# 5. MICRO-ECONOMIC ANALYSIS OF PRODUCTION

5.4 Average Cost Curve in the Long Run

5.4.1 Cost curves in the long run for actual plants

5.5 Micro-economics Applied to a Whole Fishery

5.5.1 Mathematical models for evaluation of the fish resources

The production function appears in the micro-economic analysis as one of the two determining factors of the economic sustainability of the firm. A businessman aiming at a state of equilibrium in his business, trying to maximize his profits in the short run, must simultaneously consider the technological characteristics of his installations and possible ways of using them to produce. The cost of the production process must also be considered.

The first factor is formally expressed through a production function. In any given country, a specific production technique exists, based on existing installations in the various productive sectors, production processes, different forms of organization, business management and division of labour. This situation can be functionally represented by a relationship that links the value added during production, or the domestic product, to the quantities utilized from the different productive factors. These concepts constitute the aggregate production function for each sector, e.g., the aggregate function of frozen fish plants.

Knowing the production function of each sector of the fishery industry enables formulation of a response to future changes that might occur, such as: reduction of labour force, scarcity of a particular species, technological innovations. It can be utilized determine to which point it is possible to substitute one input for another. It can also be used to determine the level of operation of the plant that would constitute maximum production efficiency.

The aggregate production function can also be used as an instrument to compare the efficiency of international production and the relative price structure of products in different countries. This section looks at-various properties of the production process of a firm and introduces factors that govern the selection of production technologies. The type of production process and the properties of the production function of the company will be specifically examined.

Attention should also be paid to the role of technology and technological advances in changing the capacity of the company to produce goods and services, and the pressure on the firm to adopt new technologies.

Production is a series of activities through which inputs or resources used (raw material, labour, capital, land and managerial talent) are transformed into products (goods or services) over a specific period of time. Economists use the term production function to refer to the physical relationship between inputs utilized by the business and its products (goods and services) per unit of time (Henderson and Quandt, 1971). This relationship can be expressed symbolically as:

Q = f(Xa, Xb, Xc,… Xn)                                             (5.1)

where Xa, Xb, Xc,… Xn represent quantities of different types of inputs and Q the total quantity of product per period of time, for specific combinations of these inputs. There is a production function for each methodology. A company can modify the quantities of the product it generates by varying the quantities of the resources that it combines according to a productive technique, changing from one technology to another, or using both operations. It is assumed that companies use the most efficient technique such that it achieves maximum production of each alternative combination of inputs.

## 5.1 Production Function in the Short Run

The following parameters, which are relevant to this analysis, are defined in the micro-economic treatment of the production function:

A fixed input (F1) is defined as that input whose quantity cannot be quickly changed in the short run, in response to the desire of the company to change its production. Inputs are not fixed in the absolute sense, even in the short run. In practice, however, the cost of implementing changes in a fixed input can be prohibitive. Examples of fixed inputs are: pieces of equipment or machinery, space available for production, management personnel.

On the other hand, variable-inputs (VI) are those inputs whose quantities can be easily changed in response to the desire to increase or reduce the level of production, for example, electricity, raw materials, direct labour. Sometimes variable inputs are limited in variation due to contracts (e.g., steady supply of raw material) or law (e.g., labour laws); in such cases it is possible to talk of semi-variable inputs (SVI).

The short run (SR) is the period in which the company cannot vary its fixed inputs. Nevertheless, the short run is long enough to allow variation of the variable inputs. The long run (LR) is defined as the period that is long enough to allow the variation of all inputs, none of which are fixed, not even the technology. For example, while in the short run a firm can increase its production by working extra hours, in the long run, the company can decide to build and expand its production area to install capital-intensive machines and avoid overtime.

The quantity of fixed input's in a plant is a determining factor of the scale of operations. This scale of a plant determines in turn the maximum production limit per unit of time that the company is capable of producing in the short run. Production can vary in the short run, by reducing or increasing the use of variable inputs in relation to the quantity of fixed inputs. In the long run, production can be increased or decreased by changing the scale of production of the plant, the technology used and the use of all or any of the inputs. To analyse the short-term production function, the following concepts must be defined:

Average Product (AP) is the total production per unit of input used, and marginal product (MP) is the change in the quantity produced per unit of time, resulting from a unit change in the quantity of the variable input. The shapes of the AP and MP curves determine the shape of the corresponding production function or total product (TP).

