In his *General Theory*, John
Maynard Keynes (1936: Ch.11) proposed an
investment function of the sort I = I_{0} + I(r) where the relationship between
investment and interest rate was of a rather naive form. Firms were presumed to
"rank" various investment projects depending on their "internal rate of
return" (or "marginal efficiency of investment") and thereafter, faced with
a given rate of interest, chose those projects whose internal rate of return exceeded the
rate of interest. With an infinite number of projects available, this amounted to arguing
that firms would invest until their marginal efficiency of investment was equal to the
rate of interest, i.e. MEI = r.

More elaborate considerations of Keynes's theory, however, were forced to
ask *what* is the internal rate of return? This is far from evident. Keynes defined
the internal rate of return as the "marginal efficiency of capital", which Abba Lerner (1944, 1953), more accurately, rebaptized as
the "marginal efficiency of investment" (MEI). Keynes claimed that this could be
defined as follows:

"I define the marginal efficiency of capital as being equal to the rate of discount which would make the present value of the series of annuities given by the returns expected from the capital asset during its life just equal its supply price" (Keynes , 1936: p. 135)

In constrast, Keynes defines the "*supply price* of the capital
asset...not the market price at which an asset of the type in question can actually be
purchased in the market, but the price which would just induce a manufacturer newly to
produce an additional unit of such assets, i.e. what is sometimes called its *replacement
cost*" (1936: p.135). Consequently:

"The relation between the prospective yield of a capital asset and its supply price or replacement cost, i.e. the relation between the prospective yield of one more unit of that type of capital and the cost of producing that unit, furnishes us with the

marginal efficiency of capitalof that type" (Keynes , 1936: p.135).

In order to come to grips to what Keynes is talking about, we need to
disentagle his English a bit. Let a_{1}, a_{2}, a_{3}, .., etc. be
the expected stream of returns of a particular investment project. Consequently, at a
given rate of interest r, the market present value of these returns is merely ・/font> _{t }a_{t}/(1+r)^{t} where we are summing
from t to infinity.

Let C be the cost of undertaking the project - or rather, the replacement cost of capital or "supply price" of capital goods (i.e. what the capital goods industries sell them for). Then, Keynes proposed that the internal rate of return (or marginal efficiency of investment) would be the discount rate d * where:

・/font>

_{t}a_{t}/(1+d *)^{t}= C

We can conceive of this via Figure 3 in return/present value space.
Consider the line V which denotes the present value of a *particular* project at
different discount rates d . Obviously, as the discount rate d increases, then the present value of that particular project
declines, i.e. V = ・/font> _{t}a_{t}/(1+d )^{t} falls as d rises. The
replacement cost of capital, C, is given exogenously by the capital goods industries.
Thus, the marginal efficiency of investment MEI, or "internal rate of return",
of *this* particular project is defined here as d *, i.e.
the d that equates the present value of the project with its
capital cost. Whether this particular project will be undertaken or not, then, depends on
the rate of interest on the bond market - specifically, if d *
> r, then this project is undertaken; if d * < r, then it
is shelved.

Figure 3- Keynes's Internal Rate of Return

Several things can already be noted from Figure 3. The first is that if
expectations or "animal spirits" are bouyant enough such that the expected
stream of returns on this project rises (i.e. {a_{t}} rise) then the V curve will
shift to the right (e.g. to V｢ in Figure 3) and, consequently,
the corresponding internal rate of return will increase (to d ｢ in Figure 3). Conversely, if the supply price of capital rises (C
rises to C｢ for instance), then the corresponding internal
rate of return on this project declines (to d ｢ ｢ in Figure 3).

