Development Economics
Rural Land Market
Tapas Kundu
University of Oslo
Spring 2011
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To p ic s
Rural land economy
Topics
1
Land size and productivity
1
2
2
Market
1
2
3
Sales market
Tenancy market
Tenancy contracts
1
2
3
4
Theory
Empirical evidence
Contracts and incentives
Risk sharing
Limited liability
Land reform
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L a n d s iz e a n d p r o d u c t iv ity
Land size and productivity
Theory
1
An old debate
2
Technological return to scale
3
Incentive problem
1
2
Imperfect insurance market
Imperfect labour market
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L a n d s iz e a n d p r o d u c t iv ity
Imperfect labour market
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L a n d s iz e a n d p r o d u c t iv ity
Land size and productivity
Empirical evidence
1
Relative dominance of the incentive problem against technological return
to scale in developing countries (Binswanger, Deininger and Feder (1995);
See Ray (Ch 12) for a good discussion
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L an d m arket
Land market
Land Sales
Thinner than what standard economic logic argues
Asset value of land is more than its simple production value
Used as collateral in imperfect credit market
Political status
Debt overhang- Ine¢ cient …nancing (moral hazard problem in presence of
limited liability) (Mookherjee 1997)
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R u ral L an d E con om y
Te n a n c y
Land market
Tenancy
Unequal distribution of land in developing countries
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Te n a n c y
Land market
Tenancy
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Te n a n c y
Contractual form
Let R denote the transfer from the tenant to the landlord and Y denote the
total production from cultivating the land. Write R as
R= Y +F
If
= 0 and F > 0, we have a pure …xed rent contract
If
> 0, we have a sharecropping contract
If
= 0 and F < 0, we have a pure wage contract
One can also allow for the possibility of state-contingent contracts when
there is uncertainty in the production level
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Te n a n c y
Tenancy contract
Incentives (will discuss next week)
Risk sharing (will discuss next week)
Limited liability
Ine¢ cient use of labour
Tenancy ladder - Wealthy tenants may be preferred
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Te n a n c y
Limited liability
A model of moral hazard with limited liability
e 2 [0; 1] denotes the e¤ort level by the tenant
Disutility of e¤ort d (e),with d increasing and convex and d (0) = 0
Two states: Production is H in good state or L in bad state, with
probability e and 1 e
Risk neutral tenant with wealth w and a reservation income m
First best e¤ort
M ax eH + (1
e
e) L
d (e)
Solution: Unique e that satis…es
d0 (e ) = H
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Limited liability
Suppose e is observable. Can we implement e ?
If e¤ort is observable, one can write contract contingent on the observable
e¤ort level. For example, consider the following contract
wage =
m + d (e ) if e = e
<m
otherwise
See that the tenant will accept the above contract and execute e¤ort e ;
Landlord will extract the whole rent
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Limited liability
Suppose e is not observable. Can we implement e ?
Write contract contingent on observable states
h
l
wage =
if H
if L
Landlord’s optimization problem
M ax e (H
e
h) + (1
e) (L
l)
subject to
(IR)
eh + (1
e) l
d (e)
m
(IC)
e = argmax eh + (1
e) l
d (e)
e
The optimization problem is easy to solve and one can see that the …rst
best e¤ort level is implemented.
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Limited liability
An alternate approach
Cost minimization problem
C (e; m) = min
h;l
eh + (1
e) l subject to IR; IC
Solution
h (e)
= m + d (e) + (1
l (e)
= m + d (e)
C (e; m)
= m + d (e)
e) d0 (e)
ed0 (e)
Landlord’s optimization problem
M ax eH + (1
e
F OC : H
e) L
C (e; m)
L = d0 (e)
First best e¤ort will be induced. Discussion on optimal h and l .
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Limited liability
Limited liability
Constraint: l + w 0
If l (e ) + w 0, optimal e¤ort can be reached in equilibrium
If l (e ) + w < 0, the above contract can longer induce the optimal level
of e¤ort
De…ne e0 such that
e0 d0 (e0 ) =
l (e0 ) = m + d (e0 )
w,
equivalently, limited liability constraint does not satisfy at e if and only if
e is above e0 .
Consider the following payment schedule: For e
l
h
(e)
(e)
=
e0 ,
w
0
= d (e)
w
and, for e < e0 , l (e) = l (e) and h (e) = h (e). (QUESTION: Is this
the optimal least-cost contract given limited liability constraint?)
