Excerpt

## Inhaltsverzeichnis

**CHAPTER ONE.**

**THE PRODUCTION FUNCTION.**

1.0. Introduction

1.1. The classical production function

1.2. The law of diminishing returns

1.3. Constant returns

1.4. Increasing marginal returns

1.5. Diminishing marginal returns

**CHAPTER TWO.**

**FACTOR COMBINATIONS**

2.1. The factor product relationship

2.2. Factor-factor relationship

2.3. Returns to scale

**CHAPTER THREE.**

**THE CHIOCE OF ENTERPRISES.**

3.1. The production possibility curve

3.2. Unlimited Variable input situation

3.3. Limited input situation

3.4. Economic choice of enterprises

3.5. The profit maximization point

**CHAPTER FOUR.**

**SPECIALISATION AND DIVERSIFICATION.**

4.1. Specialization

4.2. Diversification

**CHAPTER FIVE.**

**PRICE VARIATION, RISKS AND UNCERTAINTY.**

5.1. Quality and price

5.2. Price changes over time

**CHAPTER SIX.**

**LINEAR PROGRAMMING**

**CHAPTER SEVEN.**

**FARM RECORDS.**

7.1. Farm book keeping and financial accounting

7.2. Kind of records and method of book keeping

**CHAPTER EIGHT.**

**MARKETING.**

8.1. Pricing

8.2. Distribution

8.3. Promotion

**CHAPTER NINE.**

**SUPPLY OF AGRICULTURAL PRODUCTS.**

9.1. The supply and demand relations in Agriculture

**CHAPTER TEN.**

**COOPERATIVES.**

10.1. History of cooperative movement in Uganda

10.2. Uganda Cooperative Bank

10.3. Uganda Cooperative Transport Union

10.4. Uganda Cooperative Central Union

10.5. Livestock Cooperative Union

10.6. Uganda Consumer and wholesale cooperative union

10.7. Uganda Cooperative Alliance

**CHAPTER ELEVEN.**

**MARKETING BOARDS.**

11.1. Produce marketing board

11.2. Tea marketing in Uganda

11.3. Coffee Marketing board

CHAPTER TWELVE

AGRICULTURAL PLANNING

References

**DEDICATED TO KATE.**

**THE PRODUCTION FUNCTION.**

## 1.0. Introduction.

Improved agricultural systems need management skills such as planning and coordination of activities. Undesirable practices such as unbalanced utilization of resources, poor timing of activities lead to poor performance in the agricultural sector. Dynamic scheduling of activities, proper factor combinations, have limited production processes and production potential. Unpredictability changes within the changing environment as witnessed by hazards, weather, resource failure among other factors necessitates the dynamic scheduling systems to allow high conditions of production performance. Lack of efficient processes in regard to resources and activities that are coherent within the prevailing circumstances has always led to supply shock which ultimately affects other areas such as the industrial sector. Viability of agricultural production requires appropriate management strategies and adopting appropriate practices so as to maintain and increase the profitability of production ventures in a sustainable manner.

### 1.1. The classical production function.

In the neoclassical tradition a production function has been used as an important tool of economic analysis. It is generally believed that Philip Wicksteed (1894) was the first economist to algebraically establish the relationship between output and inputs, expressed as P= f(x1,x2,…,xn); where P is output and x1,x2,…xn are inputs, although there are some evidences that John von Thunen first formulated it in the 1940’s (Humphrey, 1997).

In farm management production functions are used to find out how the crop and livestock products we are producing are affected by inputs used in producing them. A production function is defined as the physical relationship between inputs and out put. It expresses the quantity of a product forthcoming from different quantities of one or more variable inputs when all other inputs used are constant. Stated in another way, a production function is a schedule of quantities of a product with corresponding quantities of one or more variable inputs used in its production. It is based on the idea that the amount of output production process depends on the bundle of inputs used in the process. The production function is known as the input out relationship, yields curve, response curve, TP curve and factor product relationship. The factor product relationship is one of the three basic relationships in production economics. The other two basic relationships in production around which decisions center are factor-factor and product-product relationship when the choice relate to an individual firm, the agricultural sector or the national economy. It is important to note that there are two major concepts of efficiency relating to a production system that include technical efficiency and allocative efficiency (Libenstein et al.,1988). The formulation of production efficiency problems of technical efficiency such as engineering and managerial concerns have been addressed and therefore focuses on allocative efficiency. This forms a reason why a production function is correctly defined as the relationship between the maximal technically feasible output and the inputs needed to produce that output (Shephard, 1970).

