World Bank Staff Working PaperNo. 433
October 1980
Public Disclosure Authorized
Public Disclosure Authorized
Public Disclosure Authorized
Public Disclosure Authorized
AgrarianReformsin DevelopingRural
Economies
Characterized
by InterlinkedCredit
and TenancyMarkets
Prepared
by: AvishayBraverman
T. N. Srinivasan
(Consultant)
Development
Research
Centre
Copyright© 1980
TheWorldBank
1818H Street,N.W.
Washington,
D.C.20433,U.S.A.
Theviewsandinterpretations
in thisdocumentarethoseof the authors
andshouldnot be attributedto the WorldBank,to its affiliated
organizations,
or to anyindividual
actingin theirbehalf.
The views and interpretationsin this document are those of the author and
should rLotbe attributedto the World Bank, to its affiliatedorganizations,
or to any individualacting in their behalf.
WORLD BANK
Staff Working Paper No. 433
October 1980
AGRARIAN REFORMS IN DEVELOPING RURAL ECONOMIES
CHARACTERIZEDBY INTERLINKED CREDIT AND TENANCYMARKETS
The paper concentrateson a model of linkage between land, labor and
credit transactionsin the context of sharecropping. Our proof follows from
our resultthat ceterisparibus,the tenant'soptimaZeffort per hectare
a decreasing
functionof the size of the plot he cultivates.
is
The utility equivalenceresult has the fundamentalimplicationthat
policies otherthan land reform will leave the welfare of each potential tenant
unalteredwhile affecting the level of output, extent of tenancy and the welfare
of landlords. With the possibilityof linking tenancy and credit contracts,it
is shown that the landlordwill resort to linking only in a situationwhere it
will Lowerthe cost of credit to the tenant. If the governmentoffers the
tenant subsidizedcredit at a cost lower than the landlord'sopportunitycost
of funds, the landlordwill move out of the tenant's credit market and allow
the tenant to borrow from the government. The increasein surplus due to
governmentsubsidizationof tenant's credit will fully accrue to the landlord
as a consequenceof the utility equivalenceresult. Hence, government
subsidization
of tenant's
credit resuZts only in the subsidization
of landlords.
Other partial reforms by the government,however, may force the landlord to
link credit and tenancy contracts even if the governmentprovides the cheaper
source o:fcredit; this, thereby, leaves the tenant'sutility unaltered at
its pre-reformlevel while affecting total output and the extent of tenancy.
Our model is also able to provide a theoreticalunderpinningfor
two almost opposite phenomena that are sometimesobserved: low interest
consumptionloans from landlord to tenant and the opposite, high interest,
low volume loans.
One major result of the paper is valid both in the context of
interlinkedcredit and tenancy contractsand in that of sharecroppingcontracts
alone. 'Itstates that, as long as the landlord can vary thiesize of the plot
given to a tenant and there are enough potential tenants, the equilibrium
will be characterizedby "utility-equivalent"
contractseven if the landlord
does not control any other term of contractsuch as crop share, interestrate
on credit, etc. That is, in equilibrium,a tenant's utility obtained through
sharecroppingwill be the same as that which he could have obtained as a fulltime wage laborer.
Preparedby:
Avishay Braverman
T. N. Srinivasan (Consultant)
DevelopmentResearch Centre
Copyright @ 1980
The World Bank
1818 H Street, N.W.
Washington,D.C. 20433
U.S.A.
1. Introduction
It is often claimed that because the rural economy of developing
countriesis characterizedby a non-competitivemarket structure,policy
analysis in such an environmentwill differ significantlyfrom a similar
analysisof a competitiveworld. We discuss here the possibleimpact of
policiessuch as land reform, as well as alternativetenancy and credit reforms
in a rural economy characterizedby interlinkedland, labor and credit markets.
One of the many contributorsto the literatureon interlinkingstates,"It is
misleadingwhen talking about individualoperators to hypothesizethat each
producerconfrontstechnicaldata and market prices in an impersonalenvironment
and all are equally free to take behaviourin any one single market without
knowing how the markets are interlinkedby price and non-price relations,for
the fields of feasibZe
choices in the differentmarkets are not, as assumed
under competition,definablea priori
independentlyof each other."-'/While
this descriptionis suggestive,it is by no means a completedefinitionof
interlinking. After all, the typical consumer'schoice problem as usually
formulatedin micro-economictheory implies that the consumer's
actions in
the market, for each of the set of goods, are interlinkedthroughhis budget
constraint. Similarly,in a typicalproducer'schoice problem, profit maximization links his choice of inputs and outputs given his technology. In any case,
at the economy-widelevel, general equilibriumimplies simultaneousequilibrium
in ael markets,with the supply and demand in each market being dependenton all
relevantprices.
1/ See K. Bharadwaj [19741.
A possibledefinitionof interlinkedcontractscould be the following:
contractsmade between the same pair of individualsrelatingexchangesin more
than one commodity or service, the contracts being linked in an essentiaZ
way.
In other words, contractsbetween a pair of individualsin two or more commodities
that are linked by coincidence,i.e. contractsthat could as well have taken place
without change at differentpoints in time and not necessarilybetween the same
individuals,are not interlinkedin this sense. This definition,however, is
not meant to exclude intertemporallinkingof contracts. On the contrary,a
very importantaspect of interlinkingis the interlinkageof present and future
transactions.
In the present paper we concentrateon one form of linkage between
land, labor and credit contractsin the context of sharecropping. In this
context,the followingconditionslead to interlinking: (a) There is an incentive
problem due to the cost of monitoringand supervisingeffort; (b) The tenant
has no accumulatedsavings;hence, he must borrow at the beginningof the production period; and (c) There are imperfectionsin the capitalmarket in the form of
differing costs of capital to the landlordand to the tenant.
One major result of the paper is valid both in the contextof interlinked
credit and tenancycontractsand in that of sharecroppingcontractsalone. It
states that, as long as the landlordcan vary the size of the plot given to a
tenant and there are enough potentialtenants,the equilibriumwill be characterizedby "utility-equivalent"
contractseven if the landlorddoes not control
any other term of contractsuch as crop share, interestrate on credit, etc.
That is, in equilibrium,a tenant'sutility obtainedthroughsharecroppingwill
be the same as that which he could have obtainedas a full-timewage laborer.
