Given a consumer with the utility function U = C1C2 (which is C1 times C2) , where consumption in period 1 is C1 and period 2 C2. The income in period 1 (M1) is $80,000 and in period 2 (M2) $0. Interest rate r is 20%.

a)Use calculus to derive tangency condition for C1* and C2*, as a function of the interest rate r. (1 point)

b)Write down budget constraint equation. (1 point)

c) Solve for optimal choice of C1* and C2*. (2 points)

d) Is the consumer a borrower or saver? (1 point)

e) Now assume the consumer is able to earn M2= $60,000. How does this change the initial budget constraint (shifting or pivoting)? (1 point)