The Role of Cooperatives Revisited. The Possible Eﬀect of a Cooperative to Strengthen the Market Power of Farmers in West Africa.

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The Role of Cooperatives Revisited.

The Possible Effect of a Cooperative to Strengthen the

Market Power of Farmers in West Africa.

J.T. Ton

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Master thesis Econometrics Supervisors:

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The Role of Cooperatives Revisited.

The Possible Effect of a Cooperative to Strengthen the Market Power

of Farmers in West Africa.

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Foreword

A little over a year and a half ago Dennis Ostendorf and I met professor Caspar Schweigman when we started a course Operations Research in Developing Countries. This course consisted of two parts, the first dealt with a literature study and the second part was a case study. We read a lot of papers, books and theses about poor agricultural farmers in Africa and became interested in their situation with all of its difficulties. For the second part of the course we embarked on a case study where we modelled the decision of the farmer, (how much land and labor to allocate to which of his crops,) based on what we had learned in the literature. When I had to start writing my master thesis and was looking for a topic, I remembered this case study and asked professor Caspar Schweigman if he had a topic that he would like to have researched, luckily for me he had an interesting topic.

I would like to thank professor Caspar Schweigman for the interesting topic, for his comments and insights, lending me his books and also for having me as a guest in his house. I would like to say that I really enjoyed our talks. I also like to thank all others who showed their interest in my thesis, either reading parts of my thesis or by simply having a nice discussion about the topic. It helped me get a better understanding of the situation I have been studying.

Before you start reading I would like to give some instructions as to how to read this thesis. The interested reader is of course invited to read all parts. To reader without any mathematical background I recommend the summary, chapter 1 and 2 which introduce the topic of this thesis and chapter 8 the conclusion, since none of these chapters contain any mathematics.

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Summary

Een Nederlandstalige versie van deze samenvatting is te vinden in bijlage A.

Many West African farmers grow cereals, part of these cereals are used for own consumption and the surplus is sold on the local market. Cereals are consumed throughout the year, however they are harvested only once a year. After the harvest there is ample supply of cereals, which causes the market price of cereal to be low. Some farmers who need money borrow it from a trader under the condition that the loan needs to be repaid immediately after the harvest; this is called a forced sales contract. Farmers could cooperate by establishing a cooperative cereal bank. This cereal bank could help farmers with selling their harvest. The cereal bank can benefit from advantages of bulk and has access to the regional market, on which cereals are traded at a different price. Hence the cereal bank could offer the farmers a better price.

The goal of this thesis is to provide insight into this situation and to find out how establish-ing a cereal bank helps the farmers in sellestablish-ing their harvest. This is done by developestablish-ing several models. First of all we focus on the situation of the farmer. The micro model without cereal bank ”tells” when farmers should sell which part of their harvest when there is no cereal bank. The two micro models with a cereal bank ”tell” when farmers should sell their harvest and whether to sell this to the cereal bank or on the local market. One model does this for the case where the participants in the cereal bank coordinate their strategies and the other model assumes that each farmer optimises his own profit individually. The last model, the macro model with a cereal bank, is about the situation in which cereal banks are established throughout the country.

The pricing strategy of the cereal bank is to charge the same price as on the regional market minus a small percentage to cover transaction costs. Since each farmer is a member of the cereal bank, they should share in profits or losses of the cereal bank.

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The macro model with cereal bank is about the influence of establishing cereal banks on a large scale. Farmers and cereal banks take the price on the market as given, based on this price they decide how much of their cereals to sell each period. However, all this supply together influences the price on the market. When the strategies from the micro models with cereal bank are gener-alised, then less cereals will be supplied on the market and at the end of the year the demand for cereals will be somewhat lower. Therefore it is to be expected that at the beginning of the year the cereal price is going to be a little higher and at the end of the year a little lower, hence the price increase will be smaller than before. The micro models with cereal bank are solved again with these new market prices. The results show the following: if the price increase compensates for the costs involved in storing cereals, farmers should stick to the same strategy as before. If the price increase is less, then it would be better for the farmers to sell their surplus of cereals at the beginning of the year to the cereal bank. For farmers with shortages, it is still best to buy cereals at the end of the year. When the profit in the macro model is compared to the profit in the situation without a cereal bank, it turns out that the positive effect of establishing cereal banks on a large scale does not cancel out the effect of establishing one cereal bank.

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Introduction

This chapter contains the introduction of this thesis. First of all we start with the goal of this thesis. The next section describes part of the history of food security, in order to show where the interest in food security came from. Studies that dealt with economic situations in West African countries have been conducted before, we briefly mention some studies that touch upon the topic of this thesis. The chapter ends with the outline of the thesis.

1.1 The Goal of this Thesis

This master thesis takes a close look at a simplified situation of farmers in West Africa who sell their agricultural surplus on the market. What happens when farmers who live in the same village, form a cooperative food bank that will sell their agricultural outputs for them? The goal of this thesis is to provide insight into this situation and to investigate whether establishing a food bank could help farmers with the sales of their harvest, for example by giving them a better price for their harvest. The data that is used in this thesis comes from studies on West African countries in order to make this study as realistic as possible.

1.2 A Brief History of Food Security

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1.3. OTHER STUDIES CHAPTER 1. INTRODUCTION

Over the last decades different initiatives have been taken to master the food situation in several West African countries. One of these initiatives is to establish cereal banks. A great number of cooperative cereal banks have been established by village farmers in Burkina Faso (Schweigman, Jongkamp, and Yonli, 1995). Some cooperatives do very well, while others fail due to financial problems, failing harvest, mismanagement etc. (Schweigman, 2008b). A possible goal of the cereal bank is to help farmers by keeping a reserve stock for all farmers in the village. The cereal bank buys cereals from the farmers, stores them and sells them to farmers who did not grow enough cereals for their own consumption. Another possible goal is to strengthen the position of the farm-ers on the market, by doing all of the selling and buying instead of the farmfarm-ers. The cereal bank trades large quantities of cereals, this could give them advantages, such as a better negotiating power, this may result in better prices for the farmers. Chapter 2.2 discusses goals of cereal banks in more details.

1.3 Other Studies

Many studies have focused on agricultural farmers in several countries in West Africa. The strate-gies and interactions between farmers, cooperatives, the private market and the government have been studied. This thesis is based on the following studies, which have been conducted in Gronin-gen and mainly focus on the mathematical modelling aspects of the food situation in West Africa. Each of these studies focusses on a different aspect of the situation of farmers in West Africa, since each of them is linked to this research, we like to mention them here.

Yonli (1988) studied markets, stock, prices and transport of cereals on the Central Plateau in Burkina Faso. Schweigman, Thiombiano, and Yonli (1988) constructed a model which analysed the influence of the cereal bank on the selling strategy of farmers and on food security. Schweigman (1991) and Schweigman et al. (1995) made continuous models, that modelled the market strategy of a farmer selling to and purchasing from one market agent. Yonli (1997) studied cereal banks, and focused mainly on the role that cereal banks play concerning food security. Bassol´e (2000) compared the functioning of the cereal market before and after liberalisation of the market. Ruijs (2002) gave an overview of the effects of market liberalization and institutional changes in cereal trade and cereal prices in developing countries.

1.4 The Outline of the Thesis

Chapter 2 gives an overview of relevant background information. It starts with the description of the situation of the farmer in section 2.1. In section 2.2 the situation of the cooperative cereal bank is described. Then the cereal market at a national level is discussed in section 2.3, including a section about market imperfections. In section 2.4 several assumptions that are stated implic-itly in the first three sections are summarised. The chapter ends with formulating the research questions in section 2.5.

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CHAPTER 1. INTRODUCTION 1.4. THE OUTLINE OF THE THESIS the end of each chapter the selling strategy of each farmer and cereal bank is summarized in a conclusion. Chapter 7 discusses the influence of the introduction of cereal banks at a national level. Both the effect on supply and the market price of cereals is explained. The models of chapters 5 and 6 are solved again with new market prices. Then the effect on the market imperfections is discussed. This chapter end with a conclusion.

The conclusions are summarised and research questions are answered in chapter 8. Then in chapter 9 suggestions for further research are made.

