Assume an individual lives two periods. In period one she works full time and makes $100. In the second period she enters partial retirement and makes $20. She can borrow and save at the constant, risk-free interest rate r.
1. Write down her consumption in the second period, c2 as a function of her consumption in period 1, c1 and the interest rate.
2. Illustrate her budget constraint. Label the intercepts and the initial endowment point, representing the consumption bundle with no savings.
3. Sketch 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. Assume the interest rate rises. describe 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? Discuss.