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Inter-temporal consumption

# Inter-temporal consumption - OPTIMAL CONSUMPTION OVER TIME...

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OPTIMAL CONSUMPTION OVER TIME In all of our models of consumer’s behavior discussed as far, we have argued that if both goods have positive marginal utilities, the individual will always spend the entire income. The picture becomes different when the individual makes a consumption decision for several periods. For simplicity, we consider a two-period consumption plan. The consumer has a given amount of money M to be spent on a single good C over the current period t=0 and the future period t=1. Let C 0 and C 1 be the individual’s consumption levels in periods 0 and 1 respectively. To start with, assume that there is no change in price between the two periods. We normalize by setting price equal to 1. This means that out of M , C 0 is spent in period 0. By implication, ( M C 0 ) is saved in period 0. Assume that the interest rank equals r. Hence ( M C 0 ) invested at t=0 becomes (1+r)( M C 0 ), which can be spent in period 1. Because there is no future period beyond t=1, the consumer spends the entire budget at t=1. That is C 1 =(1+r)( M C 0 ) Alternatively, M C C r = + 0 1 1 That is C 0 + 1 1 + r C 1 = M This is the individual’s intertemporal budget constraint. Suppose that the consumer’s 2-period utility function is U=U(C 0 , C 1 ) we may regard this as the individual’s life time utility function, which depends on the person’s consumption profile overtime. The intertemporal optimization problem, then is

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