an elastic demand for their labor in the non-farm labor market. Therefore, they can supply as much labor
as they want at an exogenously determined market wage that we assume to be v for tenants and u for
landlords.
Fixed-Rent Tenant’s Problem
Each fixed rent tenant faces the following optimization problem 12;
max F[t1f , t2 f, hf',s]+(1-t1f - t2 f )v - β fhf [6]
t1f ,t2f
The first term gives the tenant’s income from cultivating the hf units of land.13 The second term shows his
or her outside earnings where v is the market wage and the time endowment is unity. The third term is the
fixed payment to the landlord where the rent (βf) is determined by the landlord. We assume that the
tenants’ time endowment is large enough relative to his or her time input requirements so that the time
constraint is never binding. Since F(.) is linear homogeneous, equation [6] can be re-written as follows;
max hf {f ( z1f , z2f-;s ) - (z1f + z2f )v - β f} + v [7]
z1f ,z2f
where zil = —-, V i = 1,2 and f (.) is increasing and concave in both z1 and z2.
hl
Let
f ( z1f , z2f>'s ) - (z 1 f + z2f)v = rf [8]
Then the optimal time inputs per unit of land are,
zi *f = arg max rf, Vi = 1,2 [9]
12 For clarity, all terms associated with tenants are shown in lower case and all terms associated with the landlord are
in upper case. The functions are otherwise identical for both landlords and tenants.
13 Output price is normalized to one, and income maximization is considered equivalent to utility maximization because
the allocation of the fixed time endowment across types of work is assumed independent of the overall labor-leisure
choice.