1. Chapter 10 INTERTEMPORAL CHOICE

2. c2=m2+(m1-c1)+r(m1-c1)= m2+(1+r)(m1-c1)
10.1 The Budget Constraint
Intertemporal choices: choices of consumption over time.
Saver in the first period consumption
Savings: m1- c1
Consumption in the second period
c2=m2+(m1-c1)+r(m1-c1)= m2+(1+r)(m1-c1)

3. 10.1 The Budget Constraint Budget constraint Interest rate is zero
No borrowing is allowed.

4. c2=m2-r(c1-m1)-(c1-m1)=m2+(1+r)(m1-c1)
10.1 The Budget Constraint
Borrower in the first period
Borrower if c1>m1
Interest payments r(c1-m1).
Consumption in the second period
c2=m2-r(c1-m1)-(c1-m1)=m2+(1+r)(m1-c1)

5. 10.1 The Budget Constraint future value (1+r)c1+ c2=(1+r)m1+ m2
present value
c1+ c2/(1+r)= m1+ m2/(1+r)

6. 10.3 Comparative Statics
If the consumer chooses a point where c1<m1, she is a lender.
If a person is a lender and the interest rate increases, he will remain a lender.

7. c2= m2 +((1+r)/(1+))(m1-c1)
10.5 Inflation
Normalize today’s price to one and let p2 be the price of consumption tomorrow.
p2c2=p2m2+(1+r)(m1-c1)
c2=m2+((1+r)/p2)(m1-c1)
Suppose the inflation rate isπ, we have
p2=1+
c2= m2 +((1+r)/(1+))(m1-c1)

8. 10.5 Inflation The real interest rate 1+=(1+r)/(1+)
The budget constraint becomes
c2=m2+(1+)(m1-c1)
The real rate of interest tells you how much extra consumption you can get, not how many extra dollars you can get.

9. 10.5 Inflation 1+=(1+r)/(1+)  =(r-)/(1+) 1+ 1  r-
The real rate of interest is just the nominal rate minus the rate of inflation.

10. 10.6 Present Value: A Closer Look
A consumption plan is affordable if the present value of consumption equals the present value of income.
c1+ c2/(1+r)= m1+ m2/(1+r)
The consumer would always prefer a pattern of income with a higher present value to a pattern with a lower present value.
A three-period model
c1+c2/(1+r)+c3/(1+r)2= m1+m2/(1+r)+m3/(1+r)2

11. M1+M2/(1+r)>P1+P2/(1+r)
10.8 Use of Present Value
Suppose that the income stream (M1, M2) can be purchased by making a stream of payments (P1, P2).
Good investment if
M1+M2/(1+r)>P1+P2/(1+r)
The net cash flow
(M1-P1, M2-P2)
Net present value of the investment
NPV= M1-P1＋(M2-P2)/(1+r)

12. 10.9 Bonds
Securities: financial instruments that promise certain patterns of payment schedules.
Bonds
The coupon x: a fixed number of dollars paid each period;
The maturity date T
The face value F: the amount paid on the mature date.

13. 10.9 Bonds The present discounted value of a bond:
PV=x/(1+r)+x/(1+r)2+…+F/(1+r)T
Consols or perpetuities: a bond that makes payments forever.
PV=x/(1+r)+x/(1+r)2+…=x/r