In 1767, Turgot in his work, *Observations on a Paper by Saint- P’eravy,* Turgot discusses how variations in factor proportions affect marginal productivities (Schumpeter, 1954). Malthus introduced the logarithmic production function (Stigler, 1952) and Barkai (1959) demonstrated how Ricardo’s was implicit. Ricardo used the production function to predict the trend of rent’s distributive share as the economy approaches the stationery state (Blaug, 1985).

A production function may therefore be expressed in three ways;

It can be expressed in form of arithmetic table where one column shows quantities of input used, another is corresponding quantities of total output of product. The two columns constitute the production.

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The classical production function.

The classical production function indicates the response to one variable input which is also referred to as the factor product relationship.

Y= (X1, X2, …. Xn)

The classic production function has three segments

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The production function has initial stage when production function will be increasing as you combine labor with the rest of fixed inputs namely land, machinery e.g tractors etc. This production process will be producing one product which could be cotton or milk or beans and the combination of labor and fixed inputs at this stage will be increasing as you combine labor with the rest of fixed inputs at this stage will be increasing as output increases at stage A until when you reach the point of inflection, point E, when production starts increasing at a decreasing scale. Prior to point E, production will be increasing at an increasing rate. Until we reach point F when increase in variable input leads to a decrease in total production.

Thus the classical production function has three stages in the production process. The first stage represented by A and the 2nd stage of increasing TPP at a decreasing scale and the last stage represented by C where TPP is decreasing.

In our example, it is rational to produce in stage B when the firm is experiencing the TPP but at a deceasing scale. The point at which production should be is stage B, will be determined by that point where maximum profits is realized in the production process. The increase in TPP in the first stage is brought about by the increase in MPP.

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The boundary between decreasing production at an increasing rate and increasing production at a decreasing rate is determined at a point where MPP=APP

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Output is at maximum 40 reflected by F. At this point MPP =0 implying it would be irrational to produce in stage 3 and also irrational to stop at stage 1.

When MPP>APP, APP is increasing and the APP is at maximum when MPP=APP. This is the point at which the MPP curve intersects the APP curve. When MPP<APP, APP will be decreasing. It should therefore be noted that even if the MPP has reached the maximum at the point of inflection and is declining the average productivity continues to increase as long as the MPP>APP.

### 1.2. The law of diminishing returns.

The law of diminishing returns states that in all production processes, adding more of one factor of production, while holding other factors constant, will at some point yield lower per unit returns (Samuelson & Nordhaus, 2001: 110).

Diminishing returns on the factors of production can be minimized. By doing so productivity for both the fixed and variable factors can be improved. Diversified farming practices can sustain agro-bio-diversity thereby reducing the need and use for off-farm inputs. For instance through composing and manuring, soils are produced that harbor diverse microbial and invertebrate species which in turn promote nutrient cycling (Mäider e tal 2002, Reganold et al, 1987). Farmers can achieve the well phenomena of “over yielding” through intercropping of nitrogen fixing legumes with grains i.e. higher production of each crop per unit area relative to the production in monoculture- thereby increasing yields while reducing or eliminating fertilizer inputs (Vandemeer, 1992). Intercropping enables a variety of different crops to grow together while utilizing different resources available (e.g. crops with different rooting depth can access a larger fraction of spatially stratified nutrients and water because one crop facilitates the growth of the other (Hauggard-Neilson and Jensen, 2005). Enhancing floral diversity on farms through insectary strips, hedge rows, or retention of semi natural areas, farmers may enhance or attract natural enemies and or wild pollinators to their crops and thereby increase pest control or reduce or eliminate the need for honey bee rentals (Kremen et al 2002, Morandin and Winston 2005, Letourneau et al, 2001). The supply of the mentioned ecosystem services e.g. soil fertility, pest control, pollination is critically dependence on the maintenance of the underlying biodiversity- from soil microcrobes to flora and fauna- and on their interactions (Altien and Nicolls 2004, Hooper et al 2005, Zhang et al 2007, Hajjer et al 2008, Sheman 2008, Jackson et al 2009). This calls for proper ecology and environment policy to accommodate biodiversity for the sake of agricultural productivity in particular.

**Economic optimum with a one variable input.**

The economic optimum occurs where a value of the MPP= cost per unit of variable input. Alternatively this same point may be defined as a point where the MPP= inverse (factor-product) price ratio. Profits are maximized at the point of economic optimum.