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Chapter 2

Problem Description

This chapter gives an overview of relevant background information, starting with the situation of the farmer. The following section focuses on the cooperative cereal bank and its goals. Then we turn our attention to the cereal market at a national level and the imperfections on the market. Chapter 7.2 returns to this topic, in order to discuss how the introduction of cereal banks has an influence on the market imperfections. In the next section several assumptions, which have been stated implicitly in the first sections, are summarised. At the end of this chapter the research questions are formulated.

2.1 The Situation of the Farmer

Consider a village of farmers, where each farmer has a different size of land and a different amount of labour available to produce food, in this case cereals. Using their resources land and labour (and perhaps also some fertilizer) the farmers can grow cereals, which are harvested at the end of the growing season. It is assumed that each farmer is a profit maximizer. The agricultural output of the farmers is taken to be known at the time of Part of the cereals are necessary for consumption by the farmers family, the other part can be sold on the market. It is also possible to sell all harvest and buy cereal later in the year (i.e. the agricultural year, see section 2.1.2) for consumption. In this thesis we only consider farmers that produce food crops. How the farmers should allocate land, labour and fertilizer in order to maximize their profit under uncertain rainfall is studied by Ostendorf and Ton (2007). This study showed that the farmer sows cereals without fertilizer on an area of land which is large enough, such that he can feed his family and pay his debts in all rainfall scenarios. On the rest of his land, the farmer sows the cashcrop cotton, which carries some risk, but has the highest expected yield.

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2.1. THE SITUATION OF THE FARMER CHAPTER 2. PROBLEM DESCRIPTION since it can supply larger quantities to the market and more importantly it can benefit from the prices on the regional market.

Figure 2.1 shows a simplified version of the marketing channel both for the situation without (top) and with a cereal bank (bottom). The farmers are on the left, denoted by the letter F , they sell cereals on the local market (or to the cereal bank). Note that in the case with a cereal bank, farmers can choose between trading with the cereal bank, or on the local market. On the right we see consuming farmers, denoted by the letter C, they can buy cereals on the local market (or from the cereal bank), these can be the same farmers as on the left of the figure. Normal consumers are not included. The cereal bank acts as an intermediary by buying and selling cereals from the farmers and the regional market. Note that each farmer harvests a different amount of cereals, has a different forced sales contract.

Figure 2.1: An illustration of a village with 5 farmers, who trade directly on the local market (above) or through a cereal bank (below).

2.1.1 Consumption

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CHAPTER 2. PROBLEM DESCRIPTION 2.1. THE SITUATION OF THE FARMER

2.1.2 Agricultural Year

For the farmer the agricultural year starts in May with seeding the land, see figure 2.2. If the farmer uses fertilizer it can be applied in June. The growing period is from May until October, after which the harvesting period starts. In this thesis harvesting is taken to be one moment, October 1, although in practice the exact moment and duration of the harvesting period can vary from year to year. The agricultural year of crops varies over different countries, depending on conditions like rainfall; the present description of the agricultural year applies to Togo and is similar for other West African countries. We take the time of harvesting as the beginning of the year, after the harvest the crops can be sold and additional food can be bought when necessary. Buying and selling of crops can be done throughout the year. The period before the new harvest is called the lean period, sometimes also referred to as the hungry period. During that period there is often a shortage of food, most of the harvest has already been consumed hence the demand for food crops is very high.

Figure 2.2: The agricultural year of cereals in Togo.

In this thesis, various cereals (such as maize, sorghum and millet) are treated as one single product called cereals. This is justified since sorghum and millet have a similar price and seasonal pattern and maize plays only a marginal role.

2.1.3 Cereal Markets

After harvesting the farmer can go to the food market to sell part of his harvest. In practice there are many different local, regional and urban markets (Lutz, 1994), see figure 2.3. It is assumed that the farmer only has access to a local market and that cereal banks have access to both the local and the regional market. For a more elaborate discussion of how cereal markets work and especially on how the price on the market is formed, the reader is referred to Timmer (1993). The cereal bank can sell cereals on the regional market and receive a better price for these cereals. Therefore farmers who trade with the cereal bank could receive a better price for their cereals as well.

2.1.4 Food Price over Time

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2.1. THE SITUATION OF THE FARMER CHAPTER 2. PROBLEM DESCRIPTION

Figure 2.3: The cereal markets, based on Lutz (1994).

Figure 2.4: An illustration of the wholesale price of millet in several West African countries during the season 2007/2008 in FCFA (FAO, 2008).

There is a difference between the price that is paid by a consumer on the market and the price received by the farmer. Traders who transport the cereals between the farmer and the final con-sumer incur costs, these costs cause the differences between the prices received by farmers, cereal banks etc., see figure 2.5 for an illustration (more about what these costs entail is explained in the next section). The prices are defined as follows:

Price received by the Farmer for selling one kg of cereals on the local Market (pfm). Price on the Local Market per kg of cereals (plm).

Cost paid by the Farmer for buying one kg of cereals on the local Market (cfm). Price received by the Farmer for selling one kg of cereals to the Cereal bank (pfc). Cost paid by the Cereal bank for buying one kg of cereals from a Farmer (ccf).

Price received by the Cereal bank for selling one kg of cereals on the regional Market (pcm). Price on the Regional Market per kg of cereals (prm).

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CHAPTER 2. PROBLEM DESCRIPTION 2.1. THE SITUATION OF THE FARMER Price received by the Cereal bank for selling one kg of cereals to a Farmer (pcf).

Cost paid by the Farmer for buying one kg of cereals from the Cereal bank (cfc).

Figure 2.5: An illustration of a village with 5 farmers, who trade directly on the local market (above) or via a cereal bank (below).

The cereal price on every market generally rises during the year. In order to reflect the expecta-tions of farmers and traders, a linear cereal price during the year is estimated. With a cereal price in the first period of for example 100 FCFA and an annual price increase of 20% this results in a cereal price on the local market over time as given in table 2.1. The exact height of the price is not important, only the relative difference between the price and the different costs is important. When traders buy cereals on local markets at the beginning of the season and sell this on other markets e.g. regional markets, then the price of cereals rise, due to the costs of bringing cereals to a different market. This causes a higher price on the regional market. At the end of the year, when farmers with a shortage run out of cereals, some local markets transform from producing markets into consuming markets. Then cereals are brought from regional markets to the local market, this causes a higher price on the local market than on the regional market. Therefore we assume that the price on the regional market is a little higher at the beginning of the year, say 104 FCFA and rises less than the price on the local market. Let us assume that the price of cereals in the first period is 104 FCFA and the annual price increase is 10% on the regional market, see table 2.1. Note that the prices as defined above are derived from the local and regional market prices.

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2.1. THE SITUATION OF THE FARMER CHAPTER 2. PROBLEM DESCRIPTION

2.1.5 Marketing Costs

Marketing costs are all costs involved in the process of selling cereals from a farmer to a consumer. Figure 2.6 shows the marketing channel of cereals for the local and the regional market. There are costs involved in each part of the channel, for instance, there are costs involved in transporting cereals, gathering information, storage, and the risk associated with uncertain prices. These costs are different for each individual farmer, however in this thesis no distinction is made between farmers.

Figure 2.6: An illustration of the marketing channel of cereals on local and regional markets, based on Ruijs (2002).

According to Ruijs (2002) the marketing costs plus the profit margins are on average 17% to 18% of the price paid on the market by the final consumer. The costs of trading between the farmer and the cereal bank is smaller than between the farmer and the local market. Based on this information we make the following assumptions:

The costs between the farmer and the final consumer are assumed to be 17.5% of the local market price and the costs between the farmer and the local market are assumed to be 8.75% of the local market price. There are also costs between the cereal bank and the farmer and between the cereal bank and the regional market, we do not have information about these costs, we only know that they are not very high, therefore we make the following assumptions. The costs between the farmer and the cereal bank are assumed to be 2% of the price offered by the cereal bank. The costs between the cereal bank and the regional market are assumed to be 5% of the market price.