However, all this is for a *single* project. The rest of the story
must be told and, for this, we must consider an array of investment projects. For each
project in this array, we can compute the internal rate of return d
* on the basis of the projected stream of retrurns ({a_{t}}) of that project and
its supply price (C). Suppose we then rank the investment projects according to their
internal rate of return d *. Then, we could obtain a MEI *schedule*
which descends from the project with the highest d * to that
with the lowest d *. This is shown heuristically in Figure 4
where we have six "lumpy" investment projects:

Figure 4- Marginal Efficiency of Investment (MEI) Schedule

The histogram in Figure 4 represents the six projects (I_{1}, I_{2},
.., I_{6}) with six internal rates of return (d _{1}*,
d _{2}*, .., d _{6}*)
ranked accordingly from highest to lowest. Thus, at a given interest rate r, only projects
I_{1} through I_{4} are "profitable", i.e. have internal rates
of return greater than or equal to r, while projects I_{5} and I_{6} have
internal rates of return below that. Thus, the "investment" expenditure in this
economy is I* = I_{1} + I_{2} + I_{3} + I_{4}. If the rate
of interest were lowered, it would be possible that I_{5} could become profitable
and thus I* would increase; in contrast, if r increased, then I_{4} would no
longer be profitable and thus I* would decrease.

The MEI curve drawn in Figure 4, then, represents the equivalent of the
histogram when we have many, indeed a continuum, of available investment projects. In this
case, total investment will be where the rate of interest is equal to the marginal
efficiency of investment curve. As a result, Keynes
's (1936) theory of investment can be expressed by the naive function I = I_{0} +
I(r) where investment falls as the bond rate rises and rises when the bond rate falls.
Bouyant expectations or animal spirits expecatations imply that all projects get valued
upwards and, of course, the MEI curve shifts to the right so that the resulting I* rises.

Several problems immediately emerge in Keynes's theory. First of all, as
Armen Alchian (1955) and Jack Hirshleifer (1970) noted, the ranking of the
projects may not be independent of the interest rates. For instance, consider two
investment projects in Figure 5 whose present value curves are represented by the V_{1}
and V_{2} schedules respectively and suppose, for the sake of argument, that both
have the same replacement cost of capital, C. Notice that the curves intersect at point d _{0} - which is not implausible by any means. Now, if cost
of capital is C for both projects, then by Keynes's argument, project 1 is more profitable
than project 2 since, at C, d _{1}* > d _{2}*.

However, Alchian (1955) argued
that standard theories about the maximization of the present value of the firm read the
diagram in the reverse way. Specifically, standard theories would consider the "most
profitable project" to be that with the highest present value at a given rate of
interest. In this case, if the rate of interest, r, is above d _{0}
(at r_{A} in Figure 5, for instance) then project 1 has a higher present value
than project 2 (V_{1A} > V_{2A}). In this case, standard present value
rankings comply with the Keynesian rankings.

However, Alchian noted, if the rate of interest is *below* d _{0} (e.g. at r_{B}), then project 2 has a higher
present value than project 1 (i.e. V_{1B} < V_{2B}) thus by the
standard theory, project 2 is superior. Here is where the standard and Keynesian theories
diverge. Keynesian theory argues that even if r < d _{0},
project 1 would *still* be ranked superior to project 2 as at C , d
_{1}* > d _{2}*. But standard present-value
maximization theory would argue that project 2 would be superior.

Figure 5- The Alchian Critique

As Alchian (1955) notes, then,
Keynesian rankings are *different* from standard present-value maximization rankings.
Or rather, Keynesian theory and standard present-value maximization are consistent only if
there were only one investment project and one outside option. If there were multiple
investment projects, the Keynesian ranking would be different from the present-value
maximization ranking as the latter ranking is itself dependent on the rate of interest.

A more troublesome critique was offered up by several Post Keynesians, such as Athanasios Asimakopulos (1971, 1991) and Piero Garegnani (1978). Namely, one can question the very possibility of a downward-sloping MEI function in the presence of unemployment. In particular, we can note that Keynes's multiplier story implies that if investment is undertaken then, by the multiplier, aggregate demand and output rises. But if the marginal efficiency of investment function is dependent on expected future returns, then should not the increased income and thus aggregate demand from the multiplier imply higher future returns? If so, then the MEI function ought to shift outwards to the right. This, in turn, implies that investment ought to increase - which leads to another increase in aggregate demand and thus the MEI curve shifts out again, raising investment, etc.

