Chapter 10
INTERTEMPORAL
CHOICE
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)
10.1 The Budget Constraint

Budget constraint
 Interest rate
is zero
 No borrowing is allowed.
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)
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)

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.
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)

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.

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.
10.6 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
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)
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.
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