The principle of diminishing marginal returns is related to the quantities of product that can be obtained when increasing quantities of variable inputs per unit of time are incorporated into the production process and combined with a constant quantity of fixed input. The principle establishes that a point will be reached where the resulting increases in the quantity of output will become smaller and smaller. When the average product is increasing, the marginal product is greater than the average. When the average product reaches its maximum point, it is equal to the marginal product.

Before reaching the inevitable point of decreasing marginal returns, the quantity of end-product obtained can increase at a growing rate, as shown in Figure 5. 1. Above the inflection point of the production function, a greater use of the variable input induces a reduction in the marginal product. A production function and the associated AP and MP curves can be divided into three stages, as illustrated in Figure 5. 1. Figure 5.1 Production Function in the Short Run and the Corresponding Marginal and Average Production Functions

Stage 1 extends from zero units of variable inputs (VI) to the point where the APVI, is at its maximum (DAR). Stage 2 extends from the (DAR) to the point where the quantity of product is maximum and the MP is zero (DTR). In Stage 3, from (DTR) onwards, the total product is decreasing and the MP is negative.

These stages have a special significance in analysing the efficiency with which the resources are used. The maximum of (MP) vs (xVI ) defines the point DMR, from there onwards an increase in (V1) will mean a decrease in (MP). The first stage corresponds to the range in which the AP is increasing as a result of utilizing increasing quantities of variable inputs (raw material, labour, etc.).

A rational producer would not operate in this range, because (FI) (equipment) is being under utilized. That is, the production expected from the use of more man-hours, for example, is increasing through stage 1, which indicates that the same production could be obtained with a lower quantity of fixed input. Production is also impractical at stage 3. Additional units of VI actually reduce total production.

If the efficiency of the production process is measured by the average product, which indicates the quantity of product obtained per unit of input, the previous discussion reveals that stage 2 is the best from the point of view of efficiency. In stage 1, a very small proportion of (VI) is being used when compared with the (FI). Efficiency considerations will lead to a preference to produce around the border of stages 1 and 2.

## 5.2 Basics of Returns to Scale

The production function of the firm has been analysed in the short run, where a proportion of the firm's resources are fixed. The concept of returns to scale occurs when the company is producing during a period long enough to allow changes in any and all of its inputs, especially those usually fixed in the short run.

Returns to scale are defined for cases where all the inputs are changed in equal proportions. In the case of a firm using X, units of input 1 along with X2 units of input 2, and obtaining Q units-of product, the relation can be written as: (5.2)

Now suppose that the quantities of inputs X1 and X2 are varied by an arbitrary proportion g . Total production obviously will change. The question is in what proportion will it change? If this proportion is called p , the result is: (5.3)

1. If the change in production is more than proportional to the change in inputs (pg ), increasing returns to scale

2. If p = g , constant returns to scale

3. If p < g , decreasing returns to scale

For the same technology, it is usually certain that on expanding its scale of operation, the company will have:

1. A short period of increasing returns to scale

2. A long period of constant returns to scale, and,

3. A period of decreasing returns to scale

A company can increase use of its inputs to the point of maximum production; further increases of. inputs can produce a stage of negative yield, where production actually decreases. However, if the concept of returns to scale is used to allow changes in the technological capacity of the firm, and its size increases, companies can be (and they certainly are) capable of applying all their tools and new technologies for expanding their scale of operations without ever reaching the point of decreasing yields.

Firms with a prolonged period of constant returns to scale are common in food and fish processing.

## 5.3 Basics of Cost Functions

A fundamental point in the analysis of costs is the functional relationship that exists between costs and the production for a period of time. A cost function presents different results when the plant works with different percentages of utilization. But, as previously indicated, production is a function of how resources are used.

Thus, as the production function establishes the relationship between inputs and product, once the prices of the inputs are known, the costs for a certain production can be calculated. As a result, the level and performance of the costs of a plant, as the level of production varies, are directly related to:

1. The characteristics of its own production function

2. The purchase prices of its inputs

### 5.3.1 Total costs and unit costs

Three concepts of total costs are important to analyse the structure of costs in the short run: total fixed costs; total variable costs; and total costs.

Total Fixed Costs (TFC) can be defined as the total sum of the costs of all the fixed inputs associated with production. As the fixed inputs for a firm cannot be changed in the short run, the TFC are constant, except when the prices of the fixed inputs change (greater taxes on property, increases in insurance premiums, etc.). Also, TFC continue to exist even when production is stopped.

