Chapter 11. Preliminaries: Interest Rates
and Capital Valuation
Throughout this book, we have underlined the role of investment in the
growth process. Until now, however, we have considered that the decision to
invest was either exogenous (independent of any variable in the system) or
driven by the general aim of maximizing a sum of discounted utility °ows,
as we have described it in our chapters on optimal growth theory. But so far
we have left aside the essential role played by the rate of interest, the price of
loanable funds which is both a cost to investors in capital goods and a reward
to those agents who are willing to supply those funds. For investors, we know
from general economic principles that their decision to invest depends both
on expected future rewards and on the rate of interest.
Along a growth process, four prices are in search of an equilibrium: the
spot price of any capital good, its future price, the rental rate, and the rate
of interest. Those four prices are linked in a fundamental equation developed
formally for the ±rst time by Irving Fisher (1896). This equation will turn
out to be of central importance: it has far reaching, surprising consequences.
In particular, we will demonstrate that if competitive equilibrium enforces
it, society maximizes the sum of all future discounted
consumption
°ows it
can acquire.
Before showing this, we have to be very precise about the nature of the
interest rates and the process by which equilibrium can be reached simulta
neously on the capital goods market and on the loanable funds market. But
even before doing so, we should ask the question: ²Why do interest rates
exist in the ±rst place?³ We will also explain how both lenders and borrow
ers alike bene±t from the very existence of an equilibrium interest rate. We
will then turn to the various concepts of interest rates, their fundamental
properties, and their intimate links.
1
1
To do this we have relied in the ±rst part of this chapter on some of our previous
work. Section 1 borrows from chapter 1 of our book ²
Bond Pricing and Portfolio Analysis
 Protecting investors in the Long Run
³, MIT Press, Cambridge, Mass., 2003, pp. 1013;
section 2 is adapted from our chapter ³Protecting Investors against Changes in Interest
Rates³, in ²
Asset and Liability Management
³, W. Ziemba and S. Zenios, eds., Elsevier
North Holland, 2006, pp.69138. Note: authorizations will have to be requested from the
publishers.
1
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The reason for the existence of interest rates
Most people, when asked the innocuouslooking question about the reason
why interest rates should exist in the ±rst instance, respond that since in°a
tion is a pervasive phenomenon common to all places and times, it is therefore
only natural that lenders will want to protect themselves against rising prices;
borrowers might well agree with that, therefore establishing the existence of
an equilibrium rate of interest.
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 Fall '08
 OLIVIERDELAGRANDVILLE
 Interest Rates, Interest, The Land, Forward contract, Forward price, Spot price

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