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In this example, let the variable input be labor and the product be maize, and then the price/unit of labor=$5, and price /kg = $1. The total cost of input is $10. So the inverse (factor-product) price ratio is $5/$1=5

It is also assumed that the input and output prices relate to a purely competitive situation in which the farmer has no control over prices. So the results of the costs and the values are as given in the table. In the example the economic optimum occurs at about 4 units of labor and this is where profit id maximized and the value of MP is most nearly equal to the unit factor cost

Below the 4 units of labor the value of marginal product in column 7 is greater than the unit factor cost in column 8 in the diagram. And at the levels of input above 4 units profit is decreased because the value of the MP is less unit factor cost. This situation can also be represented graphically as follows;

Profit B E

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In this example, the precise point of economic optimum occurs at almost 3.7 units of labor producing about 36 kg of maize. And on the response curve TC made up of the FC and increasing VC is represented by the straight line CDE. The difference between the TVP and the TC i.e BD is profit.

On the graph showing the curve of the value of MP unit factor cost is the same for each extra unit of labor as represented by the horizontal straight line.

**Forms of production function.**

The of farm management and production economics is normally carried out by using various production functions. These are constant returns, increasing marginal returns etc. These functions are depicted in the classical production function in our figure. In real life input-output relationships usually take on one or a combination of the following three forms;

- Constant returns.

- Increasing returns.

- Decreasing returns.

### 1.3. Constant returns (constant marginal returns)

Assuming that the factor costs are constant, under perfect competition in all input markets, a firm experiencing constant returns, will have constant long run average costs, and a firm experiencing increasing returns will have decreasing long run average costs ( Fisch, 1965, Ferguson, 1969, Gelles, Gregory M.,and Mitchell Douglas W, 1996).

The production function that has constant returns may be obtained when the quantity of TP increases by the same amount for each additional unit of variable input. This relationship between the input and output that has constant returns is also termed as linear relationship. The result curve when plotted is a straight line hence the name linear.

A hypothetical example

**Yield of maize at varying levels of nitrogen fertilizer application per hectare.**

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In example land is fixed at one hectare. Nitrogen is varied in 50kg units (bags) and the maize yield increases by 8 bags for each additional unit of bag.

In the production function we have equal increments in total increments for every extra unit of input, have linear functions that experience constant increasing returns.

These production functions are typical of the first stage of the classical production function where the firm experiences increase in TP production at an increasing scale. The linear production functions exist in agriculture where technical units of plants are readily divisible. Farmers with limited capital are often faced with a linear production function or constant returns to scale with a relevant range of credit or funds which they can obtain.

If a farmer has 10 hectares and a homogeneous land, he may apply 50kg of fertilizer input. This is possible because the 10 hectare farm is divisible.

Although constant productivity of the nature mentioned above is possible, a linear production function does not generally exist when inputs per hectare or per animal is intensified.

### 1.4. Increasing marginal returns.

Increasing returns to a single factor exist when each successive unit of input for a variable resource adds more to the total product than the previous unit as shown below;

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Land is fixed at one hectare while labor is varied in person hours.

**A production function showing increasing returns of maize yield per person hour of weeding labor applied per hectare.**

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Increase in labor adds more to the total maize per hectare. Examples of increasing returns in agriculture include;

- Increasing quality of fertilizer from the previously low levels.

- Increasing intensities of weeding from the previously low levels.

### 1.5. Diminishing marginal returns.

Diminishing returns to a variable factor exist when each additional unit of input adds less output than the previous unit. This is illustrated in the following table.

Yield of maize at varying rates of labor application per hectare ( hypothetical data).

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**Examples of decreasing returns in agriculture**

Decreasing returns is the commonest form of production function in agriculture and gives rise to the law of diminishing returns. The law of diminishing returns is encountered in practically all forms of production use e.g.

- Use of labor and a fixed unit of land.

- Crop responses to fertilizer application.

- Feeding cattle for milk production.

**Elasticity of production.**

Elasticity of production can be applied to the production function or to the input-output relationship. It is defined as a percentage change in output resulting from a percentage change in input. Elasticity of production is denoted by EP and it can be represented in the equation form as follows;

EP= ∆ Y/Y ÷ ∆X/X = ∆Y / ∆X . X/Y = MPPX/APPX

Where, ∆Y/∆X = MPPX, and Y/X = APPX

In stage 1 of the classical production function MPPX> APPX and as such EP >1

In stage 2, MPPX<APPX and 0< EP<1

In stage 3, MPPX is negative and EP is also negative.

