[24].Ibid.,p.111.Similar conclusions are also reached in Amartya K.Sen,"Peasants and Dualism with or without Surplus Labor,"Journal of Political Economy（October,1966）,pp.445-46.
[25].Johnson,"Resource Allocation,"p.111.
[26].Ibid.,v.,pp.118-21.
[27].Ibid.,p.118.In the associated footnote Johnson wrote:
I have estimated net rents on crop-share-rented farms in Iowa from 1925through 1946.From 1925 through 1934 net rents on share-rented farms averaged perhaps a dollar per acre less than on cash-rented farms.From 1935through 1939 the net rents were roughly the same.From 1940 through 1946 net rents were at least four dollars an acre more on share-rented than on cash-rented farms.
[28].Ibid.,pp.119-20.
[29].Ibid.,p.120
[30].Ibid.,p.121.
[31].Ibid.,p.118.
[32].Ibid.,p.120.
[33].Ibid.,p.123.
C.A Correction of Error
To clarify the basic difference between the theory of share tenancy derived in the last chapter and the tax-equivalent analysis,a simple geometric presentation will suffice.This is illustrated in figure 5,which is an expanded version of figure 4.We are already familiar with the marginal product of tenant labor,
,and the marginal tenant receipt under share rent,
（1-r）.According to the tax-equivalent approach,equilibrium is at A,with the amount of tenant input equal to t1.
In figure 5,assume a given land area which we hold fixed for
.The result of the more general solution can be derived as follows.Given r=0.4 which defines
（1-r）,if t2of tenant labor is contractually stipulated,the landowner's share of the total product in the form of rent equals area EDBC,and the tenant's share equals OECt2.As drawn,the tenant's share is still higher than his alternative earning（area OMBt2）,with area MEA greater than area ABC,which means that the total rent（area EDBC）will be smaller than that of a wage or a fixed-rent contract（area MDB）.Given the marginal tenant receipt,
（1-r）,the corresponding average tenant receipt will be（q/t）（1-r）,which is 40 percent of the average product of tenant labor,q/t,at every point.In this case,the landowner can success-fully stipulate that the tenant work up to t3where the average tenant receipt,（q/t）（1-r）,equals the wage rate,implying that the tenant's income from farming is equal to his alternative earning.
With tenant input t3,however,the total rent received by the landowner will be equal to area MDB minus area BNP,an amount of rent smaller than that of owner cultivation,a wage or a fixed-rent contract.To maximize his wealth with a share contract subject to the constraint of tenant cost,the landowner will thus raise the rental percentage to r*.The choice of r*lowers the marginal tenant receipt to the dotted line GF,with area MGK equal to area KBL The corresponding average tenant receipt will be（q/t）（1-r*）,which necessarily cuts the marginal product of labor,
,at B.At this new rental percentage,the tenant labor stipulated is t2,the landowner's total rent equals area GDBI（which equals area MDB）,and the tenant's share equals area OGIt2,which is no greater than his alternative earning（area OMBt2）.The equilibrium condition can be iden-tified:at B we have
where r*is the equilibrium rental percentage.[1] Indeed,one of the main sources of confusion in the tax approach is the marginal tenant receipt curve,
（1-r）.Important as it may seem,it is only illusory for decision making under unrestrained private property rights.
Indeed,a closer analysis reveals that position A is not an equilibrium,even if we follow the tax-equivalent approach to analysis of a share contract and let the tenant make the decision at the margin.Suppose there are many landowners and each landowner does not specify the tenant input per acre,so that the tenant can farm any way he desires.Suppose further that there is no law prohibiting the tenant from working for more than one landowner.There is no reason for the tenant to choose to work up to ti（in figure 5）for one landowner.Imagine that the marginal tenant receipt curves in each of these farms are negatively sloping all the way.To maximize his income from farming,the tenant will choose to disperse his input resource over many farms until his input endowment is exhausted,in such a way that his marginal income（or marginal tenant receipt）from different farms is equal.[2] In this case,the tenant will be receiving an aggregate income higher than his alternative earning,and other tenants will enter to compete.
Permit our imagination to reach still further.Suppose each successive tenant entering into farming works on several farms also,and likewise equates his marginal income from different farms.As the number of tenants increases,the marginal income from different farms for each tenant will fall,implying rises in the landowners'rental shares.And tenants will continue entering as long as the aggregate income for each tenant is higher than the alternative earning.[3] Given
（1-r）as drawn,and assuming that the landowners contractually accept any amount of labor,competition among tenants will push labor input on each farm（one such farm is represented by figure 5）to t3.The resulted"overcrowded"tilling implies that rental shares are not at maximums.Competition again prevails.Given homogeneous factors of production,wealth maximization implies that the landowners will choose among tenants who offer rental percentages as high as r*,while competition among landowners implies that it will not be any higher.Given r*which defines
（1-r*）,the amount of tenant labor competitively offered and contrac-tually accepted for each farm will be t2.The market equilibrium thus reached occurs when the marginal product of tenant labor in each farm equals the marginal tenant cost（point B in figure 5）.