Under mutual agreements,economic theory implies that the total amount of tenant inputs contracted will be the amount which yields the highest（q-f）/h,or which yields the highest rent per unit of land.Since in figure 3 the marginal farming cost always equals zero,the highest value of（q-f）/h can be derived as follows.For every upward shift of f/h as a result of increasing the stipulated amount of tenant input,there is associated an upward shift of q/h.The former represents the marginal nonland cost,which increases at a constant rate（i.e.,constant marginal factor cost under pure competition）；the latter represents the marginal productivity of additional tenant（i.e.,nonland）input,which increases at a decreasing rate（i.e.,decreasing marginal product of tenant input）.[3] The highest（q-f）/h-associated with a specific f/h curve-is obtained when the marginal upward shifts of f/h and q/h are equal,or when the marginal product of tenant input equals the marginal tenant cost.The associated nonland farming cost,which defines f/h,covers the level of tenant inputs consistent with productive equilibrium.To maximize wealth,the crops chosen to be planted or rotated,and the method of produc-ing them,are,by definition,those which yield the highest present value of land to the landowner,that is,which maximize rental annuity.[4] The relevant value of（q-f）/h,or average rent,for decision making is thus the highest one derived from alternative pairs of q/h and f/h.To state it more precisely,the highest value of（q-f）/h defines the cost of land per acre as a factor of production.[5]
The marginal product of land,
—or
in figure 2—cuts q/h and（q-f）/h at their highest points.The equilibrium land size assigned to this tenant,T1,is where（q-f）/h is at a maximum.Maximizing rent per acre of land will maximize the rental annuity from the landlord's total landholdings.With the equilibrium tenant land size determined（T1）,the equilibrium rental percentage equals（q-f）/h divided by q/h（atT下标内容）.That is,the rental percentage,r,equals ar/ap as labeled in figure 3.Given this equilibrium percentage,say 70 percent,we plot the marginal contract rent curve,
r,as this percentage of
at every point.
Since the tenant contracts to pay a percentage of the total product,as indicated by
r,the cost of land is no longer a constraint with respect to the amount of land the tenant will use.To maximize his income,the tenant prefers to employ land to the point where
is zero（while holding his farming inputs constant as contractually stipulated）.The landowner,on the other hand,will limit the tenant's holding to T1,and parcel the remainder of his total holding to other tenants under similar contractual arrangements.[6] The landowner cannot successfully restrict land size to less than T1,since with rental percentage r the tenant's alternative earning will be higher elsewhere and he will give up the tenancy.
Several additional remarks can be made.First,not all tenant families are equally productive.Some will be able to produce more because of their endowments of certain"specific"factors of production,for example,varying amounts of knowledge.In competitive equilibrium,the more productive tenants will be the intramarginal tenants,and the f/h curve thus defined will include the imputed rent for the tenant.The landowners cannot success-fully discriminate among tenants of varying efficiencies even if there are no costs associated with discrimination,because land-lords employing marginal tenants（least productive tenants）will bid the more productive tenants away from a discriminating landlord.
Second,even if land is homogeneous,the land size per tenant farm may not be the same.Defining homogeneous land as land physically identical and having the same rental value per unit-that is,the（q-f）/h curves in different tenant farms yield equal heights at their peaks-the land sizes for different tenants will differ if the production functions of these tenants differ.[7] This also implies that the rental percentage for different tenant farms may not be the same.That is,in maximizing the rental annuity of his landholdings,the owner will assign different land sizes and charge different rental percentages to different tenants if their production functions require different intensities of tenant inputs.In equilibrium,given homogeneous lands,the marginal productivity of land for each farm must be equal at every margin,for it is at the highest value of（q-f）/h that land sizes are divided.
Third,the farming cost（other than the cost of land）may be shared by the tenant and the landowner jointly.In this case,the f/h curve represents the combined cost.Given q/h and f/h as in figure 3,the f/h minus the landowner's input cost will be lower,thus defining a higher（q-df）*/h curve.This higher（q-f）*/h curve（not drawn）measures not only the cost of land（rent）,but also the landowner's nonland farming cost.[8] The rental percentage charged by the landowner will accordingly be higher,with an upward shift of
r by the same percentage at every point.The implication of this is important:it does not matter whether the landowner required the tenant to invest more in land and charges a lower rental percentage or whether the landowner invests in land himself and charges the tenant a higher rental percentage;the investment will be made if it leads to a higher rental annuity.[9] It follows that for any contract the tenant does not have to possess the required amount of input.If what he has is insufficient,the tenant may raise the farming inputs by cooperating with the landowner,by subleasing,by hiring farm hands,by borrowing,or by joint tenancy with another family.Moreover,the different tenant input requirements in farms of different land grades and production functions will match tenants with different input endowments accordingly.
