Suppose you have $1,000 today and expect to receive another $1,000 one year from today. Your savings account pays an annual interest rate of 25%, and your bank is willing to lend you money at that same interest rate.
a. Suppose that you save all of your money to spend next year. How much will you be able to spend next year? How much will you be able to spend today?
b. Suppose you borrow $800 and spend $1,800 today. How much will you be able to spend next year?
c. Draw your budget constraint between "spending today" and "spending next year." What is its slope? How does the slope reflect the relative price of spending today in terms of spending next year?
d. How would your budget line shift in each of the following circumstances?
You find $400 that you'd forgotten was in your desk drawer.
Your boss informs you that you will receive a $500 bonus next year.
The interest rate rises to 50%.
e. Under which circumstance would you spend more today: finding a forgotten $400 in a desk drawer or being told that you will receive a $500 bonus next year? Under which circumstance would you spend more next year?
f. Returning to the assumption that you have $1,000 today and expect to receive $1,000 next year, suppose that you choose neither to borrow nor to lend. Illustrate the tangency of your budget line with an indifference curve.
g. In part (f), suppose that the interest rate rises to 50%. Show how your budget line shifts. Do you increase or decrease your current spending? Do you increase or decrease your future spending? Are you better off or worse off than before?
h. In part (g), decompose the change in your consumption into a substitution effect followed by an income effect. Can you determine the direction of the substitution effect? Can you determine the direction of the income effect?