John earns 100 when he is at work (period 1) and 20 after his retirement (period 2). His preference over two-period consumptions is represented by u(x1; x2) = ln x1+ 0:8 ln x2. The pure interest rate between the periods is 10%.

(i) Write down John's lifetime budget constraint.

(ii) How much does he save for the retirement when he is at work?

Q2: Kathy earns 30 when she is a student (period 1) and 200 after she graduates (period 2). Her preference over two-period consumptions is represented by u(x1; x2) = x0:5

1 + 0:9x0:5

2 . The pure interest rate between the periods is 5%.

(i) Write down Kathy's lifetime budget constraint.

(ii) How much does she borrow when she is studying?