GENERAL EQULIBRIUM with ASSETS
Fisher made three major contributions to
f
nance by extending the equilibrium
model to include
f
nancial questions. He introduced assets into the equilibrium model
(leading him to formulate the idea of the fundamental value of an asset and implicitly
the idea of arbitrage). He introduced time into the analysis. And he formulated the
impatience theory of interest. We shall introduce these new elements in exactly that
order, concentrating on assets in this chapter and time in the next chapter.
The most basic questions about
f
nance are: what should stock prices be, and what
should the interest rate be? As we shall see in the next section, interest rates are
like inverse asset prices, so the basic question (not the only question, by any means)
of
f
nance is simply, what should the prices of various assets be? Unfortunately, the
general equilibrium model does not include assets. Fisher added assets to the model
in order to study
f
nance.
The simplest and most abstract way to introduce assets is by de
f
ning an asset
by the dividends it pays, or promises to pay. Some people care about owning assets
for the joy of owning them. But for most people, assets only have value because they
pay dividends. By identifying an asset exclusively by what it pays, we are ignoring
the
f
rst class of people.
Fornowwesupposethata
l
lde
l
iver
iescanbeperfect
lyforeseen
,sowea
lsoignore
the possibility of default. Naturally, this is an unrealistic assumption, which we shall
drop later. But assuming it now will, as Ricardo said in a di
f
erent context almost a
century before Fisher, be very illuminating.
Assets are of two types: one kind is physical, like land or trees or factories.
Another kind is promises, like an IOU note or a bond. What it pays depends on
somebody keeping his promise. Since we ignore default for now, the only di
f
erence
between these is that the former are in positive supply (so many acres of land actually
exist today), while the latter are in zero net supply, since a promise sold by somebody
is a promise bought by somebody else.
Identifying assets with their payo
f
s naturally led Fisher to the conclusion that
asset prices should be equal to the value (prices times quantities) of their dividends.
This is now called the fundamental theorem of asset pricing. If asset prices were
di
f
erent from the value of their dividends, there would often be an arbitrage, where
one could sell the asset and buy the dividends directly, thus turning a pro
f
toverand
over, contradicting the hypothesis we are in equilibrium.
This insight enabled Fisher to quickly reduce a general equilibrium economy with
assets to a standard general equilibrium model without assets.
1A
s
s
e
t
s
Fisher began by introducing a new element into the model, namely assets. An as-
set
delivers
some combination of goods. For example, a tree might produce fruit
and leaves, of di
f
ering quantities. The tree itself might give no utility, but what it
1