Let us now review the solution conditions.The highest value of rent per unit of land,（q-f）/h,is derived when the marginal tenant cost equals the associated marginal product of tenant input.As illustrated in figure 3,given the highest value of（q-f）/h,the land size per tenant（T1）is determined,and the corresponding rental percentage,r,will be ar/ap.At the dividing line T1,the rent per acre of land,that is,ar,（q-f）/h or rq/h,equals the marginal product of land,
.At T1also,we have the unique condition for the rental percentage
This is identical with our mathematical solution,where we have
since in our mathematics we assume only one tenant input,f=Wt.
[1].The important distinction here is between land and inputs other than land.The substitution between labor and farming equipment,for example,is not yet important in this theory and is ignored.
[2].For simplicity of presentation,all values are measured in real terms.Note,however,that the annual yield,q,may include a variety of crops;given their relative market prices,the value of each may be expressed in terms of one crop,say rice.And payments for tenant inputs and land will likewise be in rice.
[3].To avoid semantic problems,we assume here the increase of one tenant input only.If several inputs are increased,as is usually the case,the relevant"shifts"to consider are when q/h increases at a decreasing rate.In either case,the theoretical outcome is the same.
[4].Given the appropriate discount rate,
,and the future income stream from the land,Y1,Y2……,Yn,Yinot necessarily equal to Yj,there exists a
,called the rental annuity,such that
If the private land right is perpetual,we have
,where V0 is the present value of land.
[5].The notion that rent is a cost of production began,perhaps,with J.S.Mill.And I maintain here that it is the highest rent per unit of land which really counts,for it is from this that the land value is derived.
[6].It remains to show how the last plot of land belonging to the same landlord is allocated,since it may be too small for one tenant family.One answer is that a tenant may be renting land from two or more landlords at the same time,employing land margins from both.Likewise,a tenant may own a small area of land himself,renting an extra margin from a landlord.This is evident in the existence of part-owner farmers.Therefore,if the land size of the last plot assigned to a tenant family is smaller than the equilibrium size,the tenant will employ part of his resources elsewhere,possibly outside the farming sector.
[7].The term"land homogeneity"employed here,which presupposes identical market location,renders the unambiguous condition:Given the same maximum values of（q-f）/h and the same ratios of tenant inputs to land in different farms,the rental percentages will be the same.Different production functions associated with different crops will require different intensities of tenant inputs.On the other hand,given the production function,the rental percentage and the land size per tenant will depend on（1）tlje fertility of land and（2）the cost of tenant inputs.
[8].Note that the peak of this higher（q-f）*/h curve will be to the left of T1.This is not relevant to land size division,for it will lead to a lower rent per acre.The dividing line is still T1,where the（q-f）/h,or the net return to land,is at a maximum.But the rental percentage in this case will be（q-f）*/h at T1divided by q/h.
[9].The fact that most leases under share tenancy are not perpetual has been attacked as insecure tenure which leads to misallocation of resources.But it is no more insecure than the position of hired farm hands who are subject to dismissal in case of poor performance.Indeed,a temporary lease is an effective device to insure efficient allocation.The argument that nonperpetual leases tend to discourage investment is incorrect.We find the period of lease varies according to the type of contract and the asset holdings of the contracting parties,and the frequency of tenant dismissal has been small.For a fuller discussion,see chapter 4,section C.
D.Comparison with Fixed Rent and the Market Criteria of Share Contracting
A number of questions,both theoretical and empirical,related to share tenancy deserve further inquiry,and I shall try to press them in the remaining chapters of this book.In this section,however,answers to two questions are sought.
Let us begin with the question:What are the differences between fixed-rent and share contracts?Under private ownership of resources,the basic difference between fixed rent and share tenancy lies in how the chosen labor-land ratio（or the ratio of nonland inputs to land）is expressed.With fixed rent,given the rent per acre,the tenant states how much land he will employ,and he alone decides-subject to the constraint of competition as with share tenancy-the amount of nonland inputs to be committed for every production run.Under share tenancy,however,the landowner and the tenant mutually decide the intensity of nonland to land inputs.In either case,the wealth maximizing value determines the land size per farm as well as other inputs employed.Since the set of constraints for decision making is the same for the two types of contracts,the same resource use is implied.
