Question

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1.a) Consider an agent who will live for two periods with utility function U(x1, x2) = x1 * x * . The agent receives incomes 11 and 12 in periods 1 and 2 respectively. If the market interest rate is r = 10% and 14 = $10 and 12 = $10, solve for the agent's optimal consumption in each period. Graph the budget constraint and some indifference curves.

Answer 1

Given -

r=10 %, income received in period 1 is $10 and in period 2 is $10. Optimal condition will be fulfilled at the point where slope of intertemporal consumption curve is equal to slope of utility function, that is (1+r)=MUx1/ MUx2, where x1 and x2 are consumption in period 1 and period 2 respectively.

Ginen, ITTI I = $10 I2 = $10. 8 = 10% U(X, H₂) = 24 x 3/4 optimal condition - (1+r)= MUXI Mitr'y slope of mura | Intertemporal consumption cune 7 (+0.1) = 112 da, ,-3/4 X2 314 2 2 2 2 2 -114 X, llu 4.3 a = 8.3 51 m2 = 3.32,4

80, aut At the optimal level, G+ C = I + I2 Tomta dojot tr u ller, te rochastol l Hure, Mt 2 = 1 + I2 Consumption in tr 1st period C, Da Consumption in 2nd Periode 2 > dit 3.38 = lot 10 21 2. Ito tool ltool -) 2 + 3.321 - 60+ lo 1 -) g,+ 3x1 = 10+ 9.09 2) 481 - 19.09 Tot - 19.09 = 4.77 s optimal consumption in 1st Period Also, t * = 3.3 x * = 3-3*4.77= 15.75) optimal consumpth in 2nd period - 4 22

Diagram

Diagram yam de (consump inand Period Budget constraint x + 2 y = I + Iz ty tr Slope = (1+r) Ę Optimal Level - muay - (ltr) = Selasa, 2 = MRSx, až MUAL 15.15 IC, ICI x1 = 4.77 x, consumption in 1st Period