Question

1. Alex views present and future consumption as perfect substitutes. He does, however, discount future consumption by a bit to reflect the uncertainties of his life. His utility function is therefore given by U(C1, C2) = C1+C2/(1+p), where p is the "discount rate” Alex applies to consumption in period 2. (a) Graph Alex's indifference curve map. (b) What happens with his consumption in time period 2 if the real interest rate exceeds the discount rate? (c) What happens with his consumption in time period 2 if the discount rate exceeds the real interest rate? (d) What do you conclude about the relationship between a person?s sav- ing behaviour and his or her "impatience”? Now, let us assume that Alex's utility over present and future consumption has changed to the quasilinear: U(C1, C2) = 5lnci + C2. Let us also assume equal endowment of $5 in both time periods. (e) What do you conclude about the relationship between a person's sav- ing behaviour and his or her "impatience”? Show it also graphically.

Answer 1

9 + 1) 169,)= 4+ (2 , perfect substitute Poef.. (a) Ic slope downwards, with slope =- aylay = -cite .. ou 1962 6) Now read as Intertemporal Boc. . 180 slope of BC litrl. Slope of gc (1) as r>p a XA 80 (1+r) 1 (itp)) 80 Bc is steeper than 9c, 80 only . C2. is consumed, ato , 03 MRS = 0 , (1/3) - =(1+0 - (1+0) Tite MW2 so period 2 const is Maximuon Part 10+P) 1 > K+01 80 MU? CNO Now as ea impatience Level rises, so. If f exceeds then Coq falls to zero, so. savino falls, whole income is consumed un current period only do MO2 tad to d.)

e.) uca, (2) = 5 enatca Y = 92=5 Now MRS 1,2 = Moi = 5/6 Intertemporal B.C. → M02 then at Eqm MRS = (to) from B.C. 5+62= Y, CHo) +42 C*= Y C+8) +42-5 = 5(140) + 5-4 Ca =56148) |