Irving Fisher's Theory of
Investment
Irving Fisher's theory of capital and investment was introduced in his
Nature of Capital
and Income
(1906) and
Rate of Interest
(1907), although it has its clearest and most
famous exposition in his
Theory of Interest
(1930). We shall be mostly concerned with
what he called his "second approximation to the theory of interest" (Fisher, 1930: Chs.6-
8), which sets the investment decision of the firm as an intertemporal problem.
In his theory, Fisher
assumed
(note carefully) that all capital was
circulating
capital. In
other words, all capital is used up in the production process, thus a "stock" of capital K
did not exist. Rather, all "capital" is, in fact, investment. Friedrich Hayek (1941) would
later take him to task on this assumption - in particular, questioning how Fisher could
reconcile his theory of investment with the Clarkian theory of production which underlies
the factor market equilibrium.
Given that Fisher's theory output is related not to capital but rather to investment, then we
can posit a production function of the form Y =
ƒ
(N, I). Now, Fisher imposed the
condition that investment in any time period yields output only in the next period. For
simplicity, let us assume a world with only two time periods, t = 1, 2. In this case,
investment in period 1 yields output in period 2 so that Y
2
=
ƒ
(N, I
1
) where I
1
is period 1
investment and Y
2
is period 2 output. Holding labor N constant (and thus striking it out of
the system), then the investment frontier can be drawn as the concave function where
ƒ
′
> 0 and
ƒ
′
′
< 0. The mirror image of this is shown in Figure 1 as the frontier Y
2
=
ƒ
(I
1
).
Everything below this frontier is technically feasible and everything above it is infeasible.
Letting r be the rate of interest then total costs of investing an amount I
1
is (1+r)I
1
.
Similarly, total revenues are derived from the sale of output pY
2
or, normalizing p = 1,
simply Y
2
. Thus, profits from investment are defined as
π
= Y
2
- (1+r)I
1
and the firm
faces the constraint Y
2
=
ƒ
(I
1
) (we have omitted N now). Thus, the firm's profit-
maximization problem can be written as:
max
π
=
ƒ
(I
1
) - (1+r)I
1
so that the optimal investment decision will be where:
ƒ
′
= (1+r)
In Fisher's language, we can define
ƒ
′
-1 as the "
marginal rate of return over cost