Question

Isabella has preferences U = c1c2, receives income of Y1 = 200 today and Y2 = 100
tomorrow. The interest rate for saving or borrowing is r = 0:1. What levels of
consumption c1 and c2 will Isabella choose?

Answer 1

Intertemporal budget constraint
Saving in period 1, S1 = Y1-C1
Now in second period
C2 = (1+r)S1 + Y2
C2 = (1+r)(Y1-C1) + Y2
So , C2 + (1+r)C1 = (1+r)Y1 + Y2
Now r = .1, Y1 = 200, Y2 = 100

C2 + 1.1C1 = 1.1*200 + 100

C2 + 1.1C1 = 320

At eqm, MRS = (1+r)
MRS = MU1/MU2 = C2/C1
So at eqm, C2/C1 = (1+r)
C2 = (1+r)*C1

C2 = 1.1C1
So from BC:

C2 + 1.1C1 = 320

2C2 = 320

C2* = 160

C1* = 160/1.1 = 145.45

levels of consumption c1 and c2 will Isabella choose = (145.45, 160)

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