The point of diminishing returns occurs when MPPX=APPX and EP =1. The amount of variable input at the point of diminishing returns is the minimum that would be rationally used because the efficiency of the input is maximum at that point. Thus using the definition of the diminishing returns it can be said that even without input and output prices, input use will always be extended to the point of diminishing returns. When the TPPX is maximum and MPPX=0 EP is also zero.

## CHAPTER TWO.

## FACTOR COMBINATIONS.

### 2.1. The factor product relationship.

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**More than one variable input.**

The classical production function gives the relationship between one variable input and other fixed inputs. In reality however more than one variable inputs are usually varied in production. The purpose of the classical production however is that it helps to illustrate the basic input output concepts. The farmer does not only vary the inputs but sometimes produces more than one product using the same resources e.g. beans and maize which are inter planted on the same farm use the same land, same labor and same implements e.g. hoes, pangas during digging and clearing the land.

**A two variable input and one product.**

The basic assumption that was made in the input output relationship where one input was varied was that the farmer has no control over the market prices. It was also assumed that at least one productive input was fixed in quantity so that all production processes are short run and subject to the law of diminishing returns.

**A production function relating output of maize in bags to various combinations of land and labor.**

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The table indicates the amount of maize that can be produced when different amounts of land and labor are used. These figures represent the production function relating the output of maize to the inputs of land and labor. The production function in this table can be regarded as a series of sub production functions. A production function in each row gives the amount of maize that can be produced with the fixed amount of land at that level.

The data used in the top row is the same as was used in the classical production function, so the MPPL is the difference between the two consecutive figures in the same row. On the other hand each column gives the amount of maize that can be produced by a fixed number of laborers when varying the hectares of land. The marginal product per unit of land is the difference between two consecutive figures in the same column.

### 2.2. Factor-factor relationship.

The study of the factor-factor relationship one of the five economic problems which confront agriculture producers, and which is how much to produce. In other words which method of production should be used or specifically what is the best method of combining the inputs in producing products at a target level of output. In using the economic approach to the solution of how to produce, how to produce, we select a method of production (combination of inputs) which would be the cheapest (less costly) in producing the chosen products. In this case maize are the target quantities.

The following selection looks at the various combinations of two variable inputs which will produce a given target level of output and how to select the least costly combination.

Let our target level of combination be 40 bags of maize. This level of output can be produced by a combination of 5 laborers and 1 hectare of land. These are various combinations which are not specifically precisely in the table but which would also produce 40 bags of maize. These intermediate combinations are given in the following table.

Isoquant and least cost combination for 40 bags of maize.

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In the above example the wage rate is $5 and land rent per hectare is $10,

Given that information, Inverse price ratio (IPR)= PX1/PX2= Price of labor divided by price of land.= 5/10= 0.5

Land and labor can be varied continuously as shown in the table and the data represent points on a smooth curve joining possible combinations of land and labor which yield one level of output; in this case 40 bags of maize. this curve is called the isoproduct curve. The curve is sometimes called the isoquality curve or an isoquant for each level of output as demonstrated in the figure below.

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In the figure a number of isoquants for 30, 40, 50 and 60 bags of maize are shown. This figure is similar to a contour map used in carrying out terraces in plotting topography in an area of land. Whereas contours on land represent different heights isoquants are product contours.

Characteristics of isoquants.

1. The slope of an isoquant at any point represent marginal rate of input substitution (MRITS). In our figure the slope of an isoquant at a given point shows the quality of land replaced by one extra laborer. The calculated rate of substitution of labor for land is given in the third column of the table. It is obtained by dividingthe increase in land i.e the increase in hectares of land by the increase in labor.

2. Isoquants generally have a negative slope. So the slope of the curve is negative of the marginal rate of input substitution. This is so because when we use more of one input we would expect to use less of other variable input in producing a given level of output. a proportion of an isoquant which slopes upwards and to the right represent the irrational area for production since the quality of output for the proportion of the isoquant can be produced with less for both inputs.

3. Isoquants for higher levels of output normally lie above and to the right of isoquant for lower levels of output. This means that it requires more of either or both inputs to produce more output.

4. Isoquants are convex to the origin. This means that the marginal rate of input substitution diminishes as more of one factor is used to replace the other. In our example each added unit of labor substitutes or replaces less land than the previous unit. The reason for diminishing rate of substitution is that one input is rarely a perfect substitute for the other. In our example labor cannot land and land cannot substitute labor to produce maize. Some land and some labor must be used to produce maize.

5. The spacing of the isoquant tells us the effects on TP of increasing inputs of both factors together. If isoquants are equally spaced it means that there is a constant returns as the two inputs are increased together. Where isoquants get closer there are increasing returns due to increased inputs for both factors. Conversely where isoquants become further apart implies diminishing returns to increases in both inputs.

**Least cost combination of inputs.(Economic optimum of two variable inputs).**

The least cost combination of inputs is the combination of variable input which will produce a given level of output at a minimum cost. The least cost combination can be estimated by using the MRT between two inputs as well as the respective prices of each input in order to determine the least cost combination which gives the least cost. This method is satisfactory when a few combinations produce a given output. In our example approximately 7 combinations of land and labor are needed to produce 40 bags of maize. The total cost of $5 per laborer and land cost $10 for 40 bags of maize, the least cost of $33 occurs when 3 or 4 laborers are used and between 1.3 and 1.8 hectares of land are used. The exact location of the least cost combination can be determined geometrically using the concept of MRTS and the least cost.

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The least cost combination of the isocost (least cost combination) can also be determined geometrically by drawing isoquant and isocost lines on the same graph as shown in the diagram. An isocost (i.e equal cost) line is that line which joins all combinations of the two inputs land and labor which could be purchased when a given sum of money i.e dotted line AB represent the isocost for $30. This sum could be used to hire 3 hectares of land and 1 unit of labor or 5 laborers and no land or any intermediate combination of land and labor along the straight line AB, joining these two points similar with line CDE represents an isocost line for $32.50. Every output level can be represented by an isoquant and any possible outlay (cost) can be represented by an isocost line.

Given that the least cost criterion is where the isocost line is tanget to the isoquant we can draw the isoquant and the isocost line and determine the amount of land and labor which wll give the least cost combination.

The formular for least cost combination is

∆X2/∆X1 = P1/P2

The MRTS X1X2 is represented by the slope of the isoquant and the right hand side (the inverse price ratio) by the isocost line. Thus the exact cost combination of the inputs occurs as the point where the isocost line is tangent ot the isoquant given that the isoquant is convex to the origin. In our example, the least cost combination for an output of 40 bags of maize occurs at point C in the figure where the total cost is $32.50 and X1= 3.24, X2=1.55 Units.

In any other combination of various inputs on this isoquant TC is higher. For a given set of relative prices you can stress out the least cost combinations for increasing levels of output. the line joining all the least cost combinations for a given set of prices is known as the expansion path.

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Mathematical treatment of least cost combination.

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The least cost criteria is as follows;

MRTS=P1/P2

Where P1 is the price of labor (wage) and P2 is the price of land

The MRTS of X1 for X2 = ∆X2/ ∆X1

And -∆X2/∆X1 =P1/P2 at the least cost combination.

-∆X2.P2= ∆X1P1

The MRTSis is represented by the slope of the isoquant and the right hand side of the equation i.e P1/P2 is the price inverse ratio which is the slope of the isocost line. Thus the exact combination of the input is where the isocost is tangent to the isoquant.

**MP and COST versus the least cost combination**.

The MRTSIS of X1 for X2 is defined as ∆X2/∆X1 i.e change in units of land divided by change in the units of labor.

For every level of output, X2 will decrease as X1 is increased. For a small increase in the amount of X1 (labor) the change in output generated by a change in labor is referred to as MPP1. Like wise a small decrease in the amount of X2 (land) the change in the output will be –MPP2. But if total output remains constant those two changes must be equal. Thus a change in X1 into MPP2. If we divide a change in change in X into MPP2.

We get MPP1/MPP2=-∆X2/∆X1=MRTS

Another question to be answered is whether the MRTSIS = inverse price ratio of the MPs and at the point of least cost combination the MRTS must be equal to inverse price ratios of the inputs.

MRTS =P1/P2 where P1 is the unit cost of X1 and P2 is the unit cost of X2 (land).

It follows from this ratio that the least cost combination occurs when the MPP per unit expenditure is the same for each unit e.g $1. If we multiply both sides be the same price PY, may not change the equality. This implies that;

MPPX1.PY= MVPX1

MVP1/P1=MVP2/P2

In order to obtain the least cost combination we must reach a point where the value of MP per unit of expenditure is the same for each input. Profit will be maximized at this point.

Profit will be maximized with the improved and increased use of technology. In some agricultural enterprises like water-short irrigated and rain fed areas a lot needs to be done to reduce water requirements and increase the productivity of the factors of production. Researchers are developing water saving technologies such as alternate wetting and drying, continuous soil saturation (Borell, et al, 1997), direct seed drying, ground cover systems (Lin et al, 2002) and a system of rice intensification (Stoop et al, 2002); but it is important to not that these systems have a loophole of prolonged periods of flooding and therefore water losses still remain high. The production system of rice without constant flooding, water in non-puddled soils , referred to as “aerobic rice” is considered and taken to be one of the most promising technologies in terms of water saving. In this system, rice is sown directly into dry soil and irrigation is given to keep the soil sufficiently moist for good plant growth, but the soil is never flooded (Bouman, 2001). In many societies however, especially the tropics, agriculture tends to depend on weather. Even when there is lot rain water during the dry weather, agriculture is greatly affected during drought. Irrigation is not used in these societies.

Other notable technologies, such as in areas where farmers have been able to grow more than one crop as a result of direct seeding, the benefits have been even more pronounced (Pandey and Velasco, 1999). Direct seeding offers such advantages as faster and easier sowing, reduced labor and less drudgery, earlier crop maturity, by 7-10 days, more efficient water use, less methane emission and often higher profit in areas with assured water supply than that of transplanting (Balasubramanian and Hill, 2000). It is reported in Brazil that high yields can be sustained when aerobic rice is grown once in four crops, but not under continuous mono cropping (Guimaraes and Stone, 2000). Aerobic soil conditions and dry tillage practices, beside alternate wetting and drying conditions are conducive for germination and growth of highly competitive weeds, which causes grain yield losses of 50-91 percent (Singh et al, 2006). In the tropics, upland price grown under favorable conditions typically reaches maximum yields of just over 4 tones per hectare (George et al, 2002). International Research Institute, Philippines started to develop tropical aerobic systems in 2001 by using existing improved upland and lowland germ plasm, yields a maximum of 5-6 tones per hectare, and water saving was 50-60% compared with flooded rice (Castaneda et al, 2000). Technology therefore plays a big role to maximize productivity of the production factors.

**Perfect subsititutes and complements.**

There are inputs which might be perfect substitutes e.g. fertilizers and compost manure and weeding female labor and male weeding labor. In such cases it is rational to use one of the inputs which is cheaper than the other. If compost manure is cheaper than fertilizers then compost manure should be used

instead of fertilizers. Similary whichever cheaper labor of men or female should be used. This can be illustrated by the following figure.

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In the example assume that X2 represents female labor and X1 male labor. This means that 1 ½ units of female labor are necessary to do the work of I unit of male labor. Similarly 3 units of female labor may substitute 2 units of male labor. Since male labor and female labor are considered as perfect substitutes the isoquants are straight lines. If we assume that men are paid twice the hourly wages of women; women should be employed for weeding other than men. The relative cost of weeding by women is 1.5×1=1.5 units and the relative cost of weeding by men is 1×2=2units. And thus total cost is higher if men are used. In our example the slope of the Isocost lines is P1/P2 =2, where P1 is the unit cost of X1 while P2 is the unit cost of X2. In this case the isocost lines are never equal to price ratios. The least cost method of production is therefore found at the end of an isoquant where it touches the lowest isocostline.

For the isoquant line AB the least cost is at poit A when 1 ½ units of female labor are utilized. All other points on AB lie on higher isocostlines and point B represent the most costly method of production.

**Perfect complements.**

At the other extreme from perfect substitutes are perfect complements among factors of production which implies that one factor is useless if it does not have its counterpart. A good example would be bicycle tyres with other bicycle parts. It might be difficult to increase production of bicycles using the steel parts without bicycle tyres. Another good example is agricultural labor and hoes. Hoes might be useless if there are no laborers to utilize them in the production process which means that if a farmer buys more hoes without hiring more laborers there will be no increase in production. Conversely if a farmer loses one of his workers, this worker’s hoe will not be productive. In cases of perfect complements there is a single least cost combination of inputs regardless of relative prices of the inputs. These fixed factor combinations will probably hold at all levels of output over a wide range of relative prices and ranges of output. The ratio of one hoe to one worker might be the cheapest. In such cases it is the best to think of two inputs together as a single resource in deciding the economic optimum level of output.

**More than two variable inputs.**

The rule for determining the least cost combination can be extended to more than two variable inputs. However the production function for more than two variable inputs cannot be drawn in two dimensions. The least cost combination of these resources is found when the MPP1/P1= MPP2/P2=MPP3/P3 where MPP represents marginal product and P represents the price per unit output of each input.

For more than three variable inputs,

MPP/1P1=MPP2/P2=MPP3/P3=…..=MPPn/Pn

The least cost combination of any number of inputs occurs where the marginal unit expenditure e.g. per $ is the same for all the inputs used in the production process. This then answers one of the production question, how to produce.

### 2.3. Returns to scale.

The law of diminishing returns applies when inputs of one or more factors are increased when the quantity of one factor is held constant. When all inputs are increased together (proportionately) there is a subsequent increase in scale and the law of diminishing returns does not apply. If two inputs are increased together by one percent we expect output to increase by the sum of their elasticities of their response e.g if elasticity of production of land is 0.2 and of labor is 0.6 and the both inputs are increased by 1% output will increase by 0.2+0.6=0.8%. similarly the effect of increasing all inputs by 1% (i.e increasing scale by 1% is obtained as a sum of all elasicities of response. This sum of elasticity of response is called the scale of =1, means that that a 1% increase in scale leads to an increase in output indicating constant returns to scale.

If the sum of elasticies is less than one this implies a decreasing returns to scale. If the sum is greater than one, there is an increasing returns to scale. There is an important consequence of constant or increasing returns to scale because if the prices remain constant there will be no economic optimum level of production. If all resources are varied together the farmer can go on obtaining resources and selling products at the same price. There is nothing to prevent him from increasing his profits by expanding his output indefinitely.

## CHAPTER THREE.

## THE CHOICE OF ENTERPRISES.

Production can also be used to solve the problem of what to produce. This is achieved by looking at the output output relationship for our enterprises, what can also be called enterprise combination. The comparison of the output-output relationship of enterprises also aims at maximizing profits from the two products. Most farmers are faced with a range of alternative crop or livestock enterprises that they can raise or produce. The problem arises in choosing between the different possible enterprises. This in turn involves the decision whether to concentrate on the production of one or two enterprises or whether to produce many. There is a choice to be made between a specialized and a diversified system of production. The economic principle for choosing what to produce is the principle of comparative advantage which states simply that each unit of resources should be used where they gain the greatest return. We have already discussed the fact that in the short run period, at least one but often more than one resources are fixed. This means that enterprises will compete for each other for some of the fixed resources so much so that the expansion of one enterprise must be accompanied by a reduction in another. As a result the number of enterprises that are profitable to combine in a farming system will be limited in some cases to just one enterprise. It should be noted that enterprises do not necessarily compete for all fixed resources e.g. even where the total amount land available is fixed. Swamp rice would probably not compete with sorghum for land because the two crops require different types of land. Similarly early maize may not compete with cotton for land since the two crops are grown at different seasons. This certain fixed resources are specific to individual enterprises while others may be allocated between enterprises.

**A single resource and two products; labor productivity in two competing enterprises.**

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The problem of finding the most profitable enterprise combination if found in the following hypothetical example. In this example the production of ground nuts is compared with the production of maize using labor. i.e. ground nuts and maize production are competing for labor of the farmer and his family which amount to seven workers. It is assumed that other resources specific to each enterprise are fixed so that as labor inputs are increased marginal returns diminish. i.e the law of diminishing returns applies. It is also assumed that the farmer buys and sells in a purely competitive market under a situation of perfect certainty. The total product and MPPs for labor in each of the two enterprises are given in the table. In order to find out the optimum combinations of the two enterprises prices are applied to give the marginal products for labor. Let’s assume that maize is priced at $1 per bag and groundnuts at $3.50 per bag. To give the results in the following table.

**Marginal value products in the two alternative enterprise.**

illustration not visible in this excerpt

The wage rate for labor in alternative occupations is $5 for laborer which is taken as unit factor cost. The economic optimum level of labor use in maize production occurs at about 4 laborers where the MP is $6. Since only 7 units of labor are available then the use of 4 laborers in maize production will leave 3 laborers for ground nuts production. In our example the economic optimum level of labor used in ground nuts production occurs at between 5 and 6 laborers where the MVP is equal to the unit factor cost of $5.

Clearly then the two enterprises compete for the scarce resources and hence labor has an opportunity cost within the firm starting from the point where 3 laborers are used in ground nut production, the MVP of one more unit of labor is $21. The opportunity cost expressed by the loss in value of maize caused by removing the 4th laborer used in maize production enterprise is $6. This transfer will add to the profits since maize benefits exceed extra costs. In fact the principle of comparative advantage tells us to use this unit of labor in ground nuts production since it is where it adds most to the returns.

If another unit of labor is transferred from maize to ground nuts production, the MVP is $17.50 and the opportunity cost is $11. Thus transfer of labor is still profitable since the gain is greater than the cost. It should be noted that because the total amount of labor is limited its opportunity cost at $11 is now well above the wage cost of $5. Now 5 laborers are used in the ground nuts production and 2 laborers in the maize production. The transfer of yet another laborer to ground nuts production will not increase profits since the gain would be only $3.50 and the opportunity cost of $13. There is therefore no longer the comparative advantage to ground nuts production. Thus most profitable combination of the two enterprises occurs where about 5 units of labor are used in the ground nuts production and about 2 laborers in maize. The same conclusion is reached if we consider unit by unit increase in labor input. To maximize profits each laborer should be used where it will add most returns. Therefore the first unit should be used in ground nuts production where it will earn $21.

Similarly the 2nd, 3rd , 4th, and the 5th laborers should all be used in ground nuts production. However the 6th laborer would earn only $6.0 in ground nuts production, whereas if used in maize production will earn $7. Thus this laborer should be used in maize production. The 7th laborer should also be used in maize production where he/she will earn $13 as opposed to $3.50 he/she will earn if used in ground nuts production.

If the labor inputs in either enterprises should be varied continuously then one most profitable situation could occur where the MVP is equal in each enterprise. Since the steps in which labor is varied are quite large in our example the MVPs are not equal.

The principle involved in allocating between alternative use in enterprises sometimes is known as the equal marginal returns.

Thus if P1 is the price per unit of Y1 and P2 is the price per unit of Y2, MP1 is the MPPX in production of Y2. The point of equal marginal returns (the point of maximization of profit) can be expressed as follows;

MPP1(P1= MPP2(P2)

But MPP times price per unit equals MVP. Therefore the above equation can be rewritten as;

MVP1=MVP2

i.e the MVP of X in producing Y1 = MVP of X in producing Y2

### 3.1. Production possibility curve.

The production possibility curve is the line joining possible combinations of outputs such as Y1 and Y2 that can be produced with a fixed input such as X. the hypothetical example shown above may be approached by using the concept of the production possibility curve. We have a variable input X (labor) which can be used to produce Y1 (maize) and Y2 (ground nuts) and all other inputs in the production of Y1 and Y2 are fixed. Thus the farm manager must determine how much of input X should be used in producing the products. The first relevant question is, how much of the input will be available? The two possible situations are

a) Unlimited.

b) Limited.

### 3.2. Unlimited variable input situation.

When the amount of available input is unlimited resource allocation is determined by equating the price of input (unit factor cost PX) to the MPP, MPPX, or the MVP , MPPX(PY) in each enterprise. Thus the farmer can use the optimum amount of input in both enterprises. One enterprise will not reduce the amount available in the use of another. In this case the two enterprises will not be competing with each other in use of input. The term unlimited means that the farmer has the sufficient quality of input to use up to the point of economic optimum in all enterprises. It does not actually imply unlimited supply of input is available and hence the input is a free good. If the supply of the input was unlimited in the sense that it was a free good then the farmer would use the input up to the point of economic optimum of the enterprise i.e where the MPP would be zero in each enterprise, where the TPP is at maximum level.

### 3.3. Limited variable input situation.

When the amount of input is limited optimum amount cannot be used in each enterprise. Thus by definition limited means that the total amount of input available is less than that amount needed to be applied up to the amount to be used. The primary purpose of the production possibility curve is to determine the most profitable combination of enterprises in input. In our example we will consider the alternative combination of maize and ground nuts produced with a fixed amount of 7 laborers. If all the 7 laborers are used in maize production no labor will be available for ground nuts production. If 6 laborers are used in maize production then 1 laboerer will be available for ground nuts production. Thus the combination of ground nuts and maize which will be produced with different allocations of 7 laborers may be shown as below.

**[...]**

- Quote paper
- DOCTOR Akampurira Abraham (Author), 2013, Principles of Agricultural Economics, Munich, GRIN Verlag, https://www.grin.com/document/232004

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