Question

Problem 3. (Life cycle hypothesis) A student graduates from college at age 25 without any initial wealth or savings and starts working. The annual income of the student is $60,000. When the student retires later in life at the age of 65 she doesn't expect to get any retirement benefits and will rely on her savings. We assume that the person does not earn any interest on the savings and that her life expectancy is 85 years. Also, assume that the person is infinitely patient and values future consumption in the same way as the current consumption (a) If this person spends her income smoothly during life, what will be her annual consumption? b) What is the average propensity to consume the current income during her working years? c) What is her annual savings? d) What is the amount of savings that this person has available at the time of her retirement? e) How does this person modify her annual consumption if her retirement age changes to 68? And if her life esperi omx:v it.lnnsrer.a IaoMI." tQtulututive, prost arxca ฮาร".rrvaq:h.)

Answer 1

(a)

Remaining life in years = 85 – 25 = 60

Remaining work life in years = 65 – 25 = 40

Total income = 40 × $60,000 = $2,400,000

Therefore,

Annual consumption = $2,400,000/60 = $40,000

(b)

     Average propensity to consume    = Annual consumption / Annual income

                                                            = 40,000/60,000

                                                            = 0.67

(c)

Over the working life,

Annual savings = 60,000 – 40,000 = 20,000

(d) At the time of retirement,

Savings available = 20,000 × 40 = 800,000

(e) As mentioned in the question, qualitative answers are enough here.

- Increase in retirement age will increase total lifetime income and therefore annual consumption will increase.

- Increase in life expectancy will increase the number of years that a given lifetime income will be required to be divided, and therefore annual consumption will decrease.