Vesta will live only for two periods. In period 0

she will earn $50,000.

In period 1 she will retire on Latmos Hill and live on her savings. Her utility function is u(c0, c1) = c0c1 where c0 is consumption in period 0, and c1 is consumption in period 1. She can borrow and lend at the interest rate i = 0.10.

a) What is an expression for her consumption in period 0 as a function of the parameters

specified?

b) Having solved her utility maximization problem, suppose

the interest rate rises

Will

her period 0 consumption increase, decrease, or stay the same?

Explain.