# Life-cycle Income Hypothesis

Life-cycle Income Hypothesis

Italian-American Economist Franco Modigliani, winner of Nobel Memorial Prize in Economics in 1985, originated the Life-cycle Income Hypothesis base on Irving Fisher's model of inter-temporal choice. In Modigliani's Life-cycle Hypothesis, or LCH in abbreviation, builds on the assumption that individuals consumes its wealth and income over the lifetime. It assumes that inidividuals will seek to smooth out the total wealth and income over its lifetime, which gives rise to the equation $C=\left(W+RY\right)/T$ where W = initial endowed wealth, R = Retirement Years, Y = Income and T = Number of years of the individual's lifespan.

Rewriting the equation or consumption function, $C=\left(1/T\right)W+\left(R/T\right)Y$. If every individual plans their consumption in such way, the aggregate consumption function of the economy, will take the form $C=aW+bY$, where parameter a is the marginal propensity to consume out of accumulated wealth and b is the marginal propensity to consume out of income.

LCH solve the consumption puzzle proposed by Simon Kuznet, which observes that in the Long Run, the average propensity to consume (APC) of individual will be constant, as the consumption function of individuals will pass through the origin. This can be best illustrated in the diagram below:

The Short Run Consumption Function denoted by W0 represents the initial endowed wealth level of a particular individual. In the short run, an increase in his income will triger an increase of consumption level from C0 to C1. However, in the long run, the increase in his income from Y0 to Y1 will leads to an increase in his wealth level. Hence in the long run, this will induce an upward shift of the consumption function from W0 to W1, which implies an increase in consumption from C0 to C2 instead of C1. Connecting the coordinates C0Y0 and C2Y1, we will derive an upward sloping long run consumption function which passes through the origin. This sums up Franco Modigliani's Life-cycle Hypothesis, which explains the Kuznet's Consumption Puzzle of constant Average Propensity to Consume in the long run.

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