北大ceer笔记9.ppt

Chapter Ten Intertemporal Choice （跨时期选择） Structure Present and future values Intertemporal budget constraint Preferences for intertemporal consumption Intertemporal choice Comparative statics Valuing securities Intertemporal Choice Persons often receive income in “lumps”; e.g. monthly salary. How is a lump of income spread over the following month (saving now for consumption later)? Or how is consumption financed by borrowing now against income to be received at the end of the month? Present and Future Values Begin with some simple financial arithmetic. Take just two periods; 1 and 2. Let r denote the interest rate per period. Future Value E.g., if r = 0.1 then $100 saved at the start of period 1 becomes $110 at the start of period 2. The value next period of $1 saved now is the future value of that dollar. Future Value Given an interest rate r the future value one period from now of $1 is  Given an interest rate r the future value one period from now of $m is Present Value （现值） Suppose you can pay now to obtain $1 at the start of next period. What is the most you should pay? $1? No. If you kept your $1 now and saved it then at the start of next period you would have $(1+r) $1, so paying $1 now for $1 next period is a bad deal. Present Value Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? A: $m saved now becomes $m(1+r) at the start of next period, so we want the value of m for which m(1+r) = 1That is, m = 1/(1+r),the present-value of $1 obtained at the start of next period. Present Value The present value of $1 available at the start of the next period is And the present value of $m available at the start of the next period is Present Value E.g., if r = 0.1 then the most you should pay now for $1 available next period is And if r = 0.2 then the most you should pay now for $1 available next period is The Intertemporal Choice Problem Let m1 and m2 be incomes received in periods