Presume an individual lives two periods. In period 1 she works full time and makes $100. In period 2 she enters partial retirement and makes $20. She can borrow and save at the constant, risk-free interest rate r.
1. Write her consumption in period 2, c2 as a function of her consumption in period 1, c1 and the interest rate.
2. Draw her budget constraint. Label the intercepts and the initial endowment point, representing the consumption bundle with no savings.
3. Draw indifference curve for the case where she is a saver. In a dashed line on the same figure, draw the indifference curve for the case where there is no access to borrowing or savings. In which is utility higher? How do we know?
4. Presume the interest rate rises. Draw the effect on the budget constraint.
5. Do we know if the increase in the interest rate will cause her to increase or decrease savings? Describe.