Chapter 10 Intertemporal Choice Key Concept: 1 dollar today is worth 1+r dollars tomorrow.

1. Chapter 10 Intertemporal Choice • Key Concept: 1 dollar today is worth 1+r dollars tomorrow. • An investment opportunity which yields positive net present value is worthwhile doing.

2. Chapter 10 Intertemporal Choice • Two periods • c1 (amt of money spent in period 1), c2 • m1 (amt of money earned in period 1), m2 • c1 > m1: borrower • c1 < m1: lender

3. How does the budget line look like? • Endowment (m1,m2) • No debt or bequest left, then • c2=m2+(m1 - c1)(1+r)

4. c2=m2+(m1 - c1)(1+r) • Rearranging • (1+r)c1+c2=(1+r)m1+m2 (in future value) • c1+c2/(1+r)=m1+m2/(1+r) (in present value) • 1 dollar today = 1+r dollars tomorrow

5. Fig. 10.2

6. Fig. 10.3

7. When r increases • If before the change, a lender • after the change, still alender (better off); • If before the change, a borrower • after the change, could be a borrower (worse off) or lender (?)

8. Fig. 10.4

9. Fig. 10.5

10. Let us look at the Slutsky equation. • ∆c1/∆r = ∆c1s/∆r+(m1- c1)∆ c1m/∆m • a borrower, m1- c1 <0, assuming normal, ∆c1/∆r<0 (when interest goes high, consume less). • a lender, TE is not clear.

11. Incorporate inflation • In real terms, c1, c2, m1, m2, p1, p2 • p2c2= p2 m2+ p1(m1 - c1)(1+r) • Rearranging • c1+ p2c2/(p1 (1+r))=m1+p2m2/(p1(1+r))

12. c1+ p2c2/(p1 (1+r))=m1+p2m2/(p1(1+r)) • Denote p2/p1=1+ • Denote (1+r)/(1+)=1+, the budget line becomes • c1+c2/(1+ )=m1+m2/(1+ ) and we call  the real interest rate • If you give up one unit of c1 today, you save p1 and therefore you can get p1(1+r)/p2= 1+ tomorrow

13. Extending to 3 periods is straightforward • c1+c2/(1+r1)+c3/((1+r1)(1+r2)) =m1+m2/(1+r1)+m3/((1+r1) (1+r2))

14. An endowment with higher present value gives the consumer more consumption possibilities. • An income stream (M1,M2) can be purchased by making a stream of payment (P1,P2) where M1+M2/(1+r)-(P1+P2/(1+r))>0 (net present value), then it is worth doing

15. A financial instrument: bond • Pay a fixed coupon value x every year, at maturity date T, pay back face value F • What should the price (P) of this bond be?

16. First calculate the present value of the payment: x/(1+r)+x/(1+r)2+…+ F/(1+r)T • If P>present value, then no one would buy the bond • If P<present value, then everyone will buy the bond • Hence P=present value or net present value has to be zero.

17. (模糊) In reality, there are many interest rates. Key principle: the interest measures the opportunity cost of funds, so you should use the interest that reflects your second best alternative of using the funds. • If you don’t buy the bond, what would you do with the money left? The interest implicit behind that way of using your money is the interest you should use. • Always bear in mind that we want to make the budget set as large as possible.

18. Chapter 10 Intertemporal Choice • Key Concept: 1 dollar today is worth 1+r dollars tomorrow. • An investment opportunity which yields positive net present value is worthwhile doing.