2.1.6 Forced Sales

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CHAPTER 2. PROBLEM DESCRIPTION 2.2. COOPERATIVES The downside of forced sales is, that when the cereals are harvested and all farmers bring their produce to the market, the price will be low because of the ample supply. This can lead to the situation that a farmer needs to sell all of his harvest first and later in that year the farmer needs to buy cereals on the market to feed his family at a higher price.

2.1.7 Interest

Sometimes farmers do not produce enough cereals and do not have enough savings to buy cereals. In that case farmers need to borrow money. When borrowing money, interest has to be paid. Common interest rates, observed by D´ejou (1987), may be up to 2% to 4% per month. From now on the interest rate on debt is assumed to be 3% per month for the farmers. Since the risk of not being able to repay the debt is much smaller for a cereal bank than for individual farmers, cereal banks can lend against a more favourable interest rate. According to Bassol´e (2000), the interest rate is 14% per year. This is equal to a compounding interest of 1.1% per month for the cereal banks. From now on the interest rate on debt is assumed to be 1.1% per month for the cereal bank. It is also assumed that some interest is earned on savings, the interest rate on savings is taken to be half of the interest rate on debt for cereal banks, this is an interest rate of 7% per year, or 0.55% per month for the cereal banks. For farmers we take the interest rate to be half of that 3.5% per year, or 0.275% per month. In practice farmers might not put their savings into a savings account, the interest rate on savings (also) reflects the utility of having money.

2.1.8 Storage of Cereals

All cereals that are not sold immediately after the harvesting period needs to be stored, these cereals are called stock. The advantage of storing cereals is that it can be kept until the price of selling harvest is higher. The disadvantage is that the quality of the cereals decline throughout the year. The loss of stock is estimated by Yonli (1988) to be 8% per year or 0.69% per month for a farmer and 6% annualy or 0.51% per month for a cereal bank. The storage costs of the farmers and of the cereal bank is included in the loss of stock in this thesis.

2.2 Cooperatives

Cooperatives can be formed for many different reasons. This thesis focuses on a cooperative founded by farmers. Possible objectives of agricultural cooperatives are:

1. Increasing the efficiency of agricultural production by carrying out joint agricultural practices (e.g. water management).

2. Facilitating the buying of inputs (such as fertilizer) and strengthening the negotiating power of farmers about prices and quality of inputs.

3. Facilitating the selling of agricultural outputs and strengthening the negotiating power of farmers about selling prices.

4. Keeping safety stock for the village in case of a poor harvest. 5. Saving money or acquiring credits.

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2.3. THE NATIONAL CEREAL MARKET CHAPTER 2. PROBLEM DESCRIPTION

2.2.1 Cereal Bank

Instead of each farmer going to the market to sell part of his harvest individually, all farmers from the same village can form a cooperative which will sell their cereals for them. We assume that the cereal bank can borrow enough money to buy cereals from the farmers. The cereal bank has access to the regional market1_{. The cereal bank sets the prices at which farmers can buy and sell}

cereals from and to the cereal bank. Each participating farmer is a member of the cereal bank. Therefore the risk of the cereal bank is carried by each of the participating farmers. When the cereal bank makes a profit or loss each farmer shares in this profit or loss. Chapter 3 focuses on the pricing strategy of the cereal bank.

According to Yonli (1997) three specific goals of the cereal bank are:

- Keeping a minimum amount of cereals, to provide the village with cereals (food security). - Offering cereals in the lean period before harvesting at lower prices then on the market. - Providing an alternative channel for farmers, who where otherwise obliged to sell their

harvest (forced sales) immediately after the harvest period.

Food security is, as it suggests, making sure that you have enough food. This is done by keeping a safety stock for the year to come in case next year the harvest will not be enough for own consumption due to extreme circumstances such as a drought. Although providing food security for an entire village is one of the main goals of cereal banks, it is not the main focus of this thesis. We assume that the farmer will keep a safety stock for his family. This safety stock is implicitly taken into account by deducting it from the harvest. This thesis deals only with the last two goals.

2.3 The National Cereal Market

This section describes the national market and its imperfections. In a perfect market, goods, money and labour are efficiently allocated. The prices differences are exactly equal to the costs, which makes it impossible to make a profit or a loss. In an imperfect market there are barriers and other conditions that restrict some farmers from entering the market. Costs for participating on the market are higher than necessary. Later on, the market imperfections are reviewed to see how establishing cereal banks has an effect on the imperfections on the national market.

2.3.1 Competitive Markets

A competitive firm is one that takes the market price of output as being given and outside of its control. In a competitive market each firm takes the price as being independent of its own actions, although it is the actions of all firms together that determine the market price (Varian, 1992). When there are only a small number of suppliers on the market, they can influence or even choose the market price, this is called an oligopoly. However the number of farmers and the number of cereal banks on the national food market is not small. Therefore it is understood that the suppliers, both the farmers and the cereal banks and the consumers as well take the price as given.

2.3.2 Imperfect Markets

In neo-classical theory the ideal market form is that of perfect competition. When a market does not exhibit all properties of a perfectly competitive market, this market is called an imperfect market. Stegeman (1998) mentions several ways in which a market can be imperfect:

1. Not all producers are price-takers (oligopoly, monopoly, collusion).

1_{The cereal bank could also trade on the local market. This would mean that the cereals have to be transported}

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CHAPTER 2. PROBLEM DESCRIPTION 2.3. THE NATIONAL CEREAL MARKET 2. Not all consumers are price-takers (e.g. consumer organizations negotiate with producers). 3. Not all intermediate actors are price-takers (monopolistic trade).

4. Not all actors behave completely rational (bounded rationality2_).

5. There are heterogeneous products (quality differences result in different prices). 6. Imperfect information (e.g. not all actors know prices).

7. Asymmetric information (some actors have more information about the market than others). 8. Uncertainty (prices are not know precisely).

9. Entry barriers (economies of scale, legal barriers to entry). 10. Exit barriers (sunk costs).

11. Existence of trade policies (taxes on import, subsidies, price setting by the gouvernment). 12. Existence of transaction costs (taxes, costs of information, transport, insurance).

In the case of farmers trading on the food market in West-Africa, the market is certainly not perfect. Lutz (1994) names the following reasons undermining the perfect market:

Food crops are usually not homogeneous (5), especially at the end of the lean period when the quality of food has deteriorated and fresh crops from abroad may also be offered on the food market. There is also uncertainty about prices (6-8), since the farmers and consumers do not know exactly at which prices they can expect to sell their harvest. Moreover the price on the market differs between markets. It is customry that the buyer and seller negotiate on price and quantity. It is a known fact that farmers sell and consumers buy small quantities on the market regularly (weekly). There are various ways of measuring the quantity that is traded, which makes it difficult to mea-sure the current market price. For example, sometimes the seller pours an extra cup of grain in the bag of the buyer, after agreeing on quantity and price.

There are entry barriers (9) and exit barriers (10) on the market caused by colluding3 traders who try to keep other traders away from the market.

A more striking example of sunk costs as an exit barrier (10) is the following. Farmers start selling their cereals after they produced it, hence the costs involved in producing these cereals are sunk costs after harvesting. Because these costs have already been made and because farmers have a stock of cereals, when faced with the decision when to sell, it is better for them to accept a very low price than not to sell at all. It is possible to hang on to these cereals a little longer, but there are costs involved with storing cereals. Cereals are food crops and therefore perishable, the quality declines and after a certain period of time the cereals are not good enough anymore for consumption, which puts the farmers under pressure to sell their cereals in time.

Most important is that many different forms of transaction costs (12) exist.

These examples clearly show that food markets in West Africa are imperfect. In chapter 7.2 we return to the topic of imperfect markets, there is discussed how the establishing of cereal banks has an effect on the imperfections on the national market.

2_{Bounded rationality means that two people, who have the same information, will behave differently.}

3_{A collusion is an agreement between two or more parties, to cooperate in such a way that deprives others of}

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2.4. ASSUMPTIONS CHAPTER 2. PROBLEM DESCRIPTION

2.4 Assumptions

In the previous sections several assumptions were made implicitly. In order to get a clear overview of the assumptions that were made, they are repeated in this section.

