Capital in the Twenty-First Century (38 page)

Nothing prevents us from imagining such a society, but in all known human societies,
including the most primitive, things have been arranged differently. In all civilizations,
capital fulfills two economic functions: first, it provides housing (more precisely,
capital produces “housing services,” whose value is measured by the equivalent rental
value of dwellings, defined as the increment of well-being due to sleeping and living
under a roof rather than outside), and second, it serves as a factor of production
in producing other goods and services (in processes of production that may require
land, tools, buildings, offices, machinery, infrastructure, patents, etc.). Historically,
the earliest forms of capital accumulation involved both tools and improvements to
land (fencing, irrigation, drainage, etc.) and rudimentary dwellings (caves, tents,
huts, etc.). Increasingly sophisticated forms of industrial and business capital came
later, as did constantly improved forms of housing.

Concretely, the marginal productivity of capital is defined by the value of the additional
production due to one additional unit of capital. Suppose, for example, that in a
certain agricultural society, a person with the equivalent of 100 euros’ worth of
additional land or tools (given the prevailing price of land and tools) can increase
food production by the equivalent of 5 euros per year (all other things being equal,
in particular the quantity of labor utilized). We then say that the marginal productivity
of capital is 5 euros for an investment of 100 euros, or 5 percent a year. Under conditions
of pure and perfect competition, this is the annual rate of return that the owner
of the capital (land or tools) should obtain from the agricultural laborer. If the
owner seeks to obtain more than 5 percent, the laborer will rent land and tools from
another capitalist. And if the laborer wants to pay less than 5 percent, then the
land and tools will go to another laborer. Obviously, there can be situations in which
the landlord is in a monopoly position when it comes to renting land and tools or
purchasing labor (in the latter case one speaks of “monopsony” rather than monopoly),
in which case the owner of capital can impose a rate of return greater than the marginal
productivity of his capital.

In a more complex economy, where there are many more diverse uses of capital—one can
invest 100 euros not only in farming but also in housing or in an industrial or service
firm—the marginal productivity of capital may be difficult to determine. In theory,
this is the function of the system of financial intermediation (banks and financial
markets): to find the best possible uses for capital, such that each available unit
of capital is invested where it is most productive (at the opposite ends of the earth,
if need be) and pays the highest possible return to the investor. A capital market
is said to be “perfect” if it enables each unit of capital to be invested in the most
productive way possible and to earn the maximal marginal product the economy allows,
if possible as part of a perfectly diversified investment portfolio in order to earn
the average return risk-free while at the same time minimizing intermediation costs.

In practice, financial institutions and stock markets are generally a long way from
achieving this ideal of perfection. They are often sources of chronic instability,
waves of speculation, and bubbles. To be sure, it is not a simple task to find the
best possible use for each unit of capital around the world, or even within the borders
of a single country. What is more, “short-termism” and “creative accounting” are sometimes
the shortest path to maximizing the immediate private return on capital. Whatever
institutional imperfections may exist, however, it is clear that systems of financial
intermediation have played a central and irreplaceable role in the history of economic
development. The process has always involved a very large number of actors, not just
banks and formal financial markets: for example, in the eighteenth and nineteenth
centuries, notaries played a central role in bringing investors together with entrepreneurs
in need of financing, such as Père Goriot with his pasta factories and César Birotteau
with his desire to invest in real estate.
¹⁴

It is important to state clearly that the notion of marginal productivity of capital
is defined independently of the institutions and rules—or absence of rules—that define
the capital-labor split in a given society. For example, if an owner of land and tools
exploits his own capital, he probably does not account separately for the return on
the capital that he invests in himself. Yet this capital is nevertheless useful, and
his marginal productivity is the same as if the return were paid to an outside investor.
The same is true if the economic system chooses to collectivize all or part of the
capital stock, and in extreme cases (the Soviet Union, for example) to eliminate all
private return on capital. In that case, the private return is less than the “social”
return on capital, but the latter is still defined as the marginal productivity of
an additional unit of capital. Is it useful and just for the owners of capital to
receive this marginal product as payment for their ownership of property (whether
their own past savings or that of their ancestors) even if they contribute no new
work? This is clearly a crucial question, but not the one I am asking here.

Too much capital kills the return on capital: whatever the rules and institutions
that structure the capital-labor split may be, it is natural to expect that the marginal
productivity of capital decreases as the stock of capital increases. For example,
if each agricultural worker already has thousands of hectares to farm, it is likely
that the extra yield of an additional hectare of land will be limited. Similarly,
if a country has already built a huge number of new dwellings, so that every resident
enjoys hundreds of square feet of living space, then the increase to well-being of
one additional building—as measured by the additional rent an individual would be
prepared to pay in order to live in that building—would no doubt be very small. The
same is true for machinery and equipment of any kind: marginal productivity decreases
with quantity beyond a certain threshold. (Although it is possible that some minimum
number of tools are needed to begin production, saturation is eventually reached.)
Conversely, in a country where an enormous population must share a limited supply
of land, scarce housing, and a small supply of tools, then the marginal product of
an additional unit of capital will naturally be quite high, and the fortunate owners
of that capital will not fail to take advantage of this.

