Question

Smith lives in a world with two time periods: current period and future period. His income in each period is $10,000.

A) Draw his intertemporal budget constraint when the interest rate is 33%.

B) If Smith consumes $10,000 in each period, show his best affordable bundle and the indifference curve that passes through it.

C) Graphically show how Smith's current consumption changes when the interest rate falls to 0%.

Answer 1

Intertemporal budget constraint: C1 + (C2/1+i) = M1 + ( M2/1+i)

C1= Period 1 consumption, C2 = Period 2 consumption, i= Interest rate ,M1= Period 1 income, M2= Period 2 Income

M1= 10000, M2= 10000, i= 33/100= 0.33

Answer A) C1 + C2/1.33= 10000 + 10000/ 1.33

X intercept ( keeping C2= 0) =17518

Y intercept ( keeping C1= 0) = 23298

Answer B) The Equilibrium is at point E where current consumption C1 as well as future consumption C2 is equal to 10000 each

[Note: The intertemporal constraint for part A is this straight line with x intercept 17518 and y intercept 23298]

Answer C)  M1= 10000, M2= 10000

C1 + C2/1+0 = M1+ M2/1+0

C1+ C2 = 10000+ 10000

• X intercept ( keeping C2=0) = 20000

• Y intercept ( keepimy C1= 0) = 20000

With the new interest rate the new intertemporal constraint is given below