Question

^{Suppose a two-period-lived household facing a financial market in which it can borrow or lend at an interest rate equal to r = 15%, and exogenous income in periods 1 and 2 equal to Vi = 1 and y2 = 3. The household maximizes where y = 3 and ß = 0.95. • Consumption growth across periods 1 and 2 is equal to: (a) 5.99% (b) 1.99% (c) 2.99% (d) 3.99% • Life time income measured in units of consumption in period 1 is: (a) 3.2 (b) 3.4 (c) 3.6 (d) 3.8 • How much does the household save of its first period income? (a) -0.9 (b) -0.5 (C) -0.2 (d) 0.0 Assume now that the interest rate is endogenous. What is the value of the equilibrium interest rate r as a function of exogenous parameters? (a) Y++1/Y4 - 1 (b) 1/B-1 (c) (1/B - 1) (d) (Y++1/Y+)'(115) - 1
The correct answers are in bold. I need help seeing the derivation of these answers from the given problem. Thank you! Income is exogenous and given in the beginning of problem (denoted by Y1 & Y2)}

Answer 1

C Page No : at Eqm, 80 from MRS1,2= (1+0) C2 = {B (HO)] / *a B.C. 1.15a + Cq = (1+8) Yi+Y 2 = 4.15 1159 + 9• (-95 (1•15)'3 = 4.15) po 15 g + 1.02999 = 4.15 9 = 4015. 21.90375 2.1799 saving SF Y-G = -1-1.90375 ~ -.9 (A). Ang

d) at Eqm c = [puto) ] Vi 4G (a) = B lito) (to)= (2) l of 10- (Text) of -1 Ang (d) . Yt