Question

Sara is 20 years old and plans to live until she is 80. Her behavior is consistent with the life-cycle hypothesis and she intends to perfectly consumption smooth. For simplicity, assume that the interest rate is zero (i.e. there is no discounting of future dollar amounts).

a. Sara is currently earning $120,000 a year. She will earn this same salary across her whole career and then retire when she is 70. How much does she spend each year in order to perfectly consumption smooth? Explain briefly.

b. Suppose now that Sara has to go to medical school for ten years (earning no income there). She then works from age 30 to age 70, earning $120,000 a year, followed by ten years of retirement. If Sara perfectly consumption smooths, how much does she spend each year?1

c. (Extra credit) Explain how liquidity constraints might present a problem for Sara to achieve the consumption plan in (b).

Answer 1

A. Sara will work for a total of 70-20=50 years. In these 50 years, she will earn

50*120000=6000000.

She will spend these equally over 80-20=60 years, for a smooth consumption. So, each year she should spend

6000000/60=100000 per year.

B. Now she will earn for 40 years.

Total earnings=40*120000=4800000

Spending per year for a smooth spending=4800000/50=96000 per year.

C. As Sara spends less each year than she earns (because she is saving for retirement), she will be depositing/investing this extra money. Often, these investments are not liquid. This means that it is not easy to convert them instantly into usable money. For example, some money might be in deposits which are not easily convertible. And when the time for usage comes, it might be tough to convert them quickly.

This way, liquidity constraints might present a problem for Sara to achieve the consumption plan .