The interesting question is therefore not whether the marginal productivity of capital
decreases when the stock of capital increases (this is obvious) but rather how fast
it decreases. In particular, the central question is how much the return on capital
r
decreases (assuming that it is equal to the marginal productivity of capital) when
the capital/income ratio
β
increases. Two cases are possible. If the return on capital
r
falls more than proportionately when the capital/income ratio
β
increases (for example, if
r
decreases by more than half when
β
is doubled), then the share of capital income in national income
α
=
r
×
β
decreases when
β
increases. In other words, the decrease in the return on capital more than compensates
for the increase in the capital/income ratio. Conversely, if the return
r
falls less than proportionately when
β
increases (for example, if
r
decreases by less than half when
β
is doubled), then capital’s share
α
=
r
×
β
increases when
β
increases. In that case, the effect of the decreased return on capital is simply
to cushion and moderate the increase in the capital share compared to the increase
in the capital/income ratio.

Based on historical evolutions observed in Britain and France, the second case seems
more relevant over the long run: the capital share of income,
α
, follows the same U-shaped curve as the capital income ratio,
β
(with a high level in the eighteenth and nineteenth centuries, a drop in the middle
of the twentieth century, and a rebound in the late twentieth and early twenty-first
centuries). The evolution of the rate of return on capital,
r
, significantly reduces the amplitude of this U-curve, however: the return on capital
was particularly high after World War II, when capital was scarce, in keeping with
the principle of decreasing marginal productivity. But this effect was not strong
enough to invert the U-curve of the capital/income ratio,
β
, and transform it into an inverted U-curve for the capital share
α
.

It is nevertheless important to emphasize that both cases are theoretically possible.
Everything depends on the vagaries of technology, or more precisely, everything depends
on the range of technologies available to combine capital and labor to produce the
various types of goods and services that society wants to consume. In thinking about
these questions, economists often use the concept of a “production function,” which
is a mathematical formula reflecting the technological possibilities that exist in
a given society. One characteristic of a production function is that it defines an
elasticity of substitution between capital and labor: that is, it measures how easy
it is to substitute capital for labor, or labor for capital, to produce required goods
and services.

For example, if the coefficients of the production function are completely fixed,
then the elasticity of substitution is zero: it takes exactly one hectare and one
tool per agricultural worker (or one machine per industrial worker), neither more
nor less. If each worker has as little as 1/100 hectare too much or one tool too many,
the marginal productivity of the additional capital will be zero. Similarly, if the
number of workers is one too many for the available capital stock, the extra worker
cannot be put to work in any productive way.

Conversely, if the elasticity of substitution is infinite, the marginal productivity
of capital (and labor) is totally independent of the available quantity of capital
and labor. In particular, the return on capital is fixed and does not depend on the
quantity of capital: it is always possible to accumulate more capital and increase
production by a fixed percentage, for example, 5 or 10 percent a year per unit of
additional capital. Think of an entirely robotized economy in which one can increase
production at will simply by adding more capital.

Neither of these two extreme cases is really relevant: the first sins by want of imagination
and the second by excess of technological optimism (or pessimism about the human race,
depending on one’s point of view). The relevant question is whether the elasticity
of substitution between labor and capital is greater or less than one. If the elasticity
lies between zero and one, then an increase in the capital/income ratio
β
leads to a decrease in the marginal productivity of capital large enough that the
capital share
α
=
r
×
β
decreases (assuming that the return on capital is determined by its marginal productivity).
¹⁵
If the elasticity is greater than one, an increase in the capital/income ratio
β
leads instead to a drop in the marginal productivity of capital, so that the capital
share
α
=
r
×
β
increases (again assuming that the return on capital is equal to its marginal productivity).
¹⁶
If the elasticity is exactly equal to one, then the two effects cancel each other
out: the return on capital decreases in exactly the same proportion as the capital/income
ratio
β
increases, so that the product
α
=
r
×
β
does not change.

The case of an elasticity of substitution exactly equal to one corresponds to the
so-called Cobb-Douglas production function, named for the economists Charles Cobb
and Paul Douglas, who first proposed it in 1928. With a Cobb-Douglas production function,
no matter what happens, and in particular no matter what quantities of capital and
labor are available, the capital share of income is always equal to the fixed coefficient
α
, which can be taken as a purely technological parameter.
¹⁷

For example, if
α
=
30 percent, then no matter what the capital/income ratio is, income from capital
will account for 30 percent of national income (and income from labor for 70 percent).
If the savings rate and growth rate are such that the long-term capital/income ratio
β
=
s
/
g
corresponds to six years of national income, then the rate of return on capital will
be 5 percent, so that the capital share of income will be 30 percent. If the long-term
capital stock is only three years of national income, then the return on capital will
rise to 10 percent. And if the savings and growth rates are such that the capital
stock represents ten years of national income, then the return on capital will fall
to 3 percent. In all cases, the capital share of income will be 30 percent.