In a two-period model, suppose that a consumers utility function is: U(c1,c2) = log(c1) + log(c2)

where c1,c2 are the consumption of a good (orange) in the two periods.

Let p1=p2=1, so that there is no inflation.

Let the endowment income in the two periods be m1=1, m2=2

Suppose that savings yield a real interest rate p of 20%

a) solve the demand for c1 given p being 20%

b) find the level of the real interest rate p such that the consumer is neither a lender nor a borrower.