Life-cycle Hypothesis

fleeting Macro

The key ideas:

1. When people decide consumption, they consider both present and future $Y$.
2. People’s saying allow them to move income from time when income is high to time when income is low.

That means, in this page, we want to figure out a question : ==Why $\frac{C}{Y}$ stays stable when $Y\uparrow$ ==

The Model

Max $U=ln(C_1)+\beta ln(C_2)$

Subject to $Y_1=S_1+C_1$ and $C_2=Y_2+(1+r)S_1$

We can use the Largrangian Multiplier method to solve the best $S^{\ast }$

See the Inter-temporal Budget Constraint

The content of hypothesis

One of the important influence factor is the retirement date, so people may be afraid if they retire, they would have less income.

They think in order to maintain the consumption during the working years, they need to save during youth.

Suppose a consumer expects to live another $T$ years, and has a wealth of $W$, and expect to earn income $Y$ per year until he retires $R$ years from now. What level of consumption will the consumer choose if he wants stable consumption over the course of his life?

Solving

It is easy to get $C=(W+RY)/T$, or can be described as $W/T+(R/T)Y$ (We write like this because we can see the influence made by whether wealth or income)

That is, the economy’s income can be described as

$$C=\alpha W+\beta Y$$

Comparison between Keynes

1. The Life-cycle Hypothesis point out that the consumption is based on wealth and income
2. The APC of Keynes is $APC=\overline{C}/Y+c$ while for Life-cycle Hypothesis is $APC=\alpha (W/Y)+\beta$

Referrence

• https://zh.wikipedia.org/zh-tw/%E7%94%9F%E5%91%BD%E9%80%B1%E6%9C%9F%E5%81%87%E8%AA%AA