Suppose You Divide Your Life into Two Periods: Working Age

question 10

Essay

Suppose you divide your life into two periods: working age and retirement age.When you work,you earn labor income Y; when retired,you earn no labor income,but must live off your savings and the interest it earns.You save the amount S while working,earning interest at rate r,so you have (1 + r)S to live on when retired.Because you don't need to consume as much when retired,you want to set consumption when working twice as high as consumption when retired.
(a)Suppose you earn $1 million over your working life,and the real interest rate for retirement saving is 50%.How much will you save and how much will you consume in each part of your life?
(b)Suppose your current income went up to $2 million when working.Now what will you save and how much will you consume each period?
(c)Suppose a social security system will pay you 25% of your working income when you are retired.Now (with Y = $1 million,as in part (a)how much will you save and how much will you consume each period?
(d)Suppose the interest rate rises (starting from the situation in part (a).Will you save more or less?

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Definitions:

Salaries

refer to a fixed regular payment, typically paid on a monthly or biweekly basis but often expressed as an annual sum, made by an employer to an employee, especially a professional or white-collar worker.

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A 1930 U.S. law that raised tariffs on thousands of imported goods, contributing to the Great Depression.

Consequences

Consequences are outcomes or effects that result from a preceding action or decision, impacting subsequent events or conditions.

First Lady Eleanor Roosevelt

The wife of President Franklin D. Roosevelt, known for her humanitarian efforts and activism for civil rights during and after her tenure as First Lady of the United States from 1933 to 1945.