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.

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

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

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

Fig. 10.2

Fig. 10.3

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

Fig. 10.4

Fig. 10.5

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.

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))

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

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

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

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?

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.

(模糊) In reality, there are many interest rates (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.

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.