As a result, it is easy to conceive that, in situations of unemployment
where the multiplier works its magic, investment is actually indeterminate - or rather, an
ever-shifting MEI curve could imply that *all* investment projects will be eventually
undertaken and not merely those that are profitable at the given rate of interest since
the profitability of projects is itself a function of aggregate demand and thus endogenous
to the problem.

There are several conceivable ways of extricating Keynes's theory from
this critique, none of which work exactly well. The first is simply to assert that while
this ever-shifting MEI problem could be true in the aggregate, it is not true at the
individual firm level. If Chrysler builds a new factory and thus pays workers more, its
investment injection will *not* lead to an equivalent increase in demand for Chrysler
cars. Rather, workers can spend their new income on Ford cars, or food or anything else,
so that, at least for the Chrysler Corporation, the investment decisions it makes do not
lead to one-for-one to increases in the demand for its products.

However, one can also reverse this proposition: while this is true for the
firm, it is still not true for the aggregate because there are *no* leakages to the
economy. In other words, the individual firm investment function may continue to be
downward sloping, but the aggregate investment function is of a different nature, i.e.
horizontal. Solving this issue, then, would require a more careful consideration of the
issue of aggregation.

Now, Keynes himself appealed to Irving Fisher's
(1930) notion - arguing that "Professor Fisher uses his "rate of return over
cost" in the same sense and for precisely the same purpose as I employ the
"marginal efficiency of capital"" (Keynes,
1936: p.141). However, as Garegnani (1978) points
out, Fisher's bases his downward-sloping investment curve on a diminishing marginal
productivity of capital argument - which can *only* be true if another factor (i.e.
labor) is fully employed and cannot be increased. Thus, in an unemployment situation, the
purported equivalence between the two concepts is not quite right.

Another way of defending the falling MEI curve would be to appeal to the increasing marginal costs of investment, as suggested by Abba Lerner (1944, 1953) and later Neoclassical theorists,
which may be thought of as arising from the rising supply price of new capital goods (e.g.
Foley and Sidrauski,
1970). This is plausible, but one must remember that supply price of capital rises *only*
because there are capacity constraints in the capital goods industry. That implies that
either we are at full employment or we are in the very short-run and capacity cannot be
increased. Garegnani (1978) argument that Keynes's theory is supposed to be one of
"long run" unemployment equilibrium, therefore would disallow the marginal
adjustment cost resolution.

There is one further resolution to the problem: namely, recognizing Michal
Kalecki's (1937) "*principle of
increasing risk*". Kalecki proposed that the more firms invest, the greater their
indebtedness and thus the greater the potential loss if their projects fail. Thus,
assessments of "profitability" become more and more conservative as firms take
on larger and larger debt needed to finance greater and greater investment. This idea of
"increasing risk", then, would be sufficient to yield us a downward sloping MEI
curve as it neither relies on full employment nor on short run rigidities arguments.

A third objection, perhaps best expressed by Robert Eisner and R.H. Strotz (1963) relates to the rather *ad
hoc* way Keynes dealt with the determination of the expected profits and returns. They
argued instead for some carefully prescribed distribution and process of expectation
formation. This, of course, is a "Neoclassical" objection - Post Keynesians, such as G.L.S. Shackle (1967), Joan Robinson (1971), Hyman Minsky (1975), Paul Davidson
(1972, 1993, 1994) and Asimakopulos (1971, 1991)
have vociferously insisted that there is no *ad hoccery* there at all. Quite the
contrary - pointing to Keynes's (1936, 1937) repeated insistence on radical uncertainty -
indeterminate or "animal spirited" expectations are quite essential to Keynes's
theory of investment.

This last point is particularly noticeable as we move from Chapter 11 to
Chapter 12 in Keynes's *General Theory* where, all of a sudden, we confront
the importance of the "daily revaluations of the Stock exchange" (Keynes, 1936:
p.151) on investment decisions. Although a central feature of Post Keynesian economics, this intimate relationship
between financial markets (specifically stock markets) and investment/production decisions
has found its way into Neo-Keynesian theory
(e.g. Tobin, 1969; Blanchard, 1981) and even as far afield as in Walrasian general equilibrium theory (e.g. Diamond, 1967; Grossman and Hart,
1979).