2. There are two persons in the economy, Mr. A and Mr. B. Mr. A has the following utility function and budget constraints: C03 C07 Max Subject to S+C = 80 C = (1+r)S Mr. B faces the following utility function and budget constraints: Max Subject to C0C02 S + C = 10 C = 80+ (1+r)S: a) Find out Mr. A's and Mr. B's optimal consumption levels and optimal savings in terms of interest rate r. b) Who is more likely to be a saver ? Who is a borrower? c) Please determine the interest rate that clears the credit market (call it r'). d) If r is 0, calculate Mr. A's and Mr. B's savings. Can the credit market clear under r=0? e) When r=r', how much Mr. A and Mr. B save individually?