"Land area" in our theoretical discussions means cultivated land. With the small portion of the cultivated land in Taiwan owned by the state excluded, all privately owned land used for farming purposes is included under cultivated land, regardless of how many crops are grown each year or whether no crop is grown. In the analysis of land rent or land area assigned to each tenant under a share contract, this spatial (physical) area is the relevant measure.[2] During the period under study in Taiwan, partly because the cultivation of the land at external margins (arable but not privately owned or cultivated) would yield zero or low returns and mainly because the external margins were owned by the state,[3] the area of cultivated land increased only slightly. This is shown in table 3, column 6.
Whereas the area of cultivated land is quite inflexible over time, that is not the case for crop area.[4] To illustrate, suppose that over a one-year period, only one crop of rice is grown on one hectare of cultivated land; then the crop area is one hectare. If, over the same physical area for the same (one-year) period, the farmer rotates one crop of rice, one crop of sweet potatoes, and one-half crop of vegetables, then the crop area will be counted as two and one-half hectares.[5] In short, crop area represents the rate of crop rotation oyer a given area of cultivated land per period of time, measured in hectares of crops actually cultivated. An increase in crop area without a corresponding increase in cultivated land means that farming intensity has increased through an increase in the rate of crop rotation.
As is seen in table 3, using 1948 as the base year, the crop area of rice and common crops after the share restriction increased by roughly the same percentage. Special crops increased more, reaching a peak of 21.5 percent increase in 1950. Vegetables increased the most in crop area, reaching a peak of 31.7 percent increase in 1951; however, the crop area for horticulture (the area harvested) decreased.[6] These varying changes in crop areas represent changes in the frequencies of crops chosen. As we shall see later, they conform to the predicted patterns of crop choice under the share restriction.
The Density and Rate of Planting
There are two general ways by which the increase of farming inputs for a fixed area of land can be committed. One way is to hold the crop area unchanged, but to increase the yield per crop by using better seeds, fertilizers, and pesticides, improving irrigation, repairing fields, and perhaps planting the plants closer to each other. This method we shall call increasing the density of planting. Another way to increase the output on a given area of land is to speed up the rate of crop rotation, thus increasing the crop area. This can be done by planting additional crops during an otherwise idle season, by "shortening" the growing time required for each crop by relaying, interplanting, or earlier harvesting. Given an additional amount of tenant inputs to be committed under the share restriction, a portion of the incremental inputs will be allocated to the density of planting and a portion will be allocated to the rate of planting.
An increase in the density of planting implies a higher cost of planting for the same crop area. Provided that the marginal product of tenant input is above zero, the yield per crop area will rise. It is also clear that an increase in the rate of planting, with a corresponding increase in crop area, implies a higher planting cost per crop area for the same crop. At least two reasons can be offered. The first is the technical problem of faster rotation; for example, it costs more to relay or interplant (to squeeze in) an extra crop than to plant the same crop without relaying. And the second, which perhaps includes the first, is that haste makes a higher cost.[7] Unlike increasing density, where the yield per crop area will rise, the increase in planting rate may lead to a lower yield per crop area.
Intramarginal and Marginal Crops
The critical test of the implication that marginal products of tenant inputs decrease is the response of the marginal crops. Imagine a tenant farm which had grown one crop of rice per year before the share restriction, and suppose that this rice crop continued to be grown afterwards but with higher density of planting. The rice yield per crop area would rise. Here, we call rice the intramarginal crop because it was grown on the farm before the share restriction as well as after. Under the share restriction, the density of planting of this rice crop would be increased, and the corresponding rise in crop hectare yield implies that both the average and marginal product of land increased. This increased yield per crop area is also consistent with decreasing marginal returns to tenant inputs. Without incremental cost data, however,confirmation of our conclusion, that the marginal cost of tenant inputs is necessarily greater than the associated marginal product, is not possible.
Suppose, on another owner-cultivated farm, rice had also been an intramarginal crop. Under the share restriction, the reallocation of nonland resources from owner farms to tenant farms would tend to lead to a decrease in the density of planting on this owner farm. The crop area yield for rice on the owner farm would decrease. In the aggregated data available, the average crop area (hectare) yield for rice might rise or fall. The aggregated average would rise if (1) resources were drawn into agriculture to the extent that the increase in rice yield on the tenant farm outweighed the decrease in yield on the owner farm, or (2) rice was dominantly the intramarginal crop of tenant farms.