and interest rates, dividend incomes, and taxes as given. La) Consider a standard casein which the consumer is free to choose her leisure time (LEISURE CHOICE). Determinte the eects of lowering the market interest rate on the current consumption and labor supply. Explain your solution using in a diagram. Make sure you label everything in your graphs. (8 points) Lb) Consider a special case in which the consumer is required to supply,r a constant fraction of time endowment to the A _.---.. labor market (NO LEISURE CHOICE). The current and future labor supplies if?\" = (h i) and N 5' = (h I?) are constant, i.e. the quantity of leisure is xed. The consumer's current and future before tax incomes are dened as y = 104$; + 1r and y'r = w'Ns' + 71'", respectively. The consumer's current and future budget constraints are given by: C+S=yT, and c\" =y' T' +(1+r)S. Now, assume that i) the credit market is imperfect so that the consumer faces a borrowing constraint such that S 2 n:; ii) the consumer's preferences are of the form UfC, C") = min {0, C'} ; and iii) y 100, y' 140, T 20,1\" 10, r 10%, and a: = 10. Compute the consumer's optimal consumption and savings. Show your solution in a diagram. Make sure you label everything in your graphs. (12 points)