Assume that Christine has an endowment of $40,000 in Year 1 and again $40,000 in Year 2.
a) Where is the endowment point as well as her choice of current (c1) and future (c2) consumption assuming that she chooses to consume $28,000 in Year 1 and faces a real interest rate of 5%?
b) Now suppose that the real interest rate increases to 10% but we keep Christine’s utility level constant. Christine decides to save 40% of her endowment in Year 1. What happens with her consumption in Year 1 and Year 2?
c) Continue from part b). The real interest rate increase makes Christine wealthier (higher utility level) and so she chooses to save now 35% of her endowment. What happens with her consumption in Year 1 and Year 2?
d) Which of the two effects described in parts b) and c) is stronger? Explain how the answer to this question determines the form of the aggregate savings curve.
Christine gets $40,000 in Year 1 and $40,000 in Year 2 as endowment. It is assumed she gets the two amounts at the start of the year and her expenses are also made at the start of the year.
In the first year she consumes $28,000. This leaves $40,000 - $28,000 = $12000. The $12,000 that she does not consume can increase by 5%, which is the real interest rate, if deposited. This increases the amount to $12,600 by the start of the second year. At this point she receives an additional $40,000 as endowment. Her endowment point here is $52,600.
If Christine saves 40% of her endowment, the amount saved in Year 1 is $16,000. This increases by 10% to $17,600 by the start of the second year. She can consume an amount equal to $57,600 in Year 2.
If Christine decides to save 35% instead of 40% of her endowment, her consumption in Year 1 is $26,000. The amount available with her in Year 2 is $55,400.
Generally, the aggregate saving increases with an increase in interest rate. In this case however, Christine is saving a lesser amount when the real interest rate increases.