The Classical Theory of Distribution and Ricardian Rent

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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 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.

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 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 w1, 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 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 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.


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, 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.
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