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The Classical Theory of Distribution and Ricardian
Rent
"Political Economy, you think, is an enquiry into the nature and
causes of wealth -- I think it should rather be called an enquiry
into the laws which determine the division of produce of industry
amongst the classes that concur in its formation. No law can be
laid down respecting quantity, but a tolerably correct one can be
laid down respecting proportions. Every day I am more satisfied
that the former enquiry is vain and delusive, and the latter the
only true object of the science."
(David Ricardo, "Letter to T.R. Malthus, October 9,
1820", in Collected Works, Vol. VIII: p.278-9).
Factor Payments and the Concept of Rent
The first thing to remember is this:
in all that follows, there are no produced factors of production, i.e. there is no
capital. More precisely, for the rest of this discussion, the word "capital" is
used in the same sense as "land", i.e. capital is assumed to be an endowed
factor of production.
Before proceeding, we ought to be clear about a few terms. By
"distribution" we mean the relative income received by the owners of factors
of production. If L units of labor are employed in the economy, each unit being
paid a wage w, then the income of laborers (the owners of labor) is wL. If K
units of (fixed, endowed) capital are employed and paid a return r, then the
income of capitalists (the owners of capital) is rK. If we denote by Y the
economy-wide level of output, then the income share of labor can be
expressed as wL/Y and the income share of capital is rK/Y. Consequently, the
relative income shares of the capital and labor can be expressed as a ratio
wL/rK. The distribution of income is about how total output in the economy Y,
is divided up among people. Edgeworth called it "the species of exchange by
which produce is divided between the parties who have contributed to its
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production " (Edgeworth, 1904). The laborers get wL, the capitalists get rK
and, possibly, there might be some residual amount. This residual amount,
the amount of income/output produced which is not paid back to the owners of
capital and labor for factor services, is R = Y - rK - wL. The residual is
usually paid out to a class of people known as entrepreneurs.
It is important not to confuse this "residual" with the "surplus". The "surplus" is
defined as the amount of output that is not paid out to factors in reward for
"factor services." So, if we define r and w as the rate of return and wage in
"reward" for factor services, the surplus is defined as S = Y - rK - wL. This
seems mathematically similar to the entrepreneurial residual, but it is, in fact,
quite different. Explicit in the definition of the surplus is the assumption that r
and w are what is called "economic earnings" alone. In contrast, the r and w
in the definition of the entrepreneurial residual include both economic
earnings and "rental earnings". So, if we define re and we as the economic
earnings of capital and labor and rr and wr as their "rental" earnings, then the
surplus is:
S = reK + weL
while the entrepreneurial residual is:
R = (re+rr)K + (we + wr)L
So, implicitly, while the residual accrues to the entrepreneur alone, the
"surplus" includes amounts that accrue to labor and capital in the form of
rental earnings.This may all seem a bit obscure and so we need to define
things a bit better. Just how do we distinguish payments for factor services
from payments derived from the surplus, i.e. between economic earnings and
rental earnings? . In general, we can define them as follows:
Economic earnings are that portion of factor payments by a
producer which is necessary and sufficient to employ the
particular factor, i.e. to obtain "command" of the factor services.
Rental earnings are any payments received by the factor above
their economic earnings and as a result of their being in fixed
supply.
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Turning to economic earnings, what does "necessary and sufficient to employ
a factor" mean? For the Classical Ricardian school, the economic earnings of
a factor are merely the payments necessary to maintain the factor "intact".
Thus, for laborers, economic earnings are wages required to keep the laborer
alive and well, i.e. "subsistence" wages. We can fix our ideas better by
examining the factor market equilibrium for a particular factor. An example for
the labor market is shown in Figure 1. The Ld curve is the economy-wide
demand for labor by firms, Ls is the economy-wide supply of labor by
households. The demand for labor is downward sloping ,specifically, as the
wage increases (holding all other factor prices constant), firms will choose
techniques of production that substitute away from labor and towards other
factors. We know, from profit-maximization, that they will choose to employ
labor until the marginal value product is equal to the wage. The labor supply
curve is upward sloping because of labor-leisure choice issues: the greater
the wage, the greater the opportunity cost of leisure, and thus the more
households substitute away from leisure and towards labor.
Fig. 1 - Factor Market Equilibrium
Factor market equilibrium is established where the economy-wide demand for
labor Ld is equal to the economy-wide supply of labor (Ls). In Figure 1, this will
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be at w*, where Ld = Ls. Notice that at a lower wage, e.g. w1, there is an
excess demand for labor as Ld = L3 > L1 = Ls. At a higher wage, e.g. w3, we
have excess supply of labor as Ld = L1 < L3 = Ls.
The wage w* in Figure 1 is the equilibrium wage. Equilibrium quantity is L*,
thus economy-wide labor earnings are, in equilibrium, w*L*, the area of the
box formed by 0L*ew* in Figure 1. Economic earnings and rental earnings are
noted in Figure 1 by the areas E (for economic earnings) and R (for rental
earnings).
