Farm size and arbitrage: Transition to large-scale commercial paradigm

Formal economic theories tell us that if information diffusion is perfect, then arbitrage by market actors will correct the price difference among markets. That means price difference is only an information asymmetry problem in those theoretical treatments.  If information is perfectly spread, then no price difference will exist for similar goods bought and sold in two markets. Nothing is said about the size of economic operation of entities and arbitrage.
We argue that even if information is perfect, arbitrage will not happen to correct the price difference between markets if the size of operation of economic entities has negative relation with price difference between two markets. This short illustration will try to expound this negative relation between the size of economic operation of entities or more formally farms' size and arbitrage. The derivation of such simple negative relation will help us to give some insightful views on the middlemen problem existing in Bangladesh - that means why middlemen problem springs up and what kind of cure we need to remove such problem.
WHY SIZE MATTERS IN ARBITRAGE? The conventional theoretical prediction about arbitrage is based on perfect information diffusion assumption, and it altogether ignores the impact of the size of operation or firms' size and arbitrage. The reason is not that information is costly to acquire and small firms can't bear such costs. The reason is something else and that is resource constraints. For small farmers exploiting the price difference sending goods to different regions is not often realistic for several reasons and they can't carry out such operations.
The factors that limit small farmers' ability to exploit price difference are: (1) They often lack the necessary financial resources for carrying the goods to different areas. (2) Their size of economic operation, which is the foremost one, severely limit their ability of bearing costs incurred in sending goods to different markets. For example, small farmers who produce potatoes in the rural areas can't send potatoes to urban market to exploit higher price in urban market because transportation and carrying costs are not worthy to bear compared to the quantity of potatoes they will sell. (3) Sending goods to different markets often requires taking risk in terms of losing the goods in the road due to accidents or bad incidents. For a small farmer taking such risk is very much impossible and they are unable to exploit the price difference in different markets. (4) Small farmers instead of taking the initiative of sending the goods on their own sometime take joint effort with big farmers and share the transportation and carrying costs. This kind of activity helps them to get a good price from the market in which price is higher.  
A close analysis of these factors, especially the second one, reveals that barraging power of small farmers is related to the size of operation. In other words, comparative bargaining power is negatively related to the size of economic operation - the larger is the size, the greater the strength of comparative bargaining power and vice versa.
THE RELATION BETWEEN SIZE AND PRICE DIFFERENCE: From the above analysis, it is now clear what the relation between size of farms and the price difference between two markets is. The relation is negative; the larger the size of farms the less is the price difference and vice versa. If we simply sate the above problem in the formal language of economics, we see that:
In the above figure, price difference between the urban and rural markets is measured on the vertical axis and the farm's size on the horizontal axis. It shows that the relation between the farm's size and the price difference between the urban and rural markets is negative; the larger is the size, the less is the difference and vice versa.  The graph shows that when the size of farm falls below some hypothetically fixed threshold level designated as SF0, price difference becomes positive, and at the threshold size of farm, the difference between the urban and rural market prices is zero. The arbitrarily fixed size SF0 is fixed and taken under such reasonable assumption that there exists a threshold size that will render zero price difference.
As shown, at the farm's size SF1, the price difference is DP and this price difference will not be corrected by arbitrage by farms since arbitrage will not happen. This theoretical relationship gives us the foundation about the relation between farms' size and price difference. Now we will derive a comparative bargaining framework that will show how large size of farms helps to exploit the price difference between two markets and eventually makes the difference almost zero.
FARM SIZE AND PRICE DIFFERENCE: We have shown that relationship between the size and price difference is negative. Now based on this negative relationship, we will develop a detailed analysis of the behaviour of price difference relating to farms' size. We will continue to develop on the potatoes production example. For this reason, it is assumed that potatoes market is perfectly competitive. Since potatoes producers have two options to sell potatoes either selling to local dealers or carrying potatoes by themselves to urban markets, the decision itself depends on the size of their operation or potato harvest. If size is small and carrying potatoes to higher-price market is not feasible, then they will probably sell potatoes to local dealers and remain satisfied with whatever price local dealers offer them. On the other hand, if the size of production is large, then they will sell to local dealers if and only if these dealers offer them the just price that is nearly equivalent to urban market price after excluding transportation and carrying costs. This behaviour is illustrated in detail with the help of the following graph.
In the above figure, Demand and Supply (D, S) of potatoes are measured on the horizontal axis and price on the vertical axis. Since market is taken to be perfectly competitive, Demand curve D (p) is flat to the horizontal axis and Supply curve S(p) is upward sloping. We assume that if there is no price difference between the two markets, price at which potatoes sold and bought is P. Now, say that there is a price difference existing between urban and rural markets. In rural market price at which potatoes are bought and sold is Pm and in urban market price is P. The price difference is (P-Pm).  The left hand side of the graph shows the supply behaviour of small farms and right hand side shows the supply behaviour of large farms.  At price P, small farms supply potatoes equal to the PT amount. But what happens if price is reduced to Pm in the local market compared to the price P in the urban market? At this price small firms should supply PmU amount of potatoes but they supply PmR amount. But why? The reason lies in to what extent these small farms are able to exploit the price difference taking other alternatives of selling potatoes. If they don't want to sell to local dealers who now bid price equal to Pm and sell at higher price in the urban market buying form small farmers, they have to figure out another way of selling their products. Since their size of potato production places sever constraint on their ability to exploit higher price in the urban market, they are in a sense forced to sell to local dealers who take the advantage of their inability to exploit price difference.
