Question

Suppose that every consumer is born without any financial wealth and lives for two periods: young and old. Income received at the beginning of each period: 1 when young, and 5 when old. The real interest rate is 5% per period.

1. What is each person’s present discounted value (PDV) of future labour income at the beginning of life?

2. Suppose the consumer plans the same (permanent) consumption at the end of each of the two periods of life, ?̅. Calculate ?̅ where the PDV at the beginning of life of life time consumption (=?̅/(1+?)+?̅/(1+?)2) equals the PDV of income (as calculated in a.)

3. At each age, what is the amount of end-of-period saving that allows the consumer to maintain the permanent consumption you found in b.? (Hints: 1. Saving can be a negative number if the consumer needs to borrow in order to maintain a certain level of consumption. 2. Income earned at the beginning of the period earns interest until it is spent at the end of the period.)

Find the PDV of lifetime saving for the consumer at the beginning of life.

4. Consider a relatively Youthful Economy where there are 1250 young people and 750 old. What is end-of-period total or aggregate saving for today’s young? For today’s old people? What is the Youthful Economy’s total or aggregate saving? (Hint: Add the total amount saved by each generation).

5. Consider a relatively Ageing Economy where there are 750 young and 1250 old. What is end-of-period total or aggregate saving for today’s young? For today’s old people? What is the Ageing Economy’s total or aggregate saving?

6. Draw one figure with 3 columns for the saving in each economy of the young, of the old and the aggregate. Explain your figure.

7. Explain why aggregate saving is different in the 2 economies. Does this example help to explain why there is a global glut in saving in the world today, which is pushing interest rates to be so low everywhere?

Answer 1