Find the optimal saving that maximizes representative consumers lifetime utility.

Consider the following two-period problem for the representative consumer. v1 =20 T1 =10 Y2=25 T2=4 r=0.05 C1 = consumption in the rst period Cg = consumption in the second period S = saving in the rst period The representative consumer wants to consume the equal amount in both periods. 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 = 3 P = 7 What is the optimal saving, S', that maximizes the representative consumer's lifetime utility? O A. -21 O B. -5.37 O c. -20 O D. +5.37 0 E. None of the above