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 S60,000. 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) Wt is the amou sis pernon has avalble at the time of her re (e) How does this person modify her annual consumption if her retirement age changes to 68? And if her life expectancy increases to 90? (Qualitative answers are enough.)

Answer 1

Answer:

Given

Annual Income I=$60000

A)

Let X be the annual consumption

so

X*(Life expectancy - Current age)=60000*(retirement age-current age)

X*(85-25)=60000*(65-25)

X=$40000

her annual consumption =$40000

B)

Average propensity to consume= 40000/60000= 0.67

C)

Her annual Saving=Income - consumption

Her Annual saving =60000-40000=$20000

D)

At time of retirement amount of saving=(60000-40000)*(65-25)=$800,000