Consider the following two-period problem for the representative consumer.

Y1 = 28

T1 = 2

Y2 = 54

T2 = 12

r = 0.05

C1 = consumption in the first period

C2 = consumption in the second period

S = saving in the first period U(C1, C2) = ln(C1) + ln(C2)

This time, the representative consumer faces a limited commitment problem. Because of such problem, the bank requires collateral when she borrows money from the bank. The collateral is the value of the houses she has (H), which can be sold in the second period for the price of P. Suppose the following values for H and P

H = 7

P = 3

What is the optimal saving, S*, that maximizes the representative consumer's lifetime utility?