Question

1. The Utility Function is given for a consumer as U = 3C2/3Cf1/3. The current income = 1000 and future income is 1500. Current r = 10%, find the savings – now assume r = 15% find new savings – find interest rate elasticity of savings.

Answer 1

1.$С1=\frac{3\times1000}{3+3}+\frac{3\times1500}{(3+3)\times(1+0.1)}=500+681.82=1181.82$

$C2=\frac{3\times1181.82(1+0.1)}{3}=1300$

S=1000-1181.82=-181.82

2.$С1=\frac{3\times1000}{3+3}+\frac{3\times1500}{(3+3)\times(1+0.15)}=500+652.17=1152.17$

$C2=\frac{3\times1152.17(1+0.15)}{3}=1324.99$

S=1000-1152.17=-152.17

$E=\frac{\frac{S2-S1}{S1}}{\frac{r2-r1}{r1}}=\frac{-0.16}{-0.33}=0.48$

demand is elastic but slightly