# A Macroeconomic Problem: Life Cycle Hypothesis

**Quantitative Finance**Level 5

**Life Cycle Hypothesis**.

Life Cycle hypothesis saids that: Consumer plans their consumption saving pattern over their life-time. This is true because consumers somehow does plan long term and potentially be their life time. See the attached image, that is a typical consumer's consumption pattern over the life time. Where the triangle shown is their wealth throughout time. . In this theory let \(C\) = Consumption, \(Y\) = Income, \(W\) = Wealth, \(T\) = Amount of LIfe this Person have.

This theory implies that: \[ C = \frac{1}{T(W)} + \frac{R}{T(Y)} \]

Find the total Wealth of this person (The area of the triangle), if a person lives 100 years old and retires at the age of 65. Also, His income before retirement is 100000 per year. Also assume he had the same income throughout his working career.

*Hint:* Wealth at Retirement is \((T-R)C\)

*Note:* This is a simplified version of the model, as most of the young people will borrow in their young years and may have negative wealth

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