Now, come to the large farms' case. At price P large farmers will supply S* potatoes. But how much will they supply at Price Pm? Will they supply S*? Not at all. Since large farmers face less sever resource constraints than small farmers do, they are able to exploit the price difference and to overcome the domination of local dealers. But how?
In the right-hand graph, we see that at price Pm large famers limit the supply to S1 which is less than the normal supply or selling potatoes to local dealers. Now until the price hits the P level, they will keep their selling of potatoes to local dealers at S1. No selling to local dealers means that they will carry their potatoes to urban markets to exploit the price difference. In fact, large farmers will reduce the selling of potatoes even below the S1level to force them offer price above P. when this strategy is worked out, local dealers will realise they don't have any alternative except offering the just price P and farmers will also realise that local dealers are not capable anyway to offer a price above P. So, they will increase the supply and reduce the price to the level P. This creates a downward sloping fraction for the supply curve of potatoes. The heavy black line portion of supply curve WKN shows a break in the continuously uprising supply curve. This broken portion depicts the comparative bargaining strength of the large farmers and how they can manipulate their supply curve faced with adverse pricing strategies of local dealers.
Now, the question is: what happens to the overall market price? Does this behaviour of large farmers affect the price difference in such a significant way that the difference ultimately becomes zero? Yes, it does. This is the stunning conclusion of the above analysis. If large farms take the initiative to exploit the price difference, the small farms will be benefited. But how? If large farms force local dealers to offer a price that is equal to P bending their supply curve to the left side, then in the rural market one price will prevail and that is P. In this case, small farmers will sell PmU amount at Pm price not PmR amount and will supply PmR at Price P not at Pm.  Once large farmers can carry out such strategies, everyone will get the just price irrespective of the size. That means whether small farmers will get the just price depends on the existence of large farmers. In other words, we can say more precisely:
If we show this in the graphical form, we get the following picture.
In the above figure, total production of potatoes by large farms is measured on the horizontal axis and price of potatoes of small farms on the vertical axis. It shows that at the zero amount of production by large farms small farmers get a minimum price P bar which is much less than P, the just price at which no price difference exists between the two markets. The relation between price of potatoes of small farms and the total production of potatoes by large farms is positive; as the amount of production by large farms increase, price of potatoes of small farms increase but up to the P. At the P the total amount of production potatoes by large farms is YL0. This is the amount of production that must be carried out by large farmers so that small farms get the just price P. Otherwise, there will be price difference. For example at YL1 level of production by large farms, small farms will get P1 price and the price difference is (P-P1).
THE THEORY AND REALITY: Now, we face the critical question: how does such theoretical discussion account for the real world problem? The above theoretical discussion contains one hidden message and that is why and when middlemen problem springs up in an economy. One answer, the foremost one, is when the proportion of total production accounted by larger farms gradually reduces, middlemen domination comes into force. In this case, arbitrage fails to happen and price difference between markets will be persistent. The second answer is that as people gradually migrate from rural areas to urban areas, middlemen problem arises because demand becomes concentrated in certain geographical areas and this demand concentration coupled with gradual reduction of the proportion of the total production by large farms must give rise to middlemen problem in a country. We argue that this is the exact kind of situation that Bangladesh is now facing and these are prime reasons of huge price difference between the urban and the rural markets.
TESTABLE IMPLICATIONS: The theory proposed above can be subject to test in our country to see whether price difference is related to the above two factors : (1) reduction of the number of large farms or reduction of the proportion of total production accounted by large farms; (2) gradual migration of people from rural to urban areas. Therefore, an empirical test can be set up to see whether the price difference is significantly related to these factors. The postulated model and behaviour of the estimated parameters are as follows:
Now, at least, we have a framework to test the middlemen problem in an empirical setup. No longer need we blame dishonesty of middlemen and their foxy behaviour in market. It seems to be total nonsense in economic studies to blame dishonesty of people as the prime factor of causing some problems, though in some cases it can be true. However, in most of the cases it must turn out to be nonsense and irrelevant to problems and their solution, and the middlemen problem is one of them.
One thing must be noted in testing such model. If the gradual migration to urban areas from rural areas is accompanied by the gradual transition from small farms to large farms, both will offset one another completely, and we rationally expect the zero price difference.
SUMMARY VIEW: The main implications of the analysis are the following. First, the traditional farming base in our country evolved from the  Leader-Follower paradigm in which large farmers played the role of leader and small farmers followed their lead and reaped the benefit from their leadership such as exploiting price differences and forcing local dealers pay the just price. Second, Leader-Follower paradigm easily breaks down in a situation in which people gradually move from the rural areas to urban areas. Third, to overcome the middlemen problem, our country must make transition from the Leader-Follower paradigm to the large-scale commercial paradigm. Finally, middlemen problem doesn't have anything to do with dishonesty of people; rather it is a problem that emerges from the incompatible and inconsistent transition happening in our agricultural sector.
Md. Jamal Hossain writes from the University of Denver, USA.
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