Some assumptions are more important than others, since they have a big influence on the re-sults of the models that are presented in the next chapters. What is assumed about the food price over time is important, since it directly influences at which moments time the harvest is best sold. - In this thesis only farmers are considered who produce a food crop (cereals), part of which

is used for own consumption and the rest is sold on the market.

- The goal of a farmer is to make a maximal amount of money under the condition that he has enough food for own consumption. The amount of cereals he produces is taken to be given, since at the time he starts selling he knows how much cereals he has produced. - There is no shortage of food crops on the market. When farmers want to buy food crops,

there is sufficient supply such that their demand can be met. There is also sufficient demand on the market. When farmers want to sell their harvest, they can always sell it.

- The food price rises throughout the year.

- Farmers only have access to the local markets, cereal banks have access to regional markets. - Both farmers and the cereal bank have access to credit. In other words, when they need a

loan, they can borrow money against interest.

- The cereal bank has enough money to buy cereals from the farmers.

- The cereal bank does not keep a safety stock for food security, the farmer keeps his own safety stock, which he deducts from the harvest at the beginning of the year.

- It is assumed that the suppliers, both the farmer and the cereal banks, and also the consumers on the market take the price on the markets as given.

What is assumed about the pricing strategy of the cereal bank is important, because if the cereal bank offers too much money for the harvest of the farmer it will go bankrupt, if they offer too little money, no farmer will want to sell his cereals to the cereal bank, this is discussed in chapter 3.

2.5 Problem Formulation

This thesis is about the possible effect of a cooperative to strengthen the market power of farmers in West Africa. Therefore we would like to address the following question:

1. How can a cereal bank help the farmers with selling their harvest?

In order to find out how much the farmers benefit from a cereal bank we take a look at the situation without and with a cereal bank. Since the cereal bank is supposed to help the farmers with selling their harvest we are also interested in the following:

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CHAPTER 2. PROBLEM DESCRIPTION 2.5. PROBLEM FORMULATION In order to answer question 1 two models are developed. The first model ”tells” us when an indi-vidual farmer should sell which amount of harvest and how much his profit is. Only the situation of each individual farmer is considered, no other types of cooperations between farmers (such as sharing information or labour) in the same village are considered. The second model ”tells” us when both the farmer and the cereal bank should sell which amount of harvest and how much the profit of the cereal bank and of the farmers is. We call these models the micro model without cereal bank and the micro model with cereal bank.

The first two models take a look at the farmers on an individual level. The prices on the market and the imperfections of the market are given by the actions of all actors on the market together. Therefore it could be interesting to take a look at the market at a national level. Which leads us to these questions:

2. What happens when cereal banks are introduced on a large scale throughout the country? 2.1. How do cereal banks influence the prices of cereals on the markets?

2.2. What is the supply on the food market compared to the previous situation? 2.3. Could the introduction of cereal banks help to make the market less imperfect?

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Chapter 3

The Strategy of the Cereal Bank

When selecting a pricing strategy the goal of the cereal bank is to improve the situation of the farmers (not to maximise their own profit). The farmers and the cereal bank take the price on the local and regional market as given. The price on the regional market is higher than on the local market in the beginning of the year, at the end of the year it is the other way around. By providing the farmers with access to the regional market and by using advantages of bulk the cereal bank tries to offer the farmers better prices. Recall the prices as defined in the previous chapter, where CCF stands for the costs of the cereal bank for buying cereals from farmers and where PCF stands for the price received by the cereal bank for selling cereals to the farmers. These are the prices that can be determined by the cereal bank, see the prices with a circle in figure 3.1. The 5% and 2% price differences are the (marketing) costs incurred for trading cereals, see the previous chapter. The PCM is 5% lower and the CCM is 5% higher than the price on the regional market.

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Chapter 4

Micro Model without Cereal Bank

In this chapter a model is derived which ”tells” each individual farmer when he should sell which quantity of cereals on the local cereal market. This is done in order to establish how farmers are doing without a cereal bank. Note that each farmer makes decisions for his own farm alone. A possible cooperation between farmers from the same village is not taken into account. Only a one year model is developed.

Let us first focus on the decisions that the farmer can take, before formulating his objective. Step by step all constraints are formulated. After the mathematical model has been formed, the model is solved for one farmer. In the section called inputs, the values of the parameters used to solve our model are given. Then different types of farmers are distinguished and the model is solved for those farmers. Finally our findings are summarised in a conclusion at the end of this chapter.

4.1 A Deterministic One Year Model

In order to be able to construct a model, some notations need to be introduced first, for a complete list of all notations used see appendix B.

Parameters:

m: The number of farmers, m = 1. τ : The number of periods, τ = 12. Sets: N = {1, . . . , m}. T = {1, . . . , τ }. Indices: n: The farmer, n ∈ N . t: Time in months, t ∈ T .

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4.1. A ONE YEAR MODEL CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK

4.1.1 The Decision of the Farmer

Decision variables:

Vnt: Quantity sold by farmer n on the local market, at time t, n ∈ N , t ∈ T .

Ant: Quantity purchased by farmer n on the local market, at time t, n ∈ N , t ∈ T .

Bnt: Amount of money borrowed by farmer n at time t, n ∈ N , t ∈ T .

Additional variables:

Snt: Stock of cereals of farmer n, at time t, n ∈ N , t ∈ T .

Knt: Capital of farmer n, at time t, n ∈ N , t ∈ T .

Dnt: Amount of debt of farmer n at time t, n ∈ N , t ∈ T .

During each period it is possible to sell or buy cereals. The amounts of cereal bought Antand sold

Vntand the amount of money borrowed Bntis measured during the period. The amounts of stock

Snt, capital Kntand debt Dntare measured at the end of the period, see figure 4.1. For example,

if you initially have a loan of Dn0 = 100 FCFA and in the first month you borrow Bn1 = 200

FCFA, than at the end of the month, you have a loan of Dn1 = 300 FCFA.

Figure 4.1: Time line.

Each period t, the farmer n has to decide how much cereals to sell or buy (he can do both in the same period, however that makes no sense, since buying is more expensive then selling) and how much money to borrow or to use to repay his loan. These three variables are the decision variables, where Vnt denotes the quantity of cereals sold in kilograms by farmer n in period t, Ant

denotes the quantity of cereals bought in kilograms by farmer n in period t and Bntdenotes the

amount of money borrowed in period t. We also introduce additional variables: Sntkeeps track of

the amount of cereals in storage in kilograms, Kntkeeps track of the amount of capital in FCFA

that farmer n has at time t and Dnt keeps track of the amount of debt in FCFA of farmer n. The

Franc CFA (FCFA) is the currency used in the following West African countries: Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Sénégal and Togo.

4.1.2 Objective Function

The goal of each farmer is to maximise his profit or put in other words to maximise the amount of capital Knτ minus his debt Dnτ he will have at the end of the year. Hence the objective function

is: max Vnt, Ant, Bnt m X n=1 Knτ − Dnτ.

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CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK 4.1. A ONE YEAR MODEL

4.1.3 Storage Balance

Parameters:

Sn0: Stock of cereals of farmer n at the beginning of the year, n ∈ N .

fn: Part of stock lost due to storage of farmer n, n ∈ N .

dnt Consumption of farmer n, at time t, n ∈ N , t ∈ T .

The level of stock at the beginning of the year Sn0 is equal to the amount of cereals harvested,

any left over cereals from previous years are not taken into account.The amount of cereals that the farmer has in stock Snt is equal to the amount he had in stock in the previous period Snt−1,

multiplied by the storage loss factor (1 - fn), plus the amount he bought Ant, minus the amount

he sold Vnt minus the amount consumed dnt:

Snt= (1 − fn)Snt−1+ Ant− Vnt− dnt, n ∈ N , t ∈ T .

4.1.4 Capital Balance

Parameters:

Kn0: Capital of farmer n at the beginning of the year, in FCFA, n ∈ N .

pfm_t: Price received by farmers for selling one kg of cereals on the local market in FCFA, at time t, t ∈ T .

cfm_t: Costs paid by farmers for buying one kg of cereals on the local market in FCFA, at time t, t ∈ T .

