Fisher's model says that consumption depends on lifetime income, and people try to achieve smooth consumption. The Life Cycle Hypothesis of Modigliani says that income varies systematically over the phases of the consumer's life cycle, and savings allow the consumer to achieve smooth consumption. The model assumes a zero interest rate for simplicity and that consumption-smoothing is optimal. What you end up with is an equation such that:
One's lifetime resources equal W + RY
To achieve smooth consumption, the consumer divides these resources equally over time:
C = alpha(W) + beta(Y)
alpha = the marginal propensity to consume out of the wealth stock (1/T), and
beta = the marginal propensity to consume out of income (R/T).
So this then solves what is called the "consumption puzzle". The life-cycle consumption function implies that
So across households, income varies more than wealth, so high income households should have a lower APC than low-income households. Over time, aggregate wealth and income grow together, causing APC to remain stable. This model shows us how we ought to behave with our income. It shows us that we ought to save money throughout our lifetime, and hold a small "net egg" until we retire. At which point we enter a period of "dissaving"--which means we draw down on our wealth. So, unlike the Keynesian consumption function, which assumed that consumption is entirely based on current income, LCH assumes that individuals consume a constant percentage of the present value of their life income. This model becomes very attractive in that sense, and almost carries with it a kind of imperative for economic behavior--that we not rely on others to save for us, perhaps, and that we ought to begin saving now for the future.