3
Newbery and Stiglitz [1978]assert, without providinga satisfactoryproof, the
same result in the contextof sharecroppingalone, while a similar,though not
identical,conclusionhas been obtainedin a differentsettingby Cheung [19691.
Our proof
effort
follows
from our result
ceteris
that
per hectare is a decreasing function
The utility
policies
other
tenant
equivalence
than land reform
of the piece
each potential
result
(i.e.,
unaltered
while
the tenant's
optimal
of the size of the pZot he cuZtivates.
has the fundamental
reform
of land he is cultivating)
tenant
paribus,
affecting
that
will
implication
confers
ownership
leave
the welfare
the level
of output,
of tenancyand the welfare of landlords. With the possibility
that
to the
of
extent
of linking
tenancy and credit contracts,it is showm that the landlordwill resort to
linking only in a situationwhere it will
Zower the cost of credit to the tenant.
If the governmentoffers the tenant subsidizedcredit at a cost lower than the
landlord'sopportunitycost of funds,
tenant's
credit
the landlordwill move out of the
market and allow the tenant to borrow from the government.
The increase
in surplus
fuZly accrue
to the landlordas a consequenceof the utility equivalence
result.
due to government
Hence, governent
the subsidization
however,
may force
if the government
subsidization
of landZords.
the landlord
subsidization
of tenant's
Other partial
to link
credit
reforms
of tenant'
credit
s credit
will
resuZts onZy in
by the government,
and tenancy
contracts
even
providesthe cheaper source of credit; this, thereby,
leaves the tenant'sutility unalteredat its pre-reformlevel while affecting
total
output
and the extent
of tenancy.
Our model is also able to provide a theoreticalunderpinningfor
two almost oppositephenomenathat are sometimesobserved:low interest
consumptionloans from landlordto tenant and the opposite,high interest,
low volume loans.
4
We begin in Section 2 with an extendeddiscussionof the various
possibleforms of linked contractsand the circumstancesin which they are
likely to arise. In Section 3, we present the model followedby a
of the equilibriumin Section 4. Section 5 discusses
characterization
policiesof credit, land and tenancyreforms as well as the impact of
taxationand technologicalprogress. Finally,in Section 6 we briefly
summarizeand relate our conclusionsto the literatureon sharecropping
and on interlinkedcredit and tenancy contracts.
2. Types of InterlinkedContracts
As stated in the introduction,interlinkedcontractsmay be
defined
in more than one commodityor service
as transactions
the same pair
and linked
of individuals
An example will
perhaps
made between
way.
in an essential
of interlinking
make the concept
suppose a landlordand a tenant enter into a contract
clearer:
in which the tenant
rents a piece of land at a stipulatedrent, and at the same time the landlord
extends the tenant credit, again on specifiedterms. If the contractin land
(credit)could have taken place independently
of that in credit (land)with
no additionalcost to either party, the two contractsare not interlinked.
feature
An essential
contracts
of this
would be infeasible
case, if it
is infeasible,
definition,
is that
therefore,
or costly
for at least
the two parties
either
delinking
one party:
transact
in all
the
in the first
the relevant
goods and servicesor do not transactin any of them: and in the second,
if it is costly, linking
rather than not linking,will benefit at least one
party.
The infeasibilityof delinkingfor both parties can arise from the
nonexistenceof certainmarkets (e.g., the market for bullocks'services)
5
however, interlinkingcovers a much wider range of contractsthan those simply
created to circumventthe absence of certain markets. Quite often the linking
of contractsoccurs when there is a moral hazard problem,which results in an
externality.-/"Moral hazard"
"inappropriable"
contract
arises
in a risk-sharing
when one party, often called the agent (tenant,insuree),can affect
the probabilitydistributionof the outcome (output,accident)throughhis
action (effort,driving habits) which the other party, often called the
principal (landlord,insurer)cannot effectivelyor cheaplymonitor. In such
a situation,the agent has an incentive
to change the probability
distribution
of the outcome,in his favor, once the parties have agreed on the terms of
the contract. Since both parties know this, the form of contractas well as
its terms will often includeprovisionsthat address the moral hazard
problem,such as for instance,the deductiblefeature of an insurancecontract.
Considerthe case of sharecropping. The tenant'seffort,which cannot be
perfectlymonitoredor inferredby the landlordthrough observation,is affected
by his capital endowmeat. If the tenant lacks capital he will try to borrow
some. The borrowingaffectshis effort and, consequently,output and the
landlord'sprofits. Since the landlordcan neither perfectlymonitor nor
enforce the tenant'seffort level (i.e., it is too costly),there is an
inherentexternalityfrom the credit market into the productionprocess.
Since, the landlordis aware of this externalityhe can internalizeit (i.e.,
address
the moral hazard problem)by linking the credit and tenancycontracts,
thus promotinggreater efficiencyin productionand increasinghis own profits.
This linkingmay constitutea Pareto superiormove as opposed to a
delinked situation,since the increasein total surplus allows for an
1/ In the broader sense, even this class of contractscan be defined as
arising due to nonexistenceof markets where the missing markets are
themselvesdefined as the markets for the externalities.
6
improvementin welfare of at least one party, without making the other party
worse-off. Such linking is clearlyvoLuntary.
Linking,
however,maynot
necessarilyconstitutea Pareto improvingmove if one party, which possesses
more market power, decreasesthe other party's welfare through interlinkingof
contracts.
party
this
would prefer
option
to accept
could be termed as forced
Such linking
delinking
if
is not allowed
the "tie-in"
that
option
by the powerful
package rather
There are two more classes
Zinking,
where the weaker
were open to him; however,
party,
the weaker party
than not to transact
of interlinked
since
chooses
at all.
contracts:
arisingfrom voluntarylinking is due to Lowering transaction
one class
costs
for both
parties. Many examplesof linking-often found in developedcountries,such
supplier'scredit, and shopping for unrelateditems in a
as "ttie-in-sales,"
large store-result, to some degree, from lower transactioncosts. Another
class constitutesa screeningdevice resultingfrom imperfectinformation
regardingthe attributesof a heterogenouspopulation.For example,in a world
where some attributes,such as tenant'smanagerialskills,are unobservable,
interlinkedcredit and tenancycontractsmay serve as a screeningdevice
for landlordsto identifymore able tenants.
