a. Suppose a consumer currently has $1000 with which to buy food for this year (c1) and for next year (c2). In both periods, the price of a unit of food is $1. In addition, they can earn 5% interest on their savings; thus for each $1 saved this year, they would receive $1.05 next year. Draw the consumer’s budget set for pairs of c1 and c2. Assuming the consumer has “standard” preferences defined over c1 and c2, depict a typical consumer’s equilibrium and discuss how this explains savings behavior.
b. Suppose that, in addition to the $1000 the consumer has today, they will receive an additional $1000 next year. It is possible to borrow against future income, providing one repays the loan plus 5% interest. Draw the consumer’s new budget set for c1 and c2. (Hint: Can the consumer afford to purchase 1000 units of c1 and 1000 units of c2? Also, the budget line has the same slope as in part a.)
c. Using the budget set obtained in part b, depict two cases: one in which an individual would choose to save part of their present income for next year and another in which a (different) individual would choose to borrow against next year’s income.