The reasoning for labelling the R and E areas in this manner can be readily
understood. When we are at the factor market equilibrium (w*, L*), every
worker is individually paid the equilibrium wage, w*. However, it may be that
some of these workers might have been willing to work at a lower wage. They
nonetheless receive w*. For instance, notice in Figure 1 that at wage w 1, the
amount of labor supplied is L1. Thus, the "economic earnings" of the first L1
workers, the payment that would have been sufficient to command their labor,
is not more than w1. However, in equilibrium, these same set of workers, L1,
are paid the equilibrium wage w*, which is considerably higher than w1. This
principle applies to all the "intramarginal" workers supplied between zero and
L*. Thus, the area below the labor supply curve reflects economic earnings,
while the area above the labor supply curve reflects, as we shall see, rental
earnings. Note the implications of the two extreme scenarios, both depicted in
Figure 2. Suppose leisure is so disliked that, in fact, workers do not consider it
a gainful alternative to employment. In this case, the labor supply curve is
vertical as shown by Ls in Figure 2. In other words, any wage rate will call
forth the entire labor force. Now, equilibrium will still be where the labor
demand and vertical labor supply curve meet at e, thus we still have a strictly
positive equilibrium wage, w* > 0 and strictly positive labor earnings (the area
of the box, w*L*). However, notice that now that all earnings of labor, w*L*,
are rental earnings and economic earnings are nil. Conversely, suppose
labor supply is supplied with infinite elasticity, i.e. we have a horizontal labor
supply curve such as Ls in Figure 2. In this case, an infinite amount of labor is
supplied when the wage is greater than w* and no labor is supplied when the
wage is below w*. Labor earnings are still defined at equilibrium e as the area
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of the box w*L*. However, note that now equilibrium labor income w*L* will be
entirely composed of economic earnings and no rental earnings are received.
Figure 2 - Pure Rental versus Pure Economic
Earnings
The reasoning for these two extreme cases is readily apparent. When the
labor supply is inelastic (vertical Ls), i.e. when there is no alternative
employment, then any earnings made by labor must necessarily arise
because firms are fighting over a limited supply of them. In other words, firms
are bidding up their wages "artificially" above what is necessary to get them to
work. The supply of workers will be L* regardless of what the wage offered is.
As such, workers are experiencing a windfall gain in this case: they would be
willing to work for less, much less (indeed, near zero), but competition among
firms has bid their wages up regardless.
In contrast, when the labor supply is perfectly elastic (horizontal Ls), then
there are no "intramarginal" workers. In other words, at least w* is necessary
to call forth any labor and, furthermore, w* calls forth an infinite amount of
labor. Labor supply is not finite at w*. This implies that, as long as firms pay at
least w*, they do not need to "fight" each other over a limited supply of
workers. As there is no "bidding war" ensuing from limited labor supply, firms
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will have no incentive to pay workers above their minimal opportunity cost
wage, w*.
These examples permit us to better define the meaning of rental earnings of a
factor as that portion of earnings that arise purely out of the fact that the factor
is in fixed supply. This concept of rent, or differential rent or Ricardian rent as
it has been variously called, was introduced simultaneously but independently
by T.R. Malthus (1815), Robert Torrens (1815), Edward West (1815) and
David Ricardo (1815), and became one of cornerstones of the Classical
Ricardian theory of distribution.
Classical theory generally did not assume that factors were fixed in supply: in
other words, they assumed that capital and labor could be "produced". In
terms of Figure 2, they believed the labor supply curve was horizontal so that
all payments to labor were economic earnings. However, following David
Ricardo (1815, 1817) they recognized that land was fixed in supply and thus
that land made rental earnings. Figure 3 illustrates the Classical Ricardian
theory of rent. Here we are assuming only two factors of production: labor (L)
and land (T), where the labor is completely variable but land is in fixed supply.
The production function is thus Y =  (L, T0), where T0 is the fixed total supply
of land. In contrast labor is supplied with infinite elasticity (a typical Classical
assumption). This is captured in Figure 3 by the infinitely-elastic labor supply
curve, Ls, at the subsistence wage rate, w.
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Fig. 3 - Ricardian (Differential) Rent
The horizontal axis in Figure 3 measures different amounts of labor being
applied to the fixed amount of land. The curves APL and MPL are the
"economically-relevant" portions of the average product and marginal product
of labor curves (i.e. the portions where marginal product of labor is
diminishing and below the average product curve, what Ricardo called the
portion above the extensive margin).
The Classical Ricardian story now proceeds as follows. For a given amount of
land, the more labor we apply to it, the smaller the marginal and average
products. This the Classicals conceived as a natural truth with regard to
agriculture alone. The basic idea was that land was in fixed supply and of
differing quality. The most fertile lands were always used first and the less
fertile ones only used later. Thus, the more the scale of production increases
(i.e. the more dollops of labor are applied), the increasingly worse land would
be taken into cultivation and thus the lower the productivity of labor on the
marginal piece of land.
Now, the Ricardians argued that at least enough output must be generated to
pay for the factors of production. The wage paid to labor is w and this reflects
economic earnings entirely, i.e. must cover "subsistence". In contrast, land,
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although a factor of production, does not need to paid for. One can justify this
in Classical terms by saying it does not need to be maintained intact; in
Neoclassical terms, this implies there are no alternative uses for land and thus
no opportunity costs to be compensated.
However, and this is the gist of the Classical Ricardian story, although land
makes no economic earnings, we see that because land is fixed in supply, it
takes receives rental earnings. In fact, as we shall see, in Figure 3, all surplus
in production resolves itself into rental payments for land. To see this, note
that we can increase the scale of production, and thus take in more land and
apply more labor, up until the marginal product of labor is equal to the
subsistence wage. This will be at L* in Figure 3. Thus, total wage payments
wL* are the area of the light-shaded box in Figure 3.
Now, at L*, average product is y = Y/L*. Thus, total output is Y = yL*, i.e. the
area of the box 0L*ay (alternatively, we could have represented total output as
the sum of the light-shaded box and the triangle ewb formed under the MPL
curve; the areas are equivalent). Consequently, the surplus produced, defined
as Y - wL, is the darkly shaded box in Figure 3. This is the amount of output
that is produced over and above payments to factors. This remainder, the
early Classicals contended, accrues to landowners, thus it is referred to as
rent.