note5 - Microeconomic Theory Econ 101A Fall 2008 GSI: Eva...

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Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 5: Consumption Saving Decisions 1 Consumption Savings Decisions Suppose a consumer has preferences of consumption of goods today, C 1 and consumption of goods in the next period, C 2 , that can be expressed by the utility function U ( C 1 ,C 2 ) = C 1 2 1 + βC 1 2 2 where 0 < β < 1 reflects the degree to which the consumer prefers consumption today relative to consumption of goods next period. Then the consumer’s utility maximization problem (UMP) can be expressed as: max C 1 ,C 2 C 1 2 1 + βC 1 2 2 s.t. p 1 C 1 + p 2 C 2 1 + R = Y 1 + Y 2 1 + R where p 1 ,p 2 are the price of the consumption goods in periods 1 and 2, Y 1 ,Y 2 are income in periods 1 and 2, and R is the net interest rate for borrowing or saving between periods 1 and 2. (Note: future income and future expenditure are discounted by 1+R. This gives us the present value of that cash flow. Another way to see it is that one unit of consumption tomorrow is worth only
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note5 - Microeconomic Theory Econ 101A Fall 2008 GSI: Eva...

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