Suppose you have $10. You can spend as much as you like today, and save the remainder for a year at 10% interest, after which you can spend your savings (including the interest).
a. Draw your budget constraint between "goods today" and "goods next year," using a dollar's worth of goods as your basic unit.
b. Suppose the government announces that it will impose a sales tax on all goods bought next year, but not this year. Illustrate the shift in your budget line. Show your new tangency, and illustrate the number of dollars that the government collects next year.
c. Suppose instead that the government announces a sales tax on all goods bought this year. Illustrate the shift in your budget line. Show your new tangency and illustrate the future value of the dollars the government collects- where the "future value" of a dollar collected today is equal to $1.10 next year.
d. Suppose instead that the government announces a permanent sales tax that raises the price of goods by the same percentage both this year and next. Illustrate the shift in your budget line. Show your new tangency and illustrate the future value of all the dollars the government collects. (The future value of a dollar collected today is $1.10; the future value of a dollar collected next year is $1.)