It follows that to maximize his income from land subject to the legal constraint of rental share reduction, (a) the owner can successfully induce the tenant to commit more farming inputs as long as the tenant receives a farming income greater than his alternative earning (since other potential tenants will offer to do so); and (b) provided that condition (a) holds, the landowner will induce more intensive farming as long as the marginal return to additional tenant inputs is greater than zero, for the rental income under the share constraint will then be higher than without additional tenant inputs. In condition (a), we have the non-land cost constraint; in (b), we have the limit of the physical constraint, namely, zero marginal returns for tenant inputs. The maximization of rental income for the landowner will be subject to whichever limit comes first. The result will be an increase in farming intensity, simply defined here as an increase in f/h, the amount of nonland farming inputs (or nonland farming cost, f) per land area. The economic implications of this are important, and we shall analyze them at some length.
But first certain assumptions must be specified. (1) After the imposition of
, assume that there is no compensating (offsetting) payment of any kind. In other words, the owner's income from land is confined strictly to
of the annual yield. (2) For analytical convenience, assume that all farming costs other than land are financed by the tenant. The relaxation of this assumption will not affect the implied allocation. And (3), assume zero transaction costs.
A.Partial Land Repossession —Illustrated with Input Adjustments for One Tenant Farm
The increase of farming intensity under the share constraint may be attained in two general ways. One is to hold the tenant inputs constant, while competition allows the landowner to reduce tenant landholding through partial repossession of land. Another way is to keep the tenant landholding unchanged, while competition induces more tenant inputs over the given land, which is also to the interest of the landowner. of course, the landowner may choose a combination of both. In any event, the result is an increase in tenant inputs on land in tenant farms. The first is discussed in this section; the second is discussed in section B. Both are different views of the same phenomenon.
Figure 6 involves manipulations of figure 3 in chapter 2. A brief review of its notations is in order. The curve f/h is a rectangular hyperbola, representing the contractually stipulated (fixed) cost of tenant inputs, f, divided by the landholding, h. Given the average product of land,
associated with the constant tenant inputs, the rent per unit of land, (q-f)/h, is defined. The initial tenant landholding is oa, where (q-f)/h is at a maximum, and the open market rental percentage equals ar/ap.
Under the additional constraint of
, however, the (q-f)/h curve is no longer relevant for decision making. Instead of maximizing rent per acre of land, (q-f)/h, the owner will now maximize (q/h)
subject to the constraint of f/h. To illustrate, suppose the initial rental percentage of 70 percent (ar/ap) is legally reduced to
of 40 percent. The landowner's share constraint is thus represented by the curve
, which is at 40 percent of the average product of land. This will be the case as long as the rent is reduced and stated according to percentage, regardless of whether the initial contract is for fixed or share rent.[1] The corresponding share for the tenant will be
.
Without resource reallocation, the rent per unit of land will now be ae instead of ar, and the tenant's income will be at times oa, which is higher than his alternative earning. To maximize (q/h)
, the landowner can reduce the tenant's landholding to ob without reducing tenant inputs, subject to the nonland cost constraint, f/h. Given f/h as shown, competitive equilibrium is reached at point h, where the tenant income from farming equals the tenant (nonland) cost. The rent per unit of land for the landowner will now be bg, which is higher than ae. To utilize the withdrawn land, the landowner can parcel it to other tenants in a similar manner, cultivate it himself, or hire laborers to till it (this last possibility was restricted in Taiwan). The result, under the strictly enforced share constraint, is a resource reallocation to a higher f/h ratio in tenant farms, or an increase in tenant farming intensity over that in an unrestrained market.
The economic implications of increasing f/h are several. Let us assume that there are only two factors of production, land, h, and tenant labor, t. Under this assumption, total nonland farming cost, f, is the prevailing wage, W, times t. Thus, given W, an increase in f/h means an increase in t/h. At the initial land size division T1, the marginal product of land,
, is ar. With the higher t/h ratio associated with landholding ob after the adjustment, the marginal product of land becomes higher. This means that the marginal product of land would be higher in adjusted tenant farms than in owner farms. On the other hand, the marginal product of tenant input will be lower than in other occupations. In other words, the marginal cost of tenant input is higher than its marginal product. Thus, nonland inputs invested in tenant farms as a result of the share restriction will yield returns at a rate less than the interst rate.
Two side remarks can be made. First, if the tenant wage rate is low enough to form f*/h (dotted line in fig. 6), and given the constraints and assumptions specified, competitive equilibrium becomes undefined. In this case, the landowner will reduce land size to oc, where (q/h)
is at a maximum and where the marginal product of tenant labor (the "other" factor) will be zero.[2] The tenant will then be receiving a residual income (which equals ij times oc), an amount which the landowner could extract in a lump sum (a compensating payment which we assume away).
