Second, the farming input which defined f does not have to be one factor alone. The economic implications of increasing the f/h ratio for several tenant inputs will be essentially the same. If several tenant inputs are increased while holding land constant, the meticulous reader may rightly point out that the marginal product of a particular factor may increase if factor complementarity is strong enough. Diminishing returns must operate for all increased tenant inputs together, however, resulting in a marginal farming cost (which includes all tenant inputs) being higher than the marginal return.
[1]. Note also that under
of the annual yield the landowner cannot convert a share contract to a fixed rent contract to protect his wealth.
[2]. Linear homogeneous production function is assumed here.
B.Increased Tenant Inputs —Illustrated with Input Adjustments for Multiple Tenants
The implication of increased farming intensity is so important that it deserves still another exposition. Treating tenant input as an explicit variable, we at the same time expand our analysis to several tenants. A few simplifying assumptions will help. Let us assume that (a) the landowner employs a large number of tenants on his landholdings; (b) the tenants are cultivating homogeneous land, producing the same product with identical production functions, and thus the initial equilibrium rental percentage for each tenant before the share restriction is the same; and (c) there is only one tenant input, say labor.
In figure 7, total product is measured along the vertical axis, and the number of tenants or tenant workers, t, is measured along the horizontal axis. The curve
is the total product of tenant workers, with the total landholding of a landowner held constant (with assumption a). Its shape exhibits diminishing marginal returns to tenant labor. The curve Wt represents the total tenant cost of farming, with W representing the wage rate and t the number of workers (with assumption c). Under a competitive tenant labor market, Wt is a straight line. The curve
is the total rent curve given the landowner's total landholdings. It is derived by subtracting the total tenant cost, Wt, from the total product,
. Without legal share restriction, the equilibrium number of tenants employed will be ot, where the total rent
is at a maximum. With ot of tenant workers employed, the total rent will be tb (= ta — ti), and the rental percentage charged for each tenant equal to tb/ta (with assumption b). In equilibrium, the marginal tenant cost equals the marginal product, i.e.,
= W =
As a result of the percentage rent reduction (say from 70 percent to 40 percent), the share constraint to the landowner is represented by the curve
, where Q is the total product and
is the restricted rental of 40 percent. That is,
is 40 percent of
at every point. The curve
, on the other hand, represents the total share for the tenants as their labor input varies. Under the constraint of
and with no adjustment in farming intensity, the landowner's total share will be td, and the tenants' share tc (= ta — td). Given the tenant cost constraint of Wt, however, the landowner will increase tenant input to t', where both
and
are maximized subject to the constraints of
and Wt; that is, Wt =
. Employing tenants ot' on the given land, the landowner's share will be t' g, and the tenants' share t' e. To the landowner, the total rent curve subject to the constraints of
and Wt will be the heavy line
, which rises with
from o to g and kinks downward along with
The portion of
from g to k measures the difference of
and Wt, which means that the constraint of Wt exceeds the con-straint of
in this portion. Thus,
has a discontinuous deriv-ative, and the marginal receipt,
, is undefined at g, where
is at a maximum.[1] If the limit of the physical constraint (point j in figure) is not reached, maximum
is attained when Wt=[123b], or the alternative earning of tenant labor equals its income as a share of
(see point e in figure). Resting at g (ore), therefore, is a new equilibrium based on the premise of rental maximization subject to the additional legal constraint of
. At this equilibrium, the marginal tenant cost,
= W, is greater than the marginal product,
.
If the tenants' alternative earnings are lower, with wage rate W', the tenant cost constraint will be represented by the dotted line W't. Given this, to maximize income the landowner will only allow the increase in tenant input to t", where
is at a maximum and where the marginal product of tenant labor is zero. With the limit of the physical constraint coming first, the constraint W' t is no longer relevant for the farming intensity deci-sion. The peak of
will now be at j, where we have
In this case, however, the tenants will be receiving residuals over their alternative earnings; and with compensating payments to the landowner assumed away, the new equilibrium under the constraint of
becomes undefined. Imagine the situation: inducing tenant input to t", the landowner wants to pause; however, other potential tenants come knocking at his door, offering him larger shares and bribes for the tenancy. Nonetheless, the condition with W't is not important to our analysis, for at any rate farming intensity is increased under the constraint of
.
Though the marginal product of land cannot be conveniently derived in figure 7 the economic implications of the legal share restriction for resource allocation are exactly the same as those derived in the preceding section. Under the share constraint, resources are directed to tenant farms from owner farms, from tenant farms unaffected by the share restriction, and from enterprises other than agriculture. Alternatively and concurrently, the tenant now works longer hours, cultivates the land more intensively, and applies more costly fertilizers. The extra resources allocated to land by tenants on tenant farms yield lower returns than similar resources employed elsewhere.