The theoretical generalization to more than one period is a multi-period wealth and income constraint. For example, the same person can gain more productive skills or acquire more productive income-earning assets to earn a higher income. In the multi-period case, something might also happen to the economy beyond the control of the individual to reduce (or increase) the flow of income. Changing measured income and its relation to consumption over time might be modeled accordingly, such as in the permanent income hypothesis.
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