The capital at the beginning of the year Kn0 is given, it is assumed that Kn0 = 0 FCFA. The

amount of capital the farmer has Knt is equal to the amount of capital had in the previous period

Knt−1, plus by the interest πnKnt−1, plus the gains from selling cereals pfmntVnt, minus the costs

of buying cereals1_cfm

ntAnt, plus the amount borrowed in that period Bnt.

Knt= (1 + πn)Knt−1+ pfmtVnt− cfmtAnt+ Bnt, n ∈ N , t ∈ T .

4.1.5 Debt Balance

Parameters:

Dn0: Debt of farmer n at the beginning of the year in FCFA, n ∈ N .

λn: Interest rate on debt for farmer n per month, n ∈ N .

The debt at the beginning of the year is given Dn0. The debt of a farmer is equal to the debt at

the end of the previous period Dnt−1 plus the additional amount that was borrowed this period

Bnt, this is multiplied by the interest (1 + λn).

Dnt= (1 + λn)(Dnt−1+ Bnt), n ∈ N , t ∈ T .

4.1.6 Forced Sales

When a farmer needs money, he may make a deal with a trader who lends him money, under the condition that the farmer will pay him back immediately after the new harvest. This can be represented in our model by a debt at the beginning of the year Dn0 ≥ 0 and the condition that

at time t = 1 the farmer should repay this debt. Note that borrowing a negative amount −Bn1

means repaying the loan.

−Bn1≥ Dn0, n ∈ N .

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4.2. INPUT OF THE MODEL CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK

4.1.7 Non-negativity Constraints

It is not possible to have a negative amount of food in stock: Snt≥ 0, n ∈ N , t ∈ T .

It is not possible to have a negative amount of money: Knt≥ 0, n ∈ N , t ∈ T .

It is not possible to have a negative amount of debt:

Dnt≥ 0, n ∈ N , t ∈ T .

The amount of cereals the farmer sells on the market can not be negative: Vnt≥ 0, n ∈ N , t ∈ T .

The amount of cereals the farmer buys on the market can not be negative: Ant≥ 0, n ∈ N , t ∈ T .

For the complete mathematical model see appendix D.1.

4.2 Input of the model

Let us for now consider one farmer with a forced sales contract and more than enough cereals for his own consumption. The exact amount of his loan has no influence on the best selling strategy, let us take the hight of the loan to be 2, 000 FCFA. A farmer needs 190 kg of cereals for his own consumption, because cereals in storage declines the farmer needs to harvest at least 199 kg. The amount of surplus does not influence the selling strategy of the farmer, it is only of importance whether there is a surplus or a shortage. For now let us assume that the farmer harvests 280 kg. The model is solved with the following values of the parameters, see table 4.1 and the prices as introduced in chapter 2, see table 4.2. These parameters and their values have already been introduced in this chapter and in chapter 2. For a complete overview of the definitions of all parameters see appendix B.

Table 4.1: The values of the parameters.

Parameters Value

Number of periods τ 12

Number of farmers participating in the cereal bank m 1 Debt at the beginning of the year of the farmer Dn0 ∀n 2, 000 FCFA

Capital at the beginning of the year of the farmer Kn0 ∀n 0 FCFA

Initial stock of the farmer Sn0 ∀n 280 kg

Consumption per person per month dn ∀n 15.83 kg

Part of stock lost due to storage for a farmer per month fn ∀n 0.69%

Interest rate on debt for farmers per month λn ∀n 3.00%

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CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK 4.3. RESULTS

Table 4.2: The price of cereals over time on the local market in FCFA. Month Index pfm_t plm_t cfm_t Oct. 1 91.25 100.00 108.75 Nov. 2 92.77 101.67 110.56 Dec. 3 94.29 103.33 112.38 Jan. 4 95.81 105.00 114.19 Feb. 5 97.33 106.67 116.00 Mar. 6 98.85 108.33 117.81 Apr. 7 100.38 110.00 119.63 May. 8 101.90 111.67 121.44 Jun. 9 103.42 113.33 123.25 Jul. 10 104.94 115.00 125.06 Aug. 11 106.46 116.67 126.88 Sep. 12 107.98 118.33 128.69

4.3 Results

For the results of the model with the farmer as specified above, see table 4.3. Note that borrowing a negative amount means repaying the loan. These results show that the strategy of the farmer is to sell part of his harvest in the first period in order to repay his debt. He sells 21.92 kg in the first period, which yields him 2, 000 FCFA, exactly enough money to repay his loan. Then he puts the rest of his cereals in storage. Each month he consumes 15.83 kg from his storage. At the end of the year, when the price is highest, he sells his surplus of cereals and makes a profit.

Table 4.3: Results of type 1.

F → LM LM → F Borrowing Stock Capital Debt Vn1 = 21.92 An1 = 0.00 Bn1 = -2,000 Sn1 = 240 Kn1 = 0 Dn1 = 0 Vn2 = 0.00 An2 = 0.00 Bn2 = 0 Sn2 = 223 Kn2 = 0 Dn2 = 0 Vn3 = 0.00 An3 = 0.00 Bn3 = 0 Sn3 = 205 Kn3 = 0 Dn3 = 0 Vn4 = 0.00 An4 = 0.00 Bn4 = 0 Sn4 = 188 Kn4 = 0 Dn4 = 0 Vn5 = 0.00 An5 = 0.00 Bn5 = 0 Sn5 = 171 Kn5 = 0 Dn5 = 0 Vn6 = 0.00 An6 = 0.00 Bn6 = 0 Sn6 = 154 Kn6 = 0 Dn6 = 0 Vn7 = 0.00 An7 = 0.00 Bn7 = 0 Sn7 = 137 Kn7 = 0 Dn7 = 0 Vn8 = 0.00 An8 = 0.00 Bn8 = 0 Sn8 = 120 Kn8 = 0 Dn8 = 0 Vn9 = 0.00 An9 = 0.00 Bn9 = 0 Sn9 = 104 Kn9 = 0 Dn9 = 0 Vn10 = 0.00 An10 = 0.00 Bn10 = 0 Sn10 = 87 Kn10 = 0 Dn10 = 0 Vn11 = 0.00 An11 = 0.00 Bn11 = 0 Sn11 = 71 Kn11 = 0 Dn11 = 0 Vn12 = 54.41 An12 = 0.00 Bn12 = 0 Sn12 = 0 Kn12 = 5,875 Dn12 = 0

4.4 Different Types of Farmers

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4.4. DIFFERENT FARMERS CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK In this section the model is solved for different types of farmers. The following six types of farmers are distinguished, see table 4.4. Note that the model of type 1 is solved above. The farmer has a surplus (type 1 and 2). The farmer has a surplus, only he no longer has a surplus after selling part of his harvest to repay his debt (type 3 and 4). This is included because this type might benefit even more from establishing a cereal bank than the other types. The the farmer does not grow enough cereals for his own consumption (type 5 and 6). Comparing type 1 and 2 with type 5 and 6 shows us the difference in strategy of farmers who have a surplus and who have a shortage. The odd numbered types are with forced sales and the even numbered types are the same situations only without forced sales.

Table 4.4: Different types of farmers.

Characteristics Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Initial debt Dn0 2,000 FCFA 0 FCFA 2,000 FCFA 0 FCFA 2,000 FCFA 0 FCFA

Harvest Sn0 280 kg 280 kg 220 kg 220 kg 160 kg 160 kg

4.4.1 Forced Sales and Capital

The results for a farmer (of type 2) without a forced sales loan and and a harvest of 280 kg can be found in table 4.5. These results show the strategy of the farmer. The farmer puts all of his harvest in storage. Each month he consumes 15.83 kg from his storage. At the end of the year, when the price is highest, he sells his surplus of cereals and makes a profit.