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Te n a n c y
Limited liability
With the new least-cost contract, the cost function looks like
C
(e; m) =
ed0 (e) w
m + d (e)
if e e0
if e < e0
Landlord’s optimization problem
M ax eH + (1
e
F OC : H
e) L
L=C
0
C
(e; m)
(e)
Implication: Tenant’s participation constraint is not binding (if e is
above e0 ), implying that the tenant keeps a part of the rent, but at the
cost of suboptimal production.
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R u ral L an d E con om y
Te n a n c y
Limited liability
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R u ral L an d E con om y
Te n a n c y
Limited liability
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Te n a n c y
Limited liability
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Te n a n c y
Limited liability
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Te n a n c y
Limited liability
tenancy ladder
Notice that e or e do not depend on m or w, but e0 does. What if we
allow m or w to vary across household? A natural assumption here is that
m can be an increasing function of w ( m0 (w) > 0 )
We can write e0 as a function of w and so of m, too (QUESTION: Why
e0 is an increasing function of w?) and …nd w1 and w2 such that
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=
e
e0 (w2 )
=
e
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Limited liability
tenancy ladder
If we vary w, for example, if we start with a very high w such that e0 (w)
is above e , the equilibrium e¤ort level will be e
As w decreases, in particular, if we just below w1 (but not su¢ ciently
below it), H L, the marginal revenue for the landlord is strictly in
between d0 (e0 (w)) and d0 (e0 (w)) + e0 (w) d00 (e0 (w)), the equilibrium
e¤ort is e0
As we further decrease w, and it gets below w2 , e0 will be even below e ,
which is then the equilibrium e¤ort
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Te n a n c y
Tenancy ladder
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Te n a n c y
Tenancy ladder
Implication
When there is excess labour supply, more wealthy labour will be
preferred, as higher e¤ort can be induced by suitably increasing the
’punishment’level in the bad state
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Te n a n c y
Recall our discussion on forms of tenancy contract
Let R denote the transfer from the tenant to the landlord and Y denote the
total production from cultivating the land. Write R as
R= Y +F
If
= 0 and F > 0, we have a pure …xed rent contract
If
> 0, we have a sharecropping contract
If
= 0 and F < 0, we have a pure wage contract
One can also allow for the possibility of state-contingent contracts when
there is uncertainty in the production level
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Te n a n c y
Appropriate provision of incentives
Suppose production is given by f (L) where f is concave function.and cost of
labour is assumed to be linear, cL.
Denote e¢ cient labour supply by L which solves
f 0 (L) = c.
With a …xed rent contract it is easy to see that the e¢ cient labour supply L
will be implemented and the landlord, if works as a rent maximizer, will take
the whole surplus, keeping the tenant’s participation constraint binding.
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Fixed rent contract and incentive
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Sharecropping and incentive
Consider a sharecropping contract with share in between 0 and 1?
Less than the e¢ cient level of
labour is exerted as tenant’s marginal return from labour is reduced.
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Sharecropping and incentive
What if we increase the tenant’s share above 1, and take out a …xed payment
as rent?
More than the e¢ cient level
of labour is exerted but that does not maximize landlord’s payo¤.
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Risk sharing
Assume tenant is risk averse
A …xed rent contract exposes the tenant to complete risk, where as a
sharecropping contract shares the risk between the tenant and the
landlord
If the tenant is risk averse, he would prefer to reduce the risk, and the
landlord can trade it o¤ with higher share in a sharecropping contract
If we follow this argument at the other extreme, one can show for highly
risk averse tenant, landlord can hire him as a wage laborer with an
extremely low wage
In fact, if e¤ort is observable, it can be shown that any implementable
sharecropping contract has no extra risk advantage over a suitable mix of
…xed rent contract and wage contract (Seminar question)
However, when e¤ort is not observable, sharecropping is a compromise
because of the work incentive problem and risk sharing incentive
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Other incentives
Double incentive problem
Cost sharing
Limited liability with …xed rent - Over investment in risky asset
Screening - When low ability tenants …nds sharecropping more preferable,
the landlord can screen tenants by o¤ering a menu, consist of a …xed rent
contract with high rent, and a suitably adjusted sharecropping contract
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L a n d re fo rm
Land Reform
So far, we …nd that Productivity tends to be higher on smaller size plots
Tenancy contracts may not result in full realization of the productivity
gain
Land sales market is typically thin
A social planner may prefer redistributing land from large-plot landowner to
small landowners or landless laborers
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L a n d re fo rm
Land Reform
By land reform, we mean a variety of things
Land transfer
Consolidation of disparate land
Land ceiling
Tenancy reform - security of tenure, increase tenant’s bargaining power
by providing lower bound on share received, increase in wage,
Several case studies. We will cover Besley and Burgess, QJE 2000, Banerjee,
Gertler and Dhatak JPE2002 (Seminar question)
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