12. Savings decisions

Bob is a tenured faculty member who teaches particle physics at a university where he earns an annual salary of $160,000. He intends to take the next year off to focus on writing a new undergraduate physics textbook, so he will not earn any income next year. He is currently deciding how much of this year's salary he should save for next year. Assume that there are no tax implications associated with the decision, and ignore what happens after next year. Therefore, next year Bob will consume whatever he saves this year plus interest, and he is not concerned with the future beyond next year.

The following graph shows Bob's preferences for consumption this year and next year. Suppose initially Bob cannot earn interest on the money he saves.

Use the green line (triangle symbol) to plot Bob's budget constraint (BC1BC1) on the following graph. Then use the black point (plus symbol) to show his optimum consumption bundle.

Note: Dashed drop lines will automatically extend to both axes.

BC1(0% Interest)Initial Optimum (0% Interest)BC2(50% Interest)New Optimum (50% Interest)020406080100120140160180200220240240220200180160140120100806040200CONSUMPTION NEXT YEAR (Thousands of dollars)CONSUMPTION THIS YEAR (Thousands of dollars)I1I2

Now suppose Bob can earn 50% real interest on any money he saves.

Use the blue line (circle symbol) to plot his new budget constraint (BC2BC2) on the previous graph. Then use the grey point (star symbol) to plot his optimum consumption bundle at this interest rate. (Hint: To plot BC2BC2, think about how much money Bob would have next year if he saved his entire income this year.)

Using the previous graph, complete the following table by indicating how much Bob should save of his current income when he cannot earn any interest on his savings and when he can earn 50% interest on his savings.

Interest Rate	Amount Bob Saves
(Percent)	(Dollars)
0
50

Which of the following statements is a good description of the results of this exercise, as well as its implications for broader consumer behavior?

All consumers, including Bob, save more money when interest rates are high, because they get a higher return on that investment.

In this case, Bob saves less money when interest rates are high. However, consumers with different preferences might save more money when interest rates are high.

All consumers, including Bob, save less money when interest rates are high, because they don't need to save as much money to have the same future income.

In this case, Bob saves more money when interest rates are high. However, consumers with different preferences might save less money when interest rates are high.