The equilibrium,in all of the above cases, is achievedin the
context of an incompleteset of markets, imperfectmarkets, or both. Hence,
welfare propositionsrelatingto such equilibriaare often of the "secondbest"
kind;
for instance,
in an environment
characterized
by market
distortions,a move toward eliminatinga subset of distortionsdoes not
necessarily
either
imply
an improvement
by creating
market power through
allocation
of welfare.
some, but not all,
reform
of resources
will
nonexistent
not necessarily
Therefore,
markets
lead
policy
intervention,
or by eliminating
to a more efficient
as compared to the pre-intervention
equilibrium.
7
Clearly,equity or the distributionalaspects of such interventionwill
depend very much on the prior structure.
Nonexistenceof markets is the rule rather than the exception,
particularlyin less developedcountries. For example,landlessrural
householdsendowedwith the labor of women and childrenfor which there is
no market
often
or because social taboos prevent them from working for others,
lease
family
labor,
laborers
case,
in land.
while
outside
transactions
The leased
in land
is farmed mostly
those members of the household
the household
in land
who can work as wage
farm do so, to a significant
and family
labor
get
by non-marketable
linked.
extent.
There
are
In this
several
other examplesof linkage of a similarnature arising from the nonexistence
of markets
for draught
power and of tenants'managerialinput.
Intertemporal
market.
linking
is quite
prominant,
If wage labor in peak agricultural
seasons
its availabilityor its cost,
a landlord
especially
in the labor
is either uncertain in
may wish to employ a permanent
or
attachedfarm laborerwhose servicesare availableto him throughoutthe year.
In this case, the linking occurs in the contractsrelatingto peak season and
off-peakseason labor: an attachedlabor contractis-an agreement to buy and
sell labor in both seasons. The unlinkedalternativeis to hire wage labor
in
each
season
separately.L/
1/ For more examplessee Bardhan [1980].
8
3. The Model
3.1 The Tenant
The form of rental contractdiscussedhere is sharecropping.
If onZy incentiveproblemsexist (i.e., the landlordcan neither force
the worker to contributea specifiedlevel of effort nor can he monitor it),
the fixed-rentcontractwill be best suited to remedy them: It will, in
fact, dominate a fixed-wageor a sharecroppingcontract. The tenant obtains
all the fruits of his effort after paying the fixed rent. Fixed rents,
however, imply that the tenant must bear all risk resulting from output
uncertaintydue to exogenousconditions(e.g.weather, illness). If the
tenant is risk averse, such a contractwill be inefficient,in which case
a sharecroppingcontractwill dominateit.
It follows that risk-sharingeffects seem to be necessary to
explainthe phenomenaof sharecropping. In addition, incentiveproblems
due to the cost of supervisionare also necessary,since any risk-sharing
postureobtained througha share contractcan also be obtainedby a linear
combinationof wage and fixed-rentcontracts (Stiglitz[1974],Newbery [1977]).
However, we shall
on the relations
not consider
between
risk
incentive
elements
effects
here,
but focus
and the tenant's
instead
only
lack of funds.
We assume that all workers are identical,facing two employment
alternatives: first, as tenants on the landlords'land, or secondly,as
wage laborersoutside the farm. Each tenant is offered a plot of land of
size H hectares for cultivation,in return for which he agrees to pay the
landlorda share (1-a) of the harvest. None of the workers possess any
savings at the beginningof the productionyear. Wage wort.3:rs
are paid
9
wages, W , during the productionperiod and, therefore,have no need to
borrow for consumption. The tenant,however,borrows at the beginningof
each season his entire consumptionneeds for the coming season and repays
his loan with interest at the end of the season
after harvest.
He does
not store any grain from one season to the next nor does he have any investment opportunity.
The tenant obtains a proportion v
of his borrowings(either
as a voluntaryor "tie-in"package with a tenancy contract- see Section 2.2
below) from his landlordat an interestrate rT per season. He obtains
the remainingproportion (1-v) of his borrowingsfrom an alternative
source (e.g.,local moneylender,cooperative,governmentcredit)at an
interestrate rA . He treats rT and rA as parametersover which he
has no influence. We assume that he cannot default (a) in order to simplify
the argumentation,and (b) because in many areas landlordsvirtuallyhold
the harvestedcrop as collateral. Clearly,if the tenant can borrow all
the present value of his consumptionat either rT or rA .
he will choose
to borrow the entire sum from the cheaper source. However,since our discussionfocusseson linking,we start by assuming that the tenant takes
v
as given, so that v > 0 will representlinking over which he has no
influence.
Labor providedby the tenant for cultivation(includingall
operationsfrom land preparationto harvesting)is denotedby
eL, where L
denotes the number of man-daysper season and e denotes the effort per
man-day of labor. Thus, eL representslabor in efficiencyunits. Output Q is a concave functionexhibitingconstantreturns to scale in H
10
and
eL. l
Thus:
(1)
Q - F(E, eL)
Assumingthe number of man-days, L , (i.e. labor in natural units) to be
exogenouslyfixed, we can set (withoutloss of generality) L - 1. Thus
we can rewrite (1) as:
Q
where x
II
F(1, ex) _
(2)
X
is man-days of labor per hectare of land. Given that L - 1,
x representsthe reciprocalof the size of the plot he is allotted. The
function f representsthe average product per hectare of land. By assumption, f' is positiveand f" is negativewhere the primes (single
and double) denote the first and second derivativesof f , respectively.
The tenant'sshare of the harvest Q
is a
and his income is therefore aQ.
By our assumptionthat the tenant borrows his entire consumption
needs at the beginning
of the season
ment opportunities,
follows
his
income
it
that
and has no carry-over
his
consumption
c
aQ at the end of the season, discountedby
stock
in any season
equals
(1 + i) where
is the effectiveinterestrate on his borrowing. Of course, i
vrT + (1 - v) rA.
or invest-
i
equals
Thus:
1/ Bell and Braverman [1978] show that landlordswill prefer cultivation
with wage labor to sharecropping,if the productionfunctionis of
constantreturns to scale and there is no uncertainty. Since we do
with wage labor,
not allow the landlordthe option of self-cultivation
the Bell-Bravermanresult does not apply to our analysisfor this and
other reasons having to do with the modellingtenant'seffort and
behavior.
11
+ vrT + (1 v)rA
where
1 + vrT + (1
-
v)rA
~discounted
share of the tenant.(4)
We assume that the tenant'sutility function U(c,e) is
strictlyquasi-concavein consumptionand leisure,where leisure is defined
as e
-e. Further,both consumptionand leisure are assumed to be normal
goods.
The potential tenant'schoice or controlvariable is e. He
will not choose to work as a tenant unless U(c, e) is at least as large
as U ,
the utilityhe could have assuredhimself by working as a wage
laborer. The supply of tenants is assumed to be infinitelyelastic at U,
i.e. U
is exogenous. Thus, we can solve the potentialtenant'schoice
problem in two steps. First, let the tenant maximize:
Max U(c(e),e) s.t. (2) and (3)
e
Let he maximizedvalue of U
(5)
be U*. Secondly,he compares U* with U.
If U* > U, he works as a tenant,otherwiseas a wage laborer.
It is immediatelyapparentfrom (2)-(5)that the parameters
a, v, rT and rA enter the tenant'sconstraintset and utility function
only through their effect on his discountedshare B. By substituting(2),
(3) and (4) in (5), maximizingwith respect to e, we get the first order
12
condition:i/
Of'(ex) 1 + U 2 =
(6)
i.e., at the margin the change in the tenant'sutility of consumptiondue
to a change in effort must compensatethe change in his disutilitydue to
the same change in effort.
Now, define effort per hectare as z
E
ex. and rewrite (6), to
obtain
U2
Of'(z) =
_
2
(7)
U1
On the L.H.S. of (7) we have the marginalrate of transformation
between consumptionand leisurethrough production(MRT) and on the R.H.S.
of (7) we have the marginalrate of substitutionbetween consumptionand
leisure throughconsumption(MRS). While MRT is a functionof a
and z,
MRS is a functionof 8, z and x. The relation (7) is crucial to the
understandingof the utility equivalenceresult and tothe impact of land
reform on output. We present it graphicallyin Figure 1. The MRT curve,
given 3, is downwardsloping in effort per hectare z, due to diminishing
marginalproductivity(i.e. f' < 0). The MRS, given 8 and x, is an
increasingfunctiondue to the normalityof both consumptionand leisure
(See Braverman-Srinivasan
[19801for a proof of this and all other propositions
discussedbelow.)
1/ It can be shown that the second order conditionis satisfiedfrom our
assumptionon U, and the strict concavityof f.
strict quasi-concavity
13
MRS(x )
MRS MRT
MRS(x;
x1
> X
*~~~~~~~~~~~~~~~~~~~~~~~~~~~
I~~~~(
af'(z) MRT
a
1
z
Figure I
TIenant's
Optimal Effort per hectare
Now considerthe impact of a ceterisparibusreductionin plot
size (an increasein x) on tenant'swelfare,effort e, and effort per hectare,
z. Clearly,his welfare declines. The impact on e
*
cannot be determined
~~unambiguously
since it depends on the relativeabsolutemagnitudesof the
income and substitutioneffectswhich are opposite in sign. However,there
is no ambiguityin the impact on z. ConsiderFigure 1: a change in the plot
size doesnot affectthe MRT curve. A reductionin plot size, however,shifts
the MRS curve outside and downward, since ceterispari1bus,
such a reduction
results in a decline in the tenant?'s
income E consumption,thereby,increasing
14
the marginalutility of consumptionvis-a-vis leisure and calling for larger
effort per hectare to restore equalitybetween MRS and MRT. This leads, therefore, to the followingproposition:
Proposition
1:
The tenant'seffort
in the size of his plot.
per hectare increases
with a reduction
This holds even if the tenant'seffort declines
with such a reductionin plot size.
Remark: The instrumentother than plot size, namely a
,
shifts both curves;
thus, in order to derive the impact of policiesthat change 8
(e.g. land
reform)we need to specifythe relativemovementsof the two curves.
3.2. The Landlord
With an infinitelyelastic supply of identicaltenants,and constant returns to scale in production,maximizingprofits is equivalentto
maximizingprofits per hectare. Hence, our model yields the same results
whether different landlordspossess differentamounts of land or not. Therefore, without loss of generality,we assume that all landlordsare identical
and possess one hectare of land each, which they divide into plots of size
l/x to give each of x
tenants. As stated earlier,the landlordmay require
that each of his tenantsget a proportion v
an interestrate rT.
of his borrowingsfrom him at
Assumingthat an alternativeuse of funds would have
earned the landlordan interestof rL per season (e.g.depositsin the
city's bank), his income g
f( z
9
can be shown as:
+ vrL + (~1
- v)rA}
15
Multiplying g by the number of tenants, x , we get the landlord'sincome G:
G
-
[1 -
{1 + vrL + (1 - v)rA}f(z)
The interestrate, rT
,
(8)
charged by the landlordon his loans to
his tenant is seen from (8) to affect his income onl through its effect on
, the discountedshare.
G with respect to his choice variables
The landlord maximizes
given the tenant'seffort function e(ex, 8). The choice variablesinclude
the plot size 1/x, and may include the tenant'scrop share a, v
are no laws against the landlordprovidingcredit) and r T
,
(if
there
the rate of
interestcharged.
4. Utility Equivalence
For the moment, let us focus only on the choice of x (the number
of tenants or, equivalently,the plot size per tenant). The landlord'sincome,
G , is an increasingfunctionof output per hectare, f , and
f
is
an increasingfunctionof its argument,effort per hectare, z , (see (8)).
Furthermore,Proposition1 states that z is an increasingfunctionof x
Therefore,
tenant's
increases
clearly
the landlord's
income increases
with
x .
Thus a decreasein each
plot size, with a correspondingincreasein the number of tenants,
the landlord's
decreases
as x
utility U* exceeds
his
income.
On the other hand, a tenant'swelfare
increases. Thus, if
utility
U
at any value
in the alternative
of
x
use of his
the tenant's
labor
(so that he chooses to be a tenant),the landlord,by reducing plot size
(increasingx), can increasehis income while pushing the tenant towards U.
As long as there are enough potential tenants,the landlord'schoice, x
16
will be to push the tenant to a utility level equalling U.-/ Thus sharecroppingwill be utility equivalentto the best alternativeuse of the
tenant'slabor. Hence,
Proposition
2:
The equilibriumin the land-labormarket will be characterized
by utility equivalentcontracts.
It should
be noted that this propositiondoes not depend for its
validityon the presence or absence of any linkage between tenancyand credit
transactions. The landlord'suse of plot size as his sole instrumentvariable
is sufficientto result in a utility equivalentcontractequilibrium,an
outcome obtainedby Cheung [1969] in a differentmodel. Our model is that
of Stiglitz [1974],subsequentlyutilizedby Newbery and Stiglitz [1978].
Assuming the tenants'utility functionto be separablein consumptionand
leisure,they claimed that competitionbetween landlordswill drive the
inequality U* > U
to equality,thereby achievingutility equivalence. We
have shown above that the utility equivalenceoutcome results from profit
maximizationby landlordsand not from competition. That there is an infinitelyelastic supply of potentialtenants at U
does not render the
propositioninsignificant,since the possibilityof an excess applicants
equilibriumat U* > U
can occur if the output share, instead of the plot
size, is the only controlvariableof the landlord. A well-knowncase of
excess applicantsequilibriumarose under the efficiency-wagehypothesis
(e.g., see Leibenstein [1957],Mirrlees [1976]and Stiglitz [1976]),
primarilybecause the landlordis not allowed to use an instrumentcompletely
1/ It can also be argued that if at an initial x , U* is less than U
the potentialtenant will not choose sharecropping. As such, in order
to obtain someone to cultivatehis land, the landlordwill have to increase the plot size, i.e., reduce x . We are ignoringthe fact that
a tenant is "indivisible"while land is divisible.
17
orthogonalto effort to reduce U* to U without affectingeffort. In
our model, the use of the power to vary the plot size, althoughnonorthogonalto effort, guaranteesthe utility equivalentcontractresult
since the tenant'seffort per hectare increaseswith a reduction in his plot
size. Additionalinstrumentssuch as cropshareand interestrate are not
needed for this purpose.
Of the two assumptionsused in derivingour result,namely,
that both consumptionand leisure are normal goods, and that the tenant
is prohibited,as part of his contract,from working as a part-timelaborer
outside the farm, the latter is perhaps more controversial. Its actuality
is primarilyan empiricalissue. It is true that tenantswork
as part-timelaborersin many villages,butthe extent of such work is
often limited. There is also some evidenceto suggest that landlords
believe that a tenant will put greatereffort into cultivation,the smaller
his plot size;
From utility equivalence U[cCx, $). e(x,
solved as a functionof the discountedshare 0.
6)1 =
U, x
can be
It is easily shown that
x'ta) > 0; i.e., in order to maintain the tenant on his iso-utilitycurve,
the landlordmust increasethe tenant'sdiscountedshare if he reduces the
plot size. Thus, when analyzingchanges in $, unless otherwisespecified,
we assume that the landlordchanges x
along the curve x(S) so as to
maintain the tenant at a welfare level of U.
Consider the impact of change in S both on effort per hectare,
z , and total effort e. It can be shown that effort per hectare increases
with an increasein 0.
Total
effort,
however,will increase (decrease)
18
with an increasein a
if the elasticityof substitutionbetween effective
labor and land, a , is bigger (smller) than 1. Formally, it can be shown
that:
de
A
1a)
where
A
<
0
The results derived so far do not utilize the credit aspects of
the model. Turning to the landlord'scredit instruments(v, rT) and crop
share x , we can write his income G
G
where e
=
as
(1 - $O)f(ex)
(10)
1 + vrL + (l-v)rA. It is seen that (a, vt rT) enter G only
through their effect on
8 and 6, since e
it is clear from (10) that G
and x
are functionsof 8
Now
.
is decreasingin 6 for given 8. Hence an
income maximizinglandlordwill, first, choose his optimal 0 ( 6)* to
be the minimum feasible 6 for any given 8 and then choose 8 to maximize
(l-8e*)f(ex).Since e
the given value of $
depends only on v which lies between 0 and 1, if
does not restrictthe choices of 0 and 1 for v, then:
0* =(1 + r )
L
and v* - 1 if r <r
L
(11)
(l+rA)
Recallingthat v
and v* - 0
if rL > rA
is the proportionof borrowingby the tenant from the land-
lord, we can state (11) as the followingproposition.
Proposition
3: The landlord,with no restrictionon his choice of crop shares,
will ensure that the tenant gets credit from the cheaper source. He does this
by linking credit to tenancy if he is the cheaper source (rL c rA) and by
not offeringany credit, if he is not.
19
Remark:
In the case of rL ' rA where linking is optimal,it remains
optimal even if there is an institutionallyimposed floor on the tenant's
crop share.
The reason is that with full linking,any given
(and a fortiori
8
l+rT
the optimal 8) can be achievedwith an infiniteset
consistingof pairs (a, rT), of which, an infinite subsetwill meet the
requiredfloor.
Proposition3 is consistentwith empiricalobservations(Bardhan
and Rudra [19781)
that
landlordsoften offer interest-freeloans to their
tenants. For example,where the landlordis the cheaper credit source and,
hence, there is linking (i.e., rL I rA), the interestrate rT chargedby
the landlordis essentiallyarbitraryand could as well be zero.
In this
case, linking is essentiallyvoluntary. However, this will not be the case,
as we will show later, if the environmentfaced bydhe parties is subject to
certain constraintssuch as governmentregulations.
Returningto the case where there is no floor on a, it can be
derived and shown that:
6*
where
S accordingas a
S
1
(12)
is the imputed share of labor in output.
<rr
In the case
r
rL >rA,0*
(1 + rA) and 8* - a*/(l + rA). Since in the first case rT
=
( + rL) and 8*=a*/(l + rT),whereas when
can be chosen to be rL' 8*e* becomes the crop share a* in either case.
Using (12) we can thus state:
20
Proposition
4:
If there is no restriction on the landlord's choice of
instruments(a, v, rT) , his optimal strategyinvolvesofferinghis tenant
a crop share a* such that a*
Remark:
In the case of rL
<
S , accordingas a
rA' since O*e
1.
a*(l + rL)
(1 + rT)
can offer an a* which is less (greater)than S, even if a
is greater
(less) than unity by choosing (a* ,'rT)with rT sufficientlyless (greater)
than rL
L.
Newbery and Stiglitz [1978] establishedProposition4 without
incorporatingcredit or its linkage to tenancy. The above remark extends
their result to a case where it is optimal for the tenant to borrow from
his landlord
It also implies that it is possible to observe crop shares
lower than the imputed share of labor even for a productionfunctionwith
an elasticityof substitutionlarger than 1.
5. Policy Analysis
5.1 Tenancy Reforms
on the tenant's
Considera reform which imposes a floor, a
share a of the harvest. This is a common feature of many agrarianreform
laws in India. In the case where rL ' rA
(a* , 1 , r*) prior
,
if in an equilibrium
to the promulgationof the reform law a* < a
the landlordwill respond to the reform by raising the crop share to aF
while simultaneouslyraising the interestrate to rT
equilibrium
*
depends only on
(aF 1 ,
B*
Tr1
1 + r)
r**
T
1 + r*
T
, it is unaffected by reform.
the tenant'swelfare is unaffectedanyway.
= +*
so that in the new
.
Since output
Given utility equivalence,
21
Considernow the followingtwo alternatives: (i) an initial
equilibriumin which the landlordis not the cheaper source of credit, i.e.,
rL > rA so that v* -0,
°
A
*
with a* < aF ,
=
rL ! rA and v* - 1
or (ii) initially
~~~~~~1
+ r
a
with a* < oF but as part of a tenancy
reform, the interestrate on the tenant'salternativesource of credit is
brought below rL .
In other words,the impositionof a floor, aF, coincides
with a change in rA which brings rA below rL . This joint reform of
tenancyand credit could be viewed as two consecutivereforms,first
a
credit reform with no tenancy reform, so that the landlordswitchesfrom
a one-asteriskto a two-asteriskequilibrium,and secondly,
reform
imposing
a floor. In this way, it suffices
first tenancy reform where rL > rA
.
a tenancy
to discuss only the
In this case, it can be shown that
the landlordcan partiallynullify the tenancy reform by forcedZy
linking
the credit and tenancycontracts. In Braverman-Srinivasan
[1980]we
demonstratedthat althoughthere is no optimal policy for the landlord
after reform, there exist policiesthat will give him an income as close
as he wishes to his income prior
to reform. By forcing the tenant to
take small loans (v is small) with a high interestrate rT- , the landlord
ensures that on the whole the tenant will both use the cheaper source of
credit, rA
,
and deduct from him yrT , which increasesthe income of the
landlord. (yrT,however,is not an orthogonallump sum levy on the tenant).
The above discussionimplies that, if linking is permitted,the
landlordcan reduce the tenancy and credit
reform
to insignificance.Suppose
1/ This is perhaps a rationalefor empiricalobservationsof tenantsbeing
chargedhigh interestfor rather small loans.
22
now that
the government
a2ong with tenancy
bans linking,
and credit
reforms.
Clearly the landlord'sincome will decline,while the tenant'swelfare continues
to be at the level
he could have achievedwhile working as a wage laborer.
What about the effect on output? Since the landlordno longer has the
instrumentby which he can maintain the pre-reformdiscountedshare, 0*, of
the tenant, the reform will raise
5.
Since we know from that
dz/dS > 0
,
1/
f(z) will go up.- Thus:
we can assert that output
Ppopoeition
S..
A tenancy reform which imposes a floor on the tenant's share
of the crop with or without credit reform (to make credit available to the
tenant at a rate lower than the landlord'sopportunitycost of capital),will
have no effect on output. If it
and tenancy
it will
transactions,
and increase
is coupled
raise
of credit
with a ban on linking
output,
reduce
the tenant's
plot
size
the number of tenants.
Now consider only a ban on linking of credit and tenancy. This
is,of course, meaninglesswhen the landlordis not the cheaper source of
credit, since no linking will be observedanyway.
Supposethe ban is
imposed when there
is linking,i.e., when r < r and v* - 1 .
L- A
immediatelyraises the cost of credit to the tenant to rA .
Clearly,
this
In the
landlord'sincome maximizationproblem, fixing v
at zero
e
from its
linking), fixes e
at
(1 + r ),
A
1 + rL prior to the ban to
(1+ rA).
functionof 9 , at any vaZue of
with the optimalvalue
of
i.e.,
,
raises
Since
,
preventing
(i.e.,
optimal
G is a monotonic
G is lower than before.
G
value
of
decreasing
Clearly,
even
G is lower. This means that landlord'sincome
definitelygoes down. What about output? As long as f(z) as a function of
6
is concave, optimal 5
for any specified e
is a decreasingfunction of
1/ Recall the interpretationof this result. An increasein 0 raises the
the number of efficiencyunits of labor per hectare,i.e., ex supplied
by each tenant, and increasesthe number of tenants througha reduction
in plot size. If the elasticityof substitutionis less than unity, effort
per tenant will decline, so that output per tenant will decline. But the
increase
in the number of tenantsmore than offsetsthis decline.
23
e.
e
Hence, as
is increasedfrom (1 + rL) to (1 + rA), optimal 6
goes down. This means that firstly,the optimal plot size increases
thereby
and secondly,
the number of tenants,
reducing
output
goes down
since f(z) is an increasingfunctionof a
Finally,considera credit reform alone where rL < rA.
With this
cheaper
reform,
source
however,
of credit,
the government
i.e.,
subsidized
rA < rL .
lends to his tenants but afterwards,
Before
credit
the reform
the landlord
withdraws
becomes the
the landlord
from the tenant's
credit market. Yet, by the utility equivalenceresult, the landlordextracts
all
the surplus
created
by the government's
cheaper
credit.
Hence,
the
governmentsubsidizationof tenants'credit results only in the subsidization
of Zandlords.
5.2 Land Reform
Suppose that startingfrom an initial equilibrium [a*, v*, r*
and x($*), each tenant is given the ownershipof the plot he cultivatesand
has to forego the opportunityto borrow from one landlord. Clearly,the
tenant'swelfare improves,for if rL > rA
With reform, a
v*
=
O 'and
=
+ **
becomes unity, rA remains unchangedso that the tenant's
(now a landowningpeasant's)discountedshare 6
increases,while the size
of the plot remains the same. Hence, without changinghis effort e , (and
its disutility)he will gain in consumptionand, hence, total utility. By
optimallyadjustinghis effort to the changed s , he can raise his utility
even further.
Now if
rL I rA * initially
v*
1.
Since the landlordis
indifferentin this case between alternativecombinationsof V(a, rT) which
24
result in his optimal S* , we can view the land reform as if it, first,
changed the interestrate chargedby the landlordto rA with a corresponding change in a
to maintain the same O* , and then raised the
tenant'scrop share to unity. The two moves togetherimply that the
tenant'spost-reformdiscountedshare is higher. From this point, the
argumentis the same as inthe previouscase.
Now, what is the effect of land reform on output? Land reform
increasesthe discountedshare S while keeping the plot size fixed. Thus
output is f[e(O)x] where x
is fixed. Hence, output will increaseif
tenant'seffort increases. Braverman-Srinivasan
[1980] providesthe following condition:
e < °0 according
aB <
This leads
Propositon
that
6:
a tenant
a=
as -c
to. the following
A land reform
21
~~~U
2
u1
>
1.
(13)
proposition:
which confers
ownership
used to cultivatein a sharecropping
to the plot
contract
of land
with a landlord
will increase,not change,or decreaseoutput, accordingas -c(l
~
U
To interpret (13) we can utilize Figure 1 again. Clearly,since
the plot size is fixed an increase (decrease)in effort impliesan increase
(decrease)in effort per hectare. The expressionin (13) is the following:
The R.H.S. term 1 is the elasticityof the MRT with respect to S for given
x and e ,
while the term on the L.H.S. is the elasticityof the MRS with
respect to B , which equals the elasticityof the marginal rate of
substitutionwith respect to consumption. A land reform which increases a
shifts the curves in Figure 1 in oppositedirections:the dominant effect
is obtainedby a comparisonof the two elasticities.
1.
25
Furthermore,considerthe case of a separableutility function,i.e.,
U(c, e) - u(t)
v(e). Then (13) becomes
-
ae > 0
according as
TO-
u
< 1=l
(14)
(4
~~ut >
The negative of the elasticityof marginal utility ( --)
is defined
by Arrow [19711as the measure of relative risk aversion. The intuitive
explanationfor the value of this elasticityto be of relevancein our case,
even though there is no uncertainty,is the following:On the one hand, an
increasein 6
increasestenant's income; hence, the marginal utility of
income declines relativeto the marginal disutilityof effort, and ceteris
pazribus,the new landowver would like to reduce his effort. On the other
hand, his share in the marginal productivityof effort increases,with
increasing a , thus creatingan incentivefor more effort. Whether the
income effect or the.marginalproduttivityeffect is the dominant force
depends solely on the elasticityof the marginal utility.
Where land reform distributesthe land to more owners than the
originalcultivators,it may increasetotal output even if -c u
since ceteris
paribus,
i 21)>
i
output per hectare increaseswith reductionsin
plot size.
Note that the above discussionalso applies to analysesof sharecroppingcontractsby substituting a
for B
.
This holds for the remaining
policy analysisas well.
5.3 Taxationand TechnologicalProgress
Suppose the governmentimposes a proportionaloutput tax at the
rate t on tenants and landlords (i.e., the rural community)in order to
raise food to feed the urban workers. Since, for any a , this tax is
26
equivalentto a reductionin the discountedshare of the tenant from
S to
u
E $(l-t) , the tenant'sdecision function e(x, $) becomes e(x, p).
It is also easily seen that the landlord'schoice set x(a) becomes x(p).
It can be shown (Braverman-Srinivasan
[1980])that du < 0 and
dt
df(z(u))
d
dt
duidt-< 0 , i.e., output declinesdue to the impositionof a
proportionaltax. The implieddecline in the aftertaxshare, p , necessitates
an increasein the tenant'splot size in order to maintain the tenant on his
reservationutility U .
The increasein plot size implies both a reduction
in the number of tenants,x , and a decline in output. We thus obtain the
followingproposition:
Proposition
7: The impositionof a proportionaloutput tax on landlordsand
tenants will cut the aftertax share of the tenant, increasethe plot size per
tenant, and reduce the number of tenants as well as total output.
Modelling a Hicks neutral technicalchange is equivalentto modelling
a proportionaloutput tax, i.e., a Hicks neutral technicalchange is a
shift
in A where the productionfunction is Af(z).
The only difference
is the directionof the impact. Hence, consideringa Hicks neutral technical
change and applying Proposition7, we obtain:
Proposition
8:
A Hicks neutral
technical
discountedshare of the tenant,
decrease
the number of tenantsas well
as total
change will
the plot
size
increase
the aftertax
per tenant
and increase
output.
Now, consider the case of a Cobb-Douglasproductionfunction. Given
the unit elasticityof substitution,the tenant's effort is independentof
v =- (l-t) (see (9)), i.e., the decline in the aftertaxshare is totally
compensatedby the increasein plot size so as to leave the tenant's effort
27
unaltered. Furthermore,it is easily seen using (12) that the optimal 8
is
unaffectedby the tax or technicalchanges. For the Cobb-Douglascase, all
technical changes can be viewed as Hicks neutral changes.
factor-augmenting
technical change and applying
Thus,consideringirrigationas a land-augmenting
Proposition8, we obtain:
Proposition
9: If the productionfunction is of the Cobb-Douglastype,
introducingirrigationwill leave the discountedshare contractunaltered,
decrease the tenant'splot size and increasethe number of tenantsas well
as total output.
5.4 Increase in the Tenant'sUtility Level in anAlternitive Occupation
Suppose,for example, that through an increasein the non-agricultural
wage rate, the utility that the tenant could obtain (i.e., U) in an
alternativeoccupationincreases. Assuming once again a Cobb-Douglasproduction
function so that the tenant's effort is independentof
the landlordcan ieet the higher U
8 , it is clear that
only by raising the plot size, therefore
reducing the number of tenants and output. Equilibrium 8 is unchanged. Hence:
Proposition
20: If the productionfunctionis Cobb-Douglas,any increasein
the utility that
the tenant can obtain in an alternativeoccupationwill raise
te.-equilibriumplot size, reduce the number of tenants and output,while
leaving the discountedcrop share unaltered.
28
5. Conclusions
In -conclusion,
we summarizeour results-andrelate them to the
literature.-VOur main result is that in a world in which (i) productiontakes
place under constantreturns to scale in land and labor in efficiencyunits,
(ii)a landlordcan subdividehis land into as many plots as he chooses, and
(iii)a tenant chooseshis effort, so as to maximize his utility-equilibrium
will be characterizedby utility equivalentcontracts. In other words, even
if a landlordhas no power over crop shares or terms of credit, by choosing
the plot size appropriately,he will force the tenant to a utility'levelequal
to that uhich
he (the tenant) could have obtainedin an alternativeoccupation
as long as there-are'enough
potential tenants. He is able to do this not only
'ecause there-is a perfectlyelastic supply of tenants at this 'reservation'
utility
reduction
level,
but also
because
the tenant's
effort
per hectare
increases
with a
in his pZot size.