F → LM LM → F Borrowing Stock Capital Debt Vn1 = 0.00 An1 = 0.00 Bn1 = 0 Sn1 = 262 Kn1 = 0 Dn1 = 0 Vn2 = 0.00 An2 = 0.00 Bn2 = 0 Sn2 = 245 Kn2 = 0 Dn2 = 0 Vn3 = 0.00 An3 = 0.00 Bn3 = 0 Sn3 = 227 Kn3 = 0 Dn3 = 0 Vn4 = 0.00 An4 = 0.00 Bn4 = 0 Sn4 = 210 Kn4 = 0 Dn4 = 0 Vn5 = 0.00 An5 = 0.00 Bn5 = 0 Sn5 = 192 Kn5 = 0 Dn5 = 0 Vn6 = 0.00 An6 = 0.00 Bn6 = 0 Sn6 = 175 Kn6 = 0 Dn6 = 0 Vn7 = 0.00 An7 = 0.00 Bn7 = 0 Sn7 = 158 Kn7 = 0 Dn7 = 0 Vn8 = 0.00 An8 = 0.00 Bn8 = 0 Sn8 = 141 Kn8 = 0 Dn8 = 0 Vn9 = 0.00 An9 = 0.00 Bn9 = 0 Sn9 = 124 Kn9 = 0 Dn9 = 0 Vn10 = 0.00 An10 = 0.00 Bn10 = 0 Sn10 = 108 Kn10 = 0 Dn10 = 0 Vn11 = 0.00 An11 = 0.00 Bn11 = 0 Sn11 = 91 Kn11 = 0 Dn11 = 0 Vn12 = 74.72 An12 = 0.00 Bn12 = 0 Sn12 = 0 Kn12 = 8,069 Dn12 = 0

4.4.2 Amount of Cereals Harvested

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CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK 4.4. DIFFERENT FARMERS

F → LM LM → F Borrowing Stock Capital Debt Vn1 = 21.92 An1 = 0.00 Bn1 = -2,000 Sn1 = 181 Kn1 = 0 Dn1 = 0 Vn2 = 0.00 An2 = 0.00 Bn2 = 0 Sn2 = 164 Kn2 = 0 Dn2 = 0 Vn3 = 0.00 An3 = 0.00 Bn3 = 0 Sn3 = 147 Kn3 = 0 Dn3 = 0 Vn4 = 0.00 An4 = 0.00 Bn4 = 0 Sn4 = 130 Kn4 = 0 Dn4 = 0 Vn5 = 0.00 An5 = 0.00 Bn5 = 0 Sn5 = 113 Kn5 = 0 Dn5 = 0 Vn6 = 0.00 An6 = 0.00 Bn6 = 0 Sn6 = 96 Kn6 = 0 Dn6 = 0 Vn7 = 0.00 An7 = 0,00 Bn7 = 0 Sn7 = 80 Kn7 = 0 Dn7 = 0 Vn8 = 0.00 An8 = 0,00 Bn8 = 0 Sn8 = 64 Kn8 = 0 Dn8 = 0 Vn9 = 0.00 An9 = 0,00 Bn9 = 0 Sn9 = 47 Kn9 = 0 Dn9 = 0 Vn10 = 0.00 An10 = 0,00 Bn10 = 0 Sn10 = 31 Kn10 = 0 Dn10 = 0 Vn11 = 0.00 An11 = 0,00 Bn11 = 0 Sn11 = 15 Kn11 = 0 Dn11 = 0 Vn12 = 0.00 An12 = 0,80 Bn12 = 103 Sn12 = 0 Kn12 = 0 Dn12 = 107

In table 4.7 we can see the results of a farmer (of type 4) who has an amount of harvest 220 kg which is a little more then needed for his own consumption. These results show that the strategy of the farmer is to put all of his cereals in storage. Each month he consumes 15.83 kg from his storage. At the end of the year, when the price is highest, he sells his surplus of cereals and makes a profit.

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4.4. DIFFERENT FARMERS CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK In table 4.8 we can see the results of a farmer (of type 5) who has an amount of harvest 160 kg which is too little for his own consumption. Moreover the farmer has a forced sales loan of 2, 000 FCFA. These results show that the strategy of the farmer is to sell part of his harvest in the first period in order to repay his debt. He sells 21.92 kg in the first period, which yields him 2, 000 FCFA, exactly enough money to repay his loan. Then he puts the rest of his cereals in storage. Each month he consumes 15.83 kg from his storage. In the ninth month the farmer no longer has enough cereals for his own consumption. At this point he takes out a loan to buy the additional amount of cereals on the market. The next month he takes out an extra loan to pay for more cereals until the end of the year. In table 4.9 we can see the results of a farmer (of type 6) who

F → LM LM → F Borrowing Stock Capital Debt Vn1 = 21.92 An1 = 0.00 Bn1 = -2,000 Sn1 = 121 Kn1 = 0 Dn1 = 0 Vn2 = 0.00 An2 = 0.00 Bn2 = 0 Sn2 = 104 Kn2 = 0 Dn2 = 0 Vn3 = 0.00 An3 = 0.00 Bn3 = 0 Sn3 = 88 Kn3 = 0 Dn3 = 0 Vn4 = 0.00 An4 = 0.00 Bn4 = 0 Sn4 = 71 Kn4 = 0 Dn4 = 0 Vn5 = 0.00 An5 = 0.00 Bn5 = 0 Sn5 = 55 Kn5 = 0 Dn5 = 0 Vn6 = 0.00 An6 = 0.00 Bn6 = 0 Sn6 = 39 Kn6 = 0 Dn6 = 0 Vn7 = 0.00 An7 = 0.00 Bn7 = 0 Sn7 = 23 Kn7 = 0 Dn7 = 0 Vn8 = 0.00 An8 = 0.00 Bn8 = 0 Sn8 = 7 Kn8 = 0 Dn8 = 0 Vn9 = 0.00 An9 = 9.03 Bn9 = 1,113 Sn9 = 0 Kn9 = 0 Dn9 = 1,147 Vn10 = 0.00 An10 = 15.83 Bn10 = 1,980 Sn10 = 0 Kn10 = 0 Dn10 = 3,221 Vn11 = 0.00 An11 = 15.83 Bn11 = 2,009 Sn11 = 0 Kn11 = 0 Dn11 = 5,386 Vn12 = 0.00 An12 = 15.83 Bn12 = 2,038 Sn12 = 0 Kn12 = 0 Dn12 = 7,647

has an amount of harvest 160 kg which is too little for his own consumption. These results show that the strategy of the farmer is to put all of his cereals in storage. Each month he consumes 15.83 kg from his storage. In the tenth month the farmer no longer has enough cereals for his own consumption. At this point he takes out a loan to buy the additional amount of cereals on the market. The next month he takes out an extra loan to pay for more cereals until the end of the year.

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CHAPTER 4. MICRO MODEL WITHOUT CEREAL BANK 4.5. CONCLUSION

4.5 Conclusion

We chose to consider the effect of forced sales and to vary the amount of harvest for two reasons. First of all because in practice these parameters are different for different farmers. Secondly be-cause having a forced sales loan and whether the farmer has a surplus or a shortage of cereals has a large influence on the selling strategy.

When the farmer has forced sales he will sell the exact amount he needs to sell in order to be able to repay his loan in the first period.

When the farmer has a surplus, the selling strategy of a farmer is to keep all of his cereals in storage and sell it in the last period. He will not borrow any money and not buy any additional cereals, because he does not need it.

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Chapter 5

Micro Model with Cereal Bank

The model in the previous chapter is used to find the best strategy for individual farmers when they only have access to a local market. In this chapter a model is developed which ”tells” both the farmer and the cereal bank when to sell which quantity of cereals on the markets and to each other. It is assumed that the farmer has access to the cereal bank and still has access to the local market too. Solving this model makes it possible to compare the situation of the farmers with and without a cereal bank. This model assumes that all farmers and the cereal bank coordinate their strategies, the next chapter revises this assumption.

Let us first focus on the decisions that the farmer and cereal bank can take, before consider-ing their objective. Note that the cereal bank is established for the benefit of the farmers. Now we can formulate all constraints step by step. After the mathematical model is formed, the values of the parameters used to solve our model are given in the section called inputs. The model is solved for the same types of farmers as in the previous model. The differences between the outcome of this and the previous model are discussed. Finally our findings are summarised in a conclusion at the end of this chapter.

5.1 A Deterministic One Year Model

The important distinction with the previous model is that the previous model finds the best decision for the individual farmer (not the entire village of farmers) and this model looks at the best decision for the cereal bank and the farmers combined. In order to be complete, notation is introduced first, for a complete list of the notation used see appendix B.

Parameters:

m: The number of farmers, m = 6. τ : The number of periods, τ = 12. Sets: N = {1, . . . , m}. T = {1, . . . , τ }. Indices: n: The farmer, n ∈ N . t: Time in months, t ∈ T .

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5.1. A ONE YEAR MODEL CHAPTER 5. MICRO MODEL WITH CEREAL BANK

5.1.1 The Decision of the Farmer and the Cereal Bank

Decision variables:

Vt: Quantity sold by the cereal bank on the regional market, at time t, t ∈ T .

Vc

nt: Quantity sold by farmer n to the cereal bank, at time t, n ∈ N , t ∈ T .

Vnt: Quantity sold by farmer n on the local market, at time t, n ∈ N , t ∈ T .

At: Quantity purchased by the cereal bank from the regional market, at time t, t ∈ T .

Ac

nt: Quantity purchased by farmer n from the cereal bank, at time t, n ∈ N , t ∈ T .

Ant: Quantity purchased by farmer n on the local market, at time t, n ∈ N , t ∈ T .

Bt: Amount of money borrowed by the cereal bank at time t, t ∈ T .

Bnt: Amount of money borrowed by farmer n at time t, n ∈ N , t ∈ T .

Additional variables:

V_tf: Quantity sold by the cereal bank to the farmers, at time t, t ∈ T .

Af_t: Quantity purchased by the cereal bank from the farmers, at time t, t ∈ T . St: Stock of cereals of the cereal bank, at time t, t ∈ T .

Snt: Stock of cereals of farmer n, at time t, n ∈ N , t ∈ T .

Kt: Capital of the cereal bank, at time t, t ∈ T .

Knt: Capital of farmer n, at time t, n ∈ N , t ∈ T .

Dt: Amount of debt of the cereal bank at time t, t ∈ T .

Dnt: Amount of debt of farmer n at time t, n ∈ N , t ∈ T .

Each period t, farmer n decides how much of the cereals to sell and buy and whether he trades with the cereal bank or on the local market. He also decides how much money to borrow or to use to repay its loan. The cereal bank has to decides how much of the cereals to sell or buy on the regional market and how much money to borrow or to use to repay its loan. These eight variables are the decision variables, they are introduced above. We also introduce additional variables to keep track of the amount of cereals in storage and the amount of capital and debt. There are two variables that denote the total amount of cereals that the cereal bank buys from and sells to the farmers. All these variables are introduced above.

5.1.2 Objective Function

The goal is to maximize the profit of the participating farmers which is defined as Knτ− Dntand

the profit of the cereal bank as well. Since the farmers are members of the cereal bank, the profit of the cereal bank can be seen as a kind of bonus for the farmers, therefore it is included in the objective function. The profit of selling cereals is defined as Kτ− Dt.

max Vt, Vntc, Vnt, At, Acnt, Ant, Bt, Bnt m X n=1 (Knτ− Dnτ) + (Kτ− Dτ). (5.1)

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CHAPTER 5. MICRO MODEL WITH CEREAL BANK 5.1. A ONE YEAR MODEL

5.1.3 Storage Balance

Parameters:

S0: Stock of cereals of the cereal bank at the beginning of the year.

Sn0: Stock of cereals of farmer n at the beginning of the year, n ∈ N .

f : Part of stock lost due to storage for a cereal bank. fn: Part of stock lost due to storage.

dnt Consumption of farmer n, at time t, n ∈ N , t ∈ T .

The amount of cereals that the cereal bank has in stock Stis equal to the amount it had in stock

in the previous period St−1, multiplied by the storage loss factor (1 - f ), minus the amount sold

Vt, plus the amount bought At.

St= (1 − f )St−1+ At+ Atf− Vt− Vtf, t ∈ T . (5.2)

The amount of cereal in stock in period t = 0 is equal to S0, S0= 0 since at that time the cereal

bank has not bought any cereals from farmers and it is assumed that the cereal bank does not have a stock of cereals from the previous year either.

V_tf = m X n=1 Ac_nt, t ∈ T . (5.3) Af_t = m X n=1 V_ntc, t ∈ T . (5.4) The Storage Balance of the Farmers

The level of stock at the beginning of the year Sn0 is equal to the amount of cereals harvested.

The amount of cereals that the farmer has in stock Snt is equal to the amount he had in stock

in the previous period Snt−1, multiplied by the storage loss factor (1 - fn), plus the amount he

bought Ant+ Acnt, minus the amount he sold Vnt+ Vntc minus the amount consumed dnt:

Snt= (1 − fn)Snt−1+ Ant− Vnt+ Acnt− V c

nt− dnt, t ∈ T , n ∈ N . (5.5)

5.1.4 Capital Balance

Parameter:

K0: Capital at the beginning of the year in FCFA, for the cereal bank n, n ∈ N .

Kn0: Capital of the farmer at the beginning of the year, in FCFA.

pfc_t: Price received by farmers for selling one kg of cereals to the cereal bank in FCFA, at time t, t ∈ T .

ccft: Costs paid by the cereal bank for buying one kg of cereals from a farmer in FCFA,

at time t, t ∈ T .

pcmt: Price received by the cereal bank for selling one kg of cereals on the regional market

in FCFA, at time t, t ∈ T .

ccmt: Costs paid by the cereal bank for buying one kg of cereals from the regional market

in FCFA, at time t, t ∈ T .

pcf_t: Price received by the cereal bank for selling one kg of cereals to a farmer in FCFA, at time t, t ∈ T .

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5.1. A ONE YEAR MODEL CHAPTER 5. MICRO MODEL WITH CEREAL BANK The capital at the beginning of the year K0 is given, it is assumed that the cereal bank has no

start capital Kn0 = 0 FCFA. In order to purchase cereals, the cereal bank is able to borrow

money, see the next section. The amount of capital in this period Kt is equal to the amount of

capital in the previous period Kt−1, plus the interest πKt−1, plus the revenue from selling cereals

pcm_tVt+ pcftV f

t , minus the costs of buying cereals (ccmtAt+ ccftA f

t), plus the amount borrowed

in that period Bt: Kt= (1 + π)Kt−1+ pcmtVt+ pcftV f t − ccmtAt− ccftA f t + Bt, t ∈ T . (5.6)

The Capital Balance of the Farmers

The capital at the beginning of the year Kn0 is given, it is assumed that Kn0 = 0 FCFA. The

amount of capital the farmer has Knt is equal to the amount of capital had in the previous period

Knt−1, plus by the interest πnKnt−1, plus the revenue from selling cereals pfmtVnt+ pfctVtc, minus

the costs of buying cereals (cfmtAnt+ cfctAnt), plus the amount borrowed in that period Bnt:

Knt= (1 + πn)Knt−1+ pfmtVnt+ pfctV c

t − cfmtAnt− cfctAnt+ Bnt, t ∈ T , n ∈ N . (5.7)

5.1.5 Debt Balance

Parameter:

D0: Debt of the cereal bank at the beginning of the year in FCFA.

Dn0: Debt of the farmer at the beginning of the year in FCFA.

λ: Interest rate on debt for the cereal bank per month. λn: Interest rate on debt for farmers per month.

The debt at the beginning of the year is given D0 = 0. The debt is equal to the debt at the end

of the previous period Dt−1plus the additional amount that was borrowed this period Bt, this is

multiplied by the interest (1 + λ).

Dt= (1 + λ)(Dt−1+ Bt), t ∈ T . (5.8)

The Debt Balance of the Farmers

The debt at the beginning of the year is given.The debt of a farmer is equal to the debt at the end of the previous period Dnt−1 plus the additional amount that was borrowed this period Bnt,

this is multiplied by the interest (1 + λn).

Dnt= (1 + λn)(Dnt−1+ Bnt), t ∈ T , n ∈ N (5.9)

5.1.6 Forced Sales

When a farmer needs money, he may make deal with a trader who will lend him money. The trader agrees to borrow him money under the condition that the farmer will pay him back immediately after the new harvest. This can be represented in our model by a debt at the beginning of the year Dn0 ≥ 0 and the condition that at time t = 1 the farmer should repay this debt. Note that

borrowing a negative amount −Bn1 means repaying the loan.

−Bn1≥ Dn0, n ∈ N . (5.10)

5.1.7 Non-negativity Constraints

It is not possible for the cereal bank to have a negative amount of food in stock:

St≥ 0, t ∈ T . (5.11)

It is not possible for the farmer to have a negative amount of food in stock:

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CHAPTER 5. MICRO MODEL WITH CEREAL BANK 5.2. INPUT OF THE MODEL It is not possible for the cereal bank to have a negative amount of money:

Kt≥ 0, t ∈ T . (5.13)

It is not possible for the farmer to have a negative amount of money:

Knt≥ 0, n ∈ N , t ∈ T . (5.14)

It is not possible for the cereal bank to have a negative amount of debt:

Dt≥ 0, t ∈ T . (5.15)

It is not possible for the farmer to have a negative amount of debt:

Dnt≥ 0, n ∈ N , t ∈ T . (5.16)

The amount of cereals the cereal bank sells on the market can not be negative:

Vt≥ 0, t ∈ T . (5.17)

The amount of cereals the farmer sells to the cereal bank can not be negative:

V_ntc ≥ 0, n ∈ N , t ∈ T . (5.18) The amount of cereals the farmer sells on the market can not be negative:

Vnt≥ 0, n ∈ N , t ∈ T . (5.19)

The amount of cereals the cereal bank purchases on the market can not be negative:

At≥ 0, t ∈ T . (5.20)

The amount of cereals the farmer purchases from the cereal bank can not be negative:

Acnt≥ 0, n ∈ N , t ∈ T . (5.21)

The amount of cereals the farmer purchases from the market can not be negative:

Ant≥ 0, n ∈ N , t ∈ T . (5.22)

For the complete mathematical model see appendix D.2.

5.2 Input of the model

There are multiple optimal solutions to this model. First one of these solutions is discussed below for the six different types of farmers and the cereal bank, also the differences with the model without a cereal bank are mentioned. After which is explained why there are multiple optimal solutions and what they look like. Then the differences between the model with and without cereal bank are reviewed and discussed.

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5.3. RESULTS CHAPTER 5. MICRO MODEL WITH CEREAL BANK

Table 5.1: Different types of farmers.

Characteristics Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Initial debt Dn0 2, 000 FCFA 0 FCFA 2, 000 FCFA 0 FCFA 2, 000 FCFA 0 FCFA

Harvest Sn0 280 kg 280 kg 220 kg 220 kg 160 kg 160 kg

The model is solved with the following values of the parameters, see table 5.2. For the prices used see tables 5.3 and 5.4. These parameters and their values have already been introduced in this chapter and in chapter 2. For a complete overview of the definitions of all parameters see appendix B.

Table 5.2: The values of the parameters.

Parameters Value

Number of periods τ 12

Number of farmers participating in the cereal bank m 6 Stock of cereals at the beginning of the year of the cereal bank S0 0 FCFA

Capital at the beginning of the year of the farmer Kn0 ∀n 0 FCFA

Capital at the beginning of the year of the cereal bank K0 0 FCFA

Debt at the beginning of the year of the cereal bank D0 0 FCFA

Interest rate on debt for farmers per month λn ∀n 3.00%

Interest rate on debt for the cereal bank per month λ 1.10% Interest rate on savings for farmers per month πn ∀n 0.275%

Interest rate on savings for the cereal bank per month π 0.55% Part of stock lost due to storage for a farmer per month fn ∀n 0.69%

Part of stock lost due to storage for the cereal bank per month f 0.51% Consumption per person per month dn ∀n 15.83 kg

Table 5.3: The price of cereals over time on the local market in FCFA. Month Index pfm_t plm_t cfm_t Oct. 1 91.25 100.00 108.75 Nov. 2 92.77 101.67 110.56 Dec. 3 94.29 103.33 112.38 Jan. 4 95.81 105.00 114.19 Feb. 5 97.33 106.67 116.00 Mar. 6 98.85 108.33 117.81 Apr. 7 100.38 110.00 119.63 May. 8 101.90 111.67 121.44 Jun. 9 103.42 113.33 123.25 Jul. 10 104.94 115.00 125.06 Aug. 11 106.46 116.67 126.88 Sep. 12 107.98 118.33 128.69

5.3 Results

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CHAPTER 5. MICRO MODEL WITH CEREAL BANK 5.3. RESULTS

Table 5.4: The price of cereals over time on the regional market in FCFA. Month Index pfc_t ccf_t pcm_t prm_t ccmt pcft cfct Oct. 1 96.82 98.80 98.80 104.00 109.20 109.20 111.38 Nov. 2 97.63 99.62 99.62 104.87 110.11 110.11 112.31 Dec. 3 98.44 100.45 100.45 105.73 111.02 111.02 113.24 Jan. 4 99.24 101.27 101.27 106.60 111.93 111.93 114.17 Feb. 5 100.05 102.09 102.09 107.47 112.84 112.84 115.10 Mar. 6 100.86 102.92 102.92 108.33 113.75 113.75 116.03 Apr. 7 101.67 103.74 103.74 109.20 114.66 114.66 116.95 May. 8 102.47 104.56 104.56 110.07 115.57 115.57 117.88 Jun. 9 103.28 105.39 105.39 110.93 116.48 116.48 118.81 Jul. 10 104.09 106.21 106.21 111.80 117.39 117.39 119.74 Aug. 11 104.89 107.03 107.03 112.67 118.30 118.30 120.67 Sep. 12 105.70 107.86 107.86 113.53 119.21 119.21 121.59

the farmer now sells cereals in the first period to the cereal bank instead of on the local market and instead of selling his surplus on the local market in the last period, he now sells his surplus to the cereal bank in the last three periods.

Month F → CB F → LM LM → F CB → F Borrowing Stock Capital Debt 1 20.66 0.00 0.00 0.00 -2,000 242 0 0 2 0.00 0.00 0.00 0.00 0 224 0 0 3 0.00 0.00 0.00 0.00 0 207 0 0 4 0.00 0.00 0.00 0.00 0 189 0 0 5 0.00 0.00 0.00 0.00 0 172 0 0 6 0.00 0.00 0.00 0.00 0 155 0 0 7 0.00 0.00 0.00 0.00 0 138 0 0 8 0.00 0.00 0.00 0.00 0 122 0 0 9 0.00 0.00 0.00 0.00 0 105 0 0 10 4.72 0.00 0.00 0.00 0 84 492 0 11 31.67 0.00 0.00 0.00 0 36 3,815 0 12 19.47 0.00 0.00 0.00 0 0 5,883 0

The Role of Cooperatives Revisited. The Possible Eﬀect of a Cooperative to Strengthen the Market Power of Farmers in West Africa.

The Role of Cooperatives Revisited.

The Possible Effect of a Cooperative to Strengthen the

Market Power of Farmers in West Africa.

J.T. Ton

The Role of Cooperatives Revisited.

The Possible Effect of a Cooperative to Strengthen the Market Power

of Farmers in West Africa.

Foreword

Summary

Contents

Chapter 1

Introduction

1.1

The Goal of this Thesis

1.2

A Brief History of Food Security

1.3

Other Studies

1.4

The Outline of the Thesis

Chapter 2

Problem Description

2.1

The Situation of the Farmer

2.1.1

Consumption

2.1.2

Agricultural Year

2.1.3

Cereal Markets

2.1.4

Food Price over Time

2.1.5

Marketing Costs

2.1.6

Forced Sales

2.1.7

Interest

2.1.8

Storage of Cereals

2.2

Cooperatives

2.2.1

Cereal Bank

2.3

The National Cereal Market

2.3.1

Competitive Markets

2.3.2

Imperfect Markets

2.4

Assumptions

2.5

Problem Formulation

Chapter 3

The Strategy of the Cereal Bank

Chapter 4

Micro Model without Cereal Bank

4.1

A Deterministic One Year Model

4.1.1

The Decision of the Farmer

4.1.2

Objective Function

4.1.3

Storage Balance

4.1.4

Capital Balance

4.1.5

Debt Balance

4.1.6

Forced Sales

4.1.7

Non-negativity Constraints

4.2

Input of the model

4.3

Results

4.4