In order to understand the choice exercised by a consumer across different periods of time we take consumption in one period as a composite commodity. Suppose there is one consumer, formula_1 commodities, and two periods. Preferences are given by formula_2 where formula_3. Income in period formula_4 is formula_5. Savings in period 1 is formula_6, spending in period formula_4 is formula_8, and formula_9 is the interest rate. If the person is unable to borrow against future income in the first period, then he is subject to separate budget constraints in each period: