By Sambodhi Sarkar

Edited by Nidhi Singh, Junior Editor, The Indian Economist

ABSTRACT:

This project first explains the concept of sharecropping and surveys the literature that explains the existence of sharecropping under different conditions. Next, it reviews a paper (Ray 1999) that explains the existence of sharecropping in an oligopsonistic rural labor market. Finally, it delves into the validity of the assumptions in the paper and checks if the model is affected by changes in the simplifying assumptions, conducts a thought experiment using the set-up of a Bertrand game in the rural labor market and finally analyzes the possible contract choices if the rural labor market were monopsonistic in nature.

SECTION 1: Introduction and Literature Review

Since Adam Smith’s days, sharecropping has been argued to be an essentially inferior system to fixed- rent tenancy. This argument is famously known as the Marshallian inefficiency, after the English economist Alfred Marshall who showed how fixed-rent tenancy gives the right incentive to achieve higher productivity.

However, contrary to economic reasoning, we often witness sharecropping agreements in the real world. Cheung (1969) highlights this and shows how given suitable variation in plot size and division of output, landowners can achieve efficiency with sharecropping. Stiglitz (1974) continues from where Cheung (1969) had left off by focusing on risk-sharing and the incentive effects of sharecropping. He studies what happens when the labor supply is inelastic and when the labor supply can vary, and obtains a series of results, two of which are striking: (i) under certain circumstances, i.e., when both parties can mix contracts, sharecropping becomes redundant; and (ii) under other, particular circumstances, effort will not be underprovided, i.e., there is no Marshallian inefficiency, and sharecropping contracts are efficient.

Newbery’s (1977) then demonstrates that sharecropping is irrelevant when agricultural risk is the only risk that exists, but that when another type of risk enters the picture (a plausible assumption as regards agriculture in developing countries), sharecropping becomes the dominant tenurial arrangement.

Since then, there has been other works trying to explain the existence of sharecropping under different conditions. Singh (1989) neatly compiles the major arguments presented to explain the existence of sharecropping under different situations and imperfections. He divides the (then) existing literature on this topic into several sections, including ones dealing with sharecropping and risk aversion of the tenant (citing Stiglitz 1974, Newbury 1977 etc.), sharecropping and limited liability (citing examples from Shetty 1988, Sengupta 1997, Basu 1992 etc.), sharecropping and cost sharing of inputs (citing Jaynes 1982, 1984 and Bardhan and Singh 1982, 1987 etc.), sharecropping and screening (citing Hallagan 1978, Allen 1982, Allen 1985a etc.). Apart from this, there are some other explanations too which are present in the economic literature ranging from sharecropping to solve the double incentive problem (eg. Eswaran and Kotwal 1985a etc.) to sharecropping to stop land exploitation arising from fixed rent tenancy (eg. Tridip Ray 2005) and sharecropping arising out of imperfections in the rural product market and seasonal variation in prices (Sen, Debapriya 2011).

For this project, I first review a paper (T. Ray, Journal of Development Economics 58 (1999) Pg. 45–60) that, in my opinion, provides a very different explanation for the existence of sharecropping. The paper shows that if the labor market is not perfect (he delves upon the case when the labor market has an oligopsonistic structure), then share tenancy can be explained as a form of strategic delegation. What makes this approach distinct is that, contrary to the conventional arguments, this paper explains share tenancy even in environments in which there is no uncertainty or asymmetric information. The review constitutes Section 2 of this project. In Section 3, I present some stray thoughts to the various assumptions made in the paper, and try to analyze the scenario where the labor market is monopsonistic in nature. Finally, I conclude in Section 4.

SECTION 2: Existence of Sharecropping in an Oligopsonistic Rural Labor Market

Basu (1993) has conjectured that “if it is accepted that landowners operate in strategic environments, it can no longer be considered irrational for a landowner to appoint an agent and give him an objective function different from that of the landowner. Thus, there seems to be some possibility here of building up a new explanation of rent-sharing arrangements.” But apart from this conjecture (and obviously this paper that I am reviewing), there hasn’t been much in the entire share tenancy literature about imperfections in the labor market.

In this paper, Ray considers a set-up in which a few landlords in a village confront the choice of cultivating their farms by adopting different tenurial arrangements, ranging from owner operation, through the fixed-rental system to share tenancy.

2.1. The Assumptions in the Paper

The following assumptions are made in the paper by Ray- 1. The landlords are the only sources of employment in the village, and they compete in the wages they pay to their workers. However, the landlords are price-takers in the food grain market (where food grain is the only crop produced in all the fields, basically implying that the output is homogenous). 2. Labor is the only input in the production process, and the labor supply curve is upward sloping, instead of the standard assumption of horizontal labor supply curve used in the development literature. 3. He makes a further assumption that unlike the text-book Bertrand model, a landlord cannot attract all the workers by paying a wage just higher than the rival landlord.

Given these assumptions, he formulates the game between the landlord and the tenants.

2.2 Formulating the Game

Ray first formulates the game in the set-up where only two landlords are present (duopsony) and then formalizes the game in a general oligopsony case (see Appendix A of the same paper).

1. Players: The two landlords and the villagers.

2. Actions: The two landlords compete in the wages they pay to their workers. A landlord can organize his farm operation in a number of ways. When the landlord cultivates the land himself he takes the wage decisions. But if he opts for a tenurial arrangement then the wage decisions are delegated to the tenant. That is, the tenant has to choose the wage rate, employ the workers, sell the product and pay the rent.

3. Preferences: The landlord wants to get maximum profits, and the villagers too seek to maximize their returns from farming on the landlords’ fields.

Let the production function for food grain for each landlord be Y = F(L) – (1) where L is the amount of labor applied, and as usual, he takes F to be differentiable with F(0)=0, F’(L)>0 and F”(L)<0.

He takes the Labor supply curve faced by landlord i to be given by

t1– (2)

 

For i = 1,2; where wi is the wage rate paid by landlord i. It is assumed that Li is differentiable in (w1, w2)and

t2

 

If the price of food grain is taken to be unity, and the wages are measured in terms of the food grain,

then the profit function for landlord i can be written as

t3– (3)

 

4. Stages of the game: In period 1, the landlords decide their mode of farm operation from the two alternatives—owner operation and tenancy. If the land is leased out, then in period 2 the landlord specifies the tenurial contract and in period 3 the tenant chooses the wage rate and produces the crop. If the land is not leased out, then the landlord decides on the wage rate in period 3 (and no move is made in period 2).

2.3. Analyzing the Game

The analysis of the game is carried out by Ray in the following manner: He first calculates the profit for the landlords in cases where both of them are owner operators, followed by the case where one has chosen to lease out to a tenant and the other continues to be an owner operator, and then the case where both of them have leased their land out to tenants. After this, he compares the profits in all these cases to find out the equilibrium outcome.

2.3.1 Both of them are owner operators

The landlord 1 chooses w1 and landlord 2 chooses w2 and their reaction functions are derived from (3).

t4– (4)

 

The reaction functions are found to be upward sloping indicating strategic complementarity, that is, one landlord responds to a wage hike of the rival landlord by increasing his own wage offer. The Nash equilibrium is found at the intersection of the two best response functions (see figure 1), and the profits are thus, where πiN stands for the profit of landlord i.

t5– (5)

General description of a tenancy

A tenancy contract specified by landlord i is defined by the pair (αi, Ki), where α is the proportion of output the tenant keeps and Ki is the lump-sum he has to pay to landlord i. It is called a share tenancy contract if 0<αi<1, whereas it is called a fixed-rental contract is the one where αi=1 and Ki >0.

Tenant i’s earning:

t6– (6)

Landlord i’s earning:

t7
where Xi is the amount the landlord i can earn elsewhere (his next best opportunity) when he can leave the responsibility of farming to a tenant.

He shows that if Yi is assumed to be the ith tenant’s reservation income, the profit maximizing landowner will chose Ki in such as a way that he gives only the reservation income. Then, I can show that

t8

 

 

2.3.2. Tenancy in farm 1 and owner operation in farm 2

Here, Ray takes a two stage game where landlord 1 chooses α1 in period 1 and in period 2 tenant 1 and landlord 2 simultaneously choose, w1 and w2, respectively. In period 2, the landlord 2’s response function is the same as derived in (4) and the tenants’ best response function is (tenant chooses w to maximize returns given α):

t10

– (7)

The intersection of the response functions gives the Nash equilibrium (in period 2) which can be written as w1(α1) and w2(α1) and then the landlord 1 choose a1 to maximize his profits. He proves that the solution, αE, is such that 0<αE<1, that is, we have a share contract in farm 1 in the subgame perfect equilibrium.

He then argues that owing to strategic complementarity in this case, the profit increases if one of the landlords can credibly commit to reduce wages, and such a commitment is only possible by delegating the farm operations to a share tenant. A sharecropper has less output incentive and hence demands less labor and pays less wage. Since both the landlord and the fixed-rent tenant have full output incentive, they cannot reduce wage credibly.

2.3.3. Tenancy in both farms

Here, both the landlords choose their share in stage one, followed by both tenants choosing their wages. Again, the reaction functions of the tenants can be set by equating the partial derivatives of their returns w.r.t. their wage to 0, and following similar analysis as 2.3.2., he shows that share-cropping emerges as the subgame perfect equilibrium in this case too. Let S depict the subgame perfect

equilibrium outcome. Let denote the profit of landlord i in the subgame perfect equilibrium when both farms are cultivated by tenants. Then, we have:

t12

 

t11

 

 

 

 

2.3.4. Choosing owner operation vs. tenancy

Ray finally delves into this choice by the landowner in stage 1 of the game (after solving for the later stages, and applying the concept of backward induction) and constructs a pay-off matrix showing the payoffs under the different forms, where O denotes owner operation and T stands for tenancy contract.

t13

 

 

 

From parts 2.3.2. and 2.3.3., he then claims that “in the strategic environment under consideration, if a landlord leases out his land he always opts for a share contract and not for a fixed-rental contract”.

In the case where Zi ≤ 0 (that is, if we assume that a landlord can himself earn a lot elsewhere if he canleave the responsibility of farming to someone else), using the fact that t15, Ray concludes that if the net cost of leasing the land to a tenant is non-positive for the landlords, then both landlords opting for share tenancy is the only subgame perfect equilibrium of the full game.

Next, in the case that Zi > 0 (that is, there is significant monitoring cost) , he concludes that if the net cost of having a tenant is strictly positive then, under different parametric configurations— both landlords working as owner operators, both of them opting for share tenancy and one of them having a share tenant while the other choosing owner operation— are all possible subgame perfect equilibrium outcomes of the full game. Share tenancy is more likely to appear the lower is the net cost of having a tenant.

Ray then extends this and shows that the above three results are valid for the n-landlords case too.

SECTION 3: Further analysis

Undoubtedly, Ray has done a neat analysis to prove that sharecropping can actually be the outcome in case of an oligopsonistic rural market. However, some questions arose in my mind-
a) Do the simplifying assumptions made by Ray in this paper actually hold in real life? If no, then how do they affect the result of this paper?

b) What if the game was actually like a Bertrand game?
c) What if the rural labor market is monopsonistic in nature (that is, controlled by a single large landowner only)? Does sharecropping still emerge as the outcome of the game?

The above questions are analyzed here.

3.1. The Validity of the Assumptions made in the paper

3.1.1. Assumption 1 states that the landlords are the only sources of employment in the village, and they compete in the wages they pay to their workers.

This, in general, is not true. Consider the case of rural India. It has to be accepted that the agrarian sector has been the pre-dominant employment source for the people in rural India. But things have been changing. For example, the Mahatma Gandhi National Rural Employment Guarantee Act (MNREGA) has created viable alternate employment opportunities in rural India (for further details, see http://nrega.nic.in/netnrega/writereaddata/Circulars/MGNREGA_SAMEEKSHA.pdf). Similarly, there has been a lot of Non-Governmental Organisations (NGOs), BPOs etc. trying to improve the productivity of villagers in India, thus helping them find alternative employment. Self-help groups, informal sector jobs add to the spectrum of employment opportunities. Clearly, the landlords aren’t the only sources of employment in the village. So the question that arises is whether this is going to affect the outcome of the model presented by Ray.

In my opinion, it can lead to a mixed response. The reasoning is as follows: The alternate employment opportunities can be thought of increasing the opportunity cost of providing agricultural labor, thus in essence, raising the tenants’ reservation income (or wage). This, in turn, will affect the Zi (as Yi increases) in the model and the final outcome will be dependent on the two cases that have been discussed in section 2.3.4.

3.1.2. The next assumption states that labor is the only input in the production process, and the labor supply curve is upward sloping, instead of the standard assumption of horizontal labor supply curve used in the development literature.
Obviously, the first part of this assumption is intrinsic to this model, and changing that will change the entire analysis drastically.

The next part of the assumption seems to have the support of careful empirical studies. For instance, Bardhan 1979 and Rosenzweig 1984 have shown that the wage response of labor supply in a poor agrarian economy is significantly positive. Thus it seems reasonable to assume that a landlord can attract more workers to work on his farm by paying a higher wage.

3.1.3. Next he assumes that unlike the text-book Bertrand model, a landlord cannot attract all the workers by paying a wage just higher than the rival landlord.
It seems to be a valid assumption because in real life, the landlords are slightly differentiated by one factor or the other. Sources of differentiation can include distance, as transportation or travel costs or reluctance to go to a long distance for work may allow wage differentials to sustain. Workers generally prefer to work on a farm closer to their residences and need to be compensated with higher wages to move to a distant farm to work. Again, Bardhan 1979, p. 81–82 observes that about 22% of the casual agricultural laborers surveyed were willing to accept wage employment inside but not outside the village. And for those who reported preparedness to accept jobs outside the village, the desired margin of wage on a job outside the village over the current one was 87%.

3.2. Bertrand Game: A Thought experiment

Let’s imagine that the game is actually a Bertrand game, by which I mean that the landlords choose the wage rates, and all the villagers now work in the fields of the landlord who pays them higher wages.
This case might be true if the village is sufficiently small, the landlords aren’t sufficiently differentiated to maintain the wage differentials and if the landlord paying the higher wage can accommodate all the workers in his fields (there isn’t any capacity constraint).

Let’s start at the point where both the landlords are offering wage rates equal to the reservation incomes of the tenants, and are earning positive economic surplus. Both the landlords can profitably deviate from this point, because by just offering them a slightly higher wage rate, the landlord can

successfully attract all the workers and produce at maximum capacity, while the other landlord has no labor input, and thus, no output and zero profits. This will continue till the point where both the landlords will earn only their normal profits. Let’s call the set of wages (w’, w’) at this point. It is obvious that (w’, w’) is the only Nash equilibrium in the case of owner operation (if wages are continuous).

Now let’s think of tenancy. Borrowing the two-stage analysis from section 2.3, in stage 2, the tenants (who are in Bertrand competition for wages) will choose (w”, w”) such that they earn only the normal profits and (w”, w”). The landlords will then set (αi, Ki) in such a way that they too receive normal profits only in the case of subgame perfect equilibrium.

It is easily understandable that w”< w’, and therefore tenants will want to work under owner operation in this case and get higher wage rates. The landlords, in this case, will receive only the normal profits (provided they are similar).

I think it is imperative to once more illustrate why such a competition may not be feasible in real life. The primary reasons according to me are: a) In real life, landlords will have capacity constraints, and b) There will be some sort of differentiation between the landlords which will prevent perfect Bertrand competition scenario from arising in real life.

3.3 When the rural labor market is a monopsony

In the paper that I have reviewed, Ray has analyzed the scenario where the rural labor market is dominated by a few landlords, that is, it is an oligopsony. Economic literature is filled with models which assume perfect competition in the labor market. But what if the rural market is actually dominated by one large landlord, and is thus a monopsony?

3.3.1. Owner operation

There is just one wage rate which is offered now in the market. Let’s call it w. Eq. (3) from the paper then becomes: π = F(L(w)) – wL(w). The landlord has no incentive to provide a wage more than the reservation wage of the worker (let’s call that Yi). Thus, w = Yi. Substituting this into the previous equation, we get: π = F(L(Yi)) – Yi L(Yi). – (8)

3.3.2. Tenancy

Given that the landlord decides upon (α, K) for the tenant, the payoff he receives is (1-α).F(L(w)) + K + X. [X is the opportunity cost from the landlord]. Since, he wants to maximize his payoffs, he has to differentiate the payoffs w.r.t α and K and set them equal to 0, and the first equation gives us α = 1 in the case of monopsony. We can also bring the arguments listed in Debraj Ray etc. which show that fixed rent tenancy yields a better outcome for the landlord and the tenant in a certain world with no imperfections. This implies that if tenancy is chosen, in the case of a monopsony, it is better for the landlord to choose fixed rent tenancy over sharecropping, in case there is no uncertainty or other imperfections.

The decision of owner operation vs. fixed rent tenancy will then be based upon the cost of having the tenant.

SECTION 4: Conclusion

I am of the view that there can be no over-arching explanation of the existence of sharecropping. I feel this because of the immense diversity in the circumstances under which sharecropping has been

witnessed in this world. Sharecropping has existed in various forms and in various times. It has disappeared, and then reappeared. Sometimes the share of outputs is half-half, sometimes it’s not. Sometimes sharecroppers are rich, sometimes they are poor. Sometimes sharecroppers produce risky crops, sometimes they don’t. The list goes on and on.

In this project, I have tried to look at a few of the prominent papers in the economic literature on the theories explaining the existence of sharecropping. The journey has taken me from giants like Stiglitz, Newbury, Marshall to Basu (Kaushik), Ray (Debraj) and Allen (Franklin). However, I chose to review a paper (Ray 1999) which has explained the existence of sharecropping in an oligopsonistic set-up in the rural market, and has successfully shown that sharecropping and owner cultivation (but not fixed rent tenancy) can arise in the rural market depending upon the different parameters. Next, I tried to investigate into the validity of the assumptions made in the paper, and have found that relaxation of the first simplifying assumption can change the outcome of the game, and that the other two assumptions have fairly strong empirical backing.

Following that, I carried out a thought experiment where the model is analyzed as it were a Bertrand game and in this case, owner operation seems to be the outcome of the game. Finally, I analyzed the situation where the rural labor market has a monopsonistic structure and have found that assuming no uncertainty and no other imperfections, fixed rent tenancy is always preferred over sharecropping.

 

References

Allen, Franklin. “On the fixed nature of sharecropping contracts.” The Economic Journal (1985): 30-48.

Bardhan, Pranab K., and T. N. Srinivasan. “Cropsharing tenancy in agriculture: a theoretical and empirical analysis.” American Economic Review 61.1 (1971): 48-64.

Basu, Kaushik. “Limited liability and the existence of share tenancy.” Journal of Development Economics 38.1 (1992): 203-220.

Chaudhuri, Ananish, and Pushkar Maitra. “Tenant characteristics and the choice of tenurial contracts in rural India.” Journal of International Development 13.2 (2001): 169-181.

Osborne, Martin J. An introduction to game theory. Vol. 3. No. 3. New York: Oxford University Press, 2004.

Ray, Debraj. Development economics. Princeton University Press, 1998.
Ray, Tridip. “Share tenancy as strategic delegation.”Journal of Development Economics 58 (1999): 45-60.

Sen, Debapriya. “A theory of sharecropping: the role of price behavior and imperfect competition.” Journal of Economic Behavior & Organization 80.1 (2011): 181-199.

Singh, Nirvikar. “2 Theories of Sharecropping.” (1987).

Sambodhi Sarkar is a graduate in Economics from St. Stephen’s College and recently won the Amartya Sen-Mehboob ul Haq Award for the best paper on The Political Economy of Public Finance at the South Asian Economics Students . He is currently working at Deutche Bank India.

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