Consider a two-period model, inhabited by two individuals, Anna and Bob (A, and B).

A has the following preferences

uA(c0,^Ac1^A) = ln(c0^A) + 0.9 ln(c1^A),

while B has the following preferences

uB(c0,^Bc1^B) = ln (c0^B) + 0.8 ln (c1^B).

Consumer A receives an incomeY0^A= 100 in period 0 andY1^A= 150 in period 1. On the other side, Consumer B receives an incomeY0B= 125 in period 0 andY1B= 100 in period 1. Assume the interest rate isr. The government wants to spendG0= 50 in period 0 andG1= 75 in period 1. These spendings are financed through lump-sum taxes. It is assumed that the government collects the necessary tax to finance its spending in each period and the tax burden is equally supported by the consumers in each period.

1. Compute the optimal consumption (c0, c1) for each individual as a function of the interest rater. [12 points]

2. Find the equilibrium interest rate that clears the credit market.