北京大学：《微观经济学》Chapter Ten Intertemporal Choice 跨时期选择

Chapter Ten Intertemporal choice 跨时期选择

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

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?

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

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 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 FV=1+r Given an interest rate r the future value one period from now of sm is FV=m(1+r)

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 FV = 1+ r. FV = m(1+ r)

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 （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: Sm saved now becomes $m(1+r)at the start of next period, so we want the value of m for which m(1+r)=1 That is, m=1/(1+r), the present-value of $1 obtained at the start of next period

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) = 1 That 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 PV 1+r And the present value of $m available at the start of the next period is PV= 1+r

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 PV r = + 1 1 . PV m r = 1+

Present value E.g., if r= 0.1 then the most you should pay now for $1 available next period is PV =S0.91 1+0·1 And if r=0.2 then the most you should pay now for $1 available next period is PV =S0.83 1+0·2

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 PV = +  =  1 1 0 1 $0 91. PV = +  =  1 1 0 2 $0 83