26 Chapter Highlights
Chapter 10
Intertemporal Choice
This is one of my favorite topics, since it uses consumer theory in such
fundamental ways, and yet has many important and practical consequences.
The intertemporal budget constraint is pretty straightforward. I sometimes
draw the kinked shape that results from different borrowing and lending rates,
just to drive the point home. It is good to spell out the importance of convexity
and monotonicity for intertemporal preferences. Ask your students what savings
behavior would be exhibited by a person with convex intertemporal preferences.
The difference between the present value and the future value formulation of
the budget constraint can be seen as a choice of numeraire.
The comparative statics is simply relabeled graphs we’ve seen before, but it
is still worth describing in detail as a concrete example.
I think that it is worth repeating the conclusion of Section 10.6 several times,
as students seem to have a hard time absorbing it. An investment that shifts
the endowment in a way that increases its present value is an investment that
every consumer must prefer (as long as they can borrow and lend at the same
interest rate). It is a good idea to express this point in several different ways.
One especially important way is to talk explicitly about investments as changes
in the endowment (Δm1,Δm2), and then point out that any investment with a
positive net present value is worthwhile.
Emphasize that present value is really a linear operation, despite appearances.
Given a table of present values, as Table 11.1, show how easy it is to calculate
present values.
The installment loan example is a very nice one. It is good to motivate it by
first considering a person who borrows $1,000 and then pays back $1,200 a year
later. What rate of interest is he paying? Show that this rate can be found by
solving the equation
1000(1 + r) = 1200,
which can be written as
1000 = 1200
1+r.
Chapter 10 27
It is then very natural to argue that the monthly rate of interest for the
installment loan is given by the ithat solves the equation
1000 = 100
1+i+100
(1 + i)2+…+100
(1 + i)12
There are (at least) two ways to compute the yearly rate. One way is to follow
the accountant’s convention (and the Truth in Lending Act) and use the formula
r=12i. Another, perhaps more sensible, way is to compound the monthly
returns and use the formula 1 + r=(1+i)12. I followed the accountant’s
convention in the figures reported in the text.
The workbook problems for this chapter are also quite worthwhile. Problem
11.1 is a nice example of present value analysis, using the perpetuity formulas.
Problem 11.6 illustrates the budget constraint with different borrowing and
lending rates.
Intertemporal Choice
A. Budget constraint
1. (m1,m
2) money in each time period is endowment
2. allow the consumer to borrow and lend at rate r
6. preferences — convexity and monotonicity are very natural
B. Comparative statics
1. if consumer is initially a lender and interest rate increases, he remains a
lender. Figure 10.4.
3. Slutsky allows us to look at the effect of increasing the price of today’s
consumption (increasing the interest rate)
a) change in consumption today when interest rate increases = substitu-
C. Inflation
1. put in prices, p1=1andp2
2. budget constraint takes the form
3. or
5. 1 + ρ=(1+r)/(1 + π) is the real interest rate
6. ρ=(r−π)/(1 + π)orρ≈r−π
28 Chapter Highlights
D. Present value — a closer look
1. future value and present value — what do they mean?
E. Present value works for any number of periods.
F. Use of present value
G. Bonds
1. coupon x, maturity date T, face value F
2. consols
H. Installment loans
1. borrow some money and pay it back over a period of time
2. what is the true rate of interest?