This result is similar to that found in Cheungt s model (1969),where
the tenant'seffort per unit of raw labor is invariant. Cheung shows that
landlordswill provide each tenant a plot of land on which the tenant can earn
no more than he could have earned in an alternativeoccupation. Whereas
enforcementof the tenant'slabor input is necessary in a Cheungianworld, it
takes a differentform in our model: it ensures that the tenant does not
split his working time between sharecroppingand an alternativeoccupation.
1/ Sharecroppingcontracts have also been analyzed in relation to the postBellum South. Discussionof pure sharecroppingwas initiatedby J. Reid
[1973],and the interlinkageof credit and tenancyarrangementsthrough
the country store was subsequentlydiscussed by Ransom and Sutch [19783.
We do not, however, elaborate on these and other works on the post-Bellum
South since they are not directlyapplicableto our model.
29
In this
in the interest
world of utility
of the landlord
from the cheapest
is lower than
ensure
tnat
vhich
extracts
gets
a surplus
to non-linking)
the nuber
is optimal,
will
given
linked
for
the plot
Unlike
size
while
the landlord's
tenancy-cum-credit
be
of capital
the landlord
interest
cost
will
by offer-
the. models of Bhaduri
is not an instrument
landlord's
per tenant,
to the tenant;
income (compared
and therefore
the utility
a smaller
Ipso facto,
labor.
cost
have accrued
leaving
cultivates
the landlord
gets his credit
opportunity
and the
between Srinivasan[1979] and Bhaduri,
lack of incentive
the tenant
with tenancy
output
of tenants,
reduce
it will
at the cheapest
credit
thus
contracts,
moneylender,
contract,
raises
per anit of his
effort
that
that would otherwise
by reducing
.mhanged. EacE tenant
less
credit
linking
where optimal,
increases
by the local
tenancy-cum-credit
1977, 1979),
linking,
to ensure
If the landlord's
that charged
the tenant
Lug a linked
(1973,
source,
equivalent
plot
of each tenant
of land devoting
a ban on linking,
income and output.
when it
In the debate
the issue was the alleged
to introduce
contracts.
yield-raising
innovation,
Using the Bhaduri
model,
Srinivasanshowed that as long as borrowingwas not an "tinferior"
good to
the tenant (which it was not in the Bhaduri model), there was no such
disincentive.
it equals
In our model,
the tenant's
imposed,only
if it
borrowingis, by definition,
discounted
is optimal.
income;
The tenant
and linking
non-inferior
is chosen,
since
not
is pushed down to his alternative
utility level, not by the credit instrument,but by plot size variations.
Finally,in our model, utility equivalenceimpliesthat nothing
short of land reform will affect the tenant'swelfare, as long as he is a
tenant. Indeed, other reforms such as settinga floor on the tenant'sshare
of the crop, making credit availableto the tenant at a cost below the
30
opportunity
cost of capital to the landlordor banning credit and tenancy
linkage,either have no effect on the equilibriumat all or have an effect
on the number of tenants,output and the landlord'sincome. Empirically,
our model providesa theoreticalunderpinningfor two almost opposite
phenomenathat are sometimesobserved:low interestconsumptionloans from
landlord
to tenant
(by Bardhan and Rudra [19781) and the opposite,high
interest,low volume loans.
Our model did not include productioncredit.anddid not allow the
tenant any bargainingpower given the infinitelyelastic supply of tenants
at U
.
linked
Bravernan and Guasch [1980] discuss productioncredit where intercredit and tenancy contracts are used as a screeningdevice for
landlords to distinguishmore able tenants. Bell and Zusman [1980],
Mitra
[1980],and Braverman-Stiglitz[1980] discuss interlinkedcredit and tenancy
contracts in the presence of uncertaintyand unequally distributedinformation.
3
31
REFERENCES
Arrow, K.J. [1971],"The Theory of Risk Aversion,"Chapter 3 in Essays
in the Theory of Risk Bearing.
Bardhan,P.K. [1980],InterlockingFactor Markets and AgrarianDevelopment:
A Review of Issues,"Oxford Economic Papers, March.
Bardhan,P.K. and A. Rudra [1980],"Interlinkageof Land, Labour and Credit
Relations: An Analysis of Village Survey Data in East India,"
Economic and Political
Weekly, February.
Bell, C.L.G. and A. Braverman [1978],'
"On the Non-Existenceof 'Marshallian'
SharecroppingContractsUnder ConstantReturns to Scale,"World
Bank, DevelopmentResearchCenter, July.
_______
and-P.
Zusman
[1980],
"On the
Interrelationship
of Credit
and
Tenancy Contracts,"World Bank, DevelopmentResearchCenter,March.
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__________
[1977],"On the Formation of Usurious Interest Rates in Backward
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Braverman,A. and J.L. Guasch [1980],"Draught-Powerin SignallingEquilibria
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Cheung, S.N. [19691,"The Theory of Share Tenancy," Chicago.
Leibenstein,H. [1957],
EconomicBackoardnessand Economic Growth, Wiley.
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32
Mitra, P. [1980],"A Theory of InterlinkedRural Transactions,"World Bank,
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Cambridge,
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Worker Adjustment to Liberalized Trade: Costs and
Assistance Policies
G. Glenday
G. Jenkins
J. Evans
427
On the Political Economy of Protection
H. Glismann
F. Weiss
428
Italian
429
Effects of Non-Tariff Barriers to Trade on Prices,
Employment, and Imports: The Case of the Swedish
Textile and Clothing Industry
C. Hamilton
430
Output and EmploymentChanges in a "Trade Sensitive"
Sector: Adjustment in the U.S. Footwear Industry
J. Mutti
M. Bale
431
The Political Economy of Protection in Belgium
P. Tharakan
432
European Community Protection Against Manufactured
Imports from DevelopingCountries: A Case Study
in the Political Economy of Protection
E. Verrydt
J. Waelbroeck
in Germany
Commercial Policies in the 1970s
E. Grilli