Similarly, total variable costs (TVC) represent the total of all the monies that the firm spends on variable inputs used in production. As the company changes its level of production in the short run, variable costs depend on the quantity produced. The TVC is zero when production is zero in that the variable inputs are not needed at that point. Thus:

TC = TFC + TVC                                             (5.4)

This expression indicates that the total costs for a given production in the short run, is the sum of the total fixed costs and the total variable costs. The following four unit costs are relevant: average fixed cost (AFC), average variable costs (AVC), average total cost (ATC) and marginal cost (MC). Average Fixed Cost is defined by the quotient between total fixed cost and the units of production:

AFC = TFC/Q                                                 (5.5)

As the total fixed cost is constant, the average fixed cost decreases as production increases; that is, the same fixed costs are distributed among more units produced. The AFC can also be calculated in the following way: the TFC is the product of the number of units of fixed inputs (FI) by the price of these inputs (PFI ). Substituting this in the expression 5.5:

AFC = TFC/Q = (PFI) x (FI)/Q= PFI x (FI/Q)             (5.6)

Since the average product of the fixed inputs has been defined as the total quantity produced (Q) divided by the number of units of fixed inputs (FI), it follows that FI/Q is the inverse of APFI.

AFC = PFI x (l/APFI)                                                 (5.7)

Average variable cost is TVC divided by the corresponding number of units produced, or:

AVC = TVC/Q                                                         (5.8)

Similarly, the AVC can be expressed as an inverse function of APVI:

AVC = TVC/Q = PFI x (FI/Q) = PVI x (l/APVI )          (5.9)

Average total cost is defined as the total costs divided by the corresponding number of units of Q:

ATC = TC/Q                                                              (5.10)

However, through Equation 5.4:

ATC = TC/Q = (TFC + TW)/Q = TFC/Q + TVC/Q = AFC + AVC

Marginal cost is the change in total costs caused by a change in the quantity of product per unit of time. As before, a distinction can be made between discrete and continuous marginal costs.

Discrete marginal cost is the change in total cost related to a 1 unit change in the quantity of the product. Continuous marginal cost is the rate of change in the total costs as production varies, and can be calculated as the first derivative of the total cost function:

MC = dTC/dQ (continuous marginal cost)                                 (5.11)

However, given that in the short run, variation in production can only be attributed to variations in variable inputs, it is the same as measuring the variation in the discrete marginal cost by the variation observed in the total costs or in the total variable cost. Thus:

MC = dTVC/dQ (continuous marginal costs in the short run)         (5.12)

Also, the MC is related to the production function. Given that changes in production in the short run are produced by increases or decreases in the variable inputs (VI), the changes in the TVC ( TVC) can be calculated by multiplying the price of the variable input (PVI) by the change produced in the variable input ( VI). Thus: TVC = PVI x VI                                                 (5.13)

Substituting. this in 5.12 and by the definition of marginal product:

MC = PVI x (l/MP)                                                     (5.14)

The marginal costs are of fundamental interest as they reflect those costs over which the firm has most direct control in the short run. It indicates the magnitude of the costs that must be saved if production was reduced by one unit, or, alternatively, the additional costs that would be incurred by increasing production by one unit.

Average costs data do not reveal this very valuable information. All of these concepts can be applied to analyse the performance of a company and its different production functions. However, it is necessary to analyse in particular the total, average and marginal cost functions for the production function in the short run, with increasing and decreasing returns in function of variable inputs. The mathematical expression in this case is:

Q = a + b x (VI) + c x (VI)2 - d x (VI)3                           (5.15)

where Q is the quantity of the product and (V1) the units of variable inputs, a, b, c and d are constants. The results are shown in Figure 5.2. Note the characteristic 'S' shape of the total cost curve. Figure 5.2 Total, Average and Marginal Costs for a Plant with Increasing and Decreasing Returns to Variable Inputs

The application of these criteria to food plants (Figure 5.3) resulted in a non-linear response for semi-variable cost curves (Zugarramurdi and Parin, 1987b). Figure 5.3 Variation of Relative TSVC (f) as a Function of Relative Plant Capacity (S)or Food Industries

Notes:

·Long Run, extended economies in food plants: canned green beans, green peas, leafy vegetables; pumpkin and peas, canned fruit juice; canned fish.

o Long Run, freezing plants: vegetables; strawberries. Long Run, agricultural production: pears, lemons.

* Short Run, canned fish.

Total semi-variable costs (TSVC) are defined as the variable costs that are not directly proportional to output like administrative services, maintenence and supervision.

### 5.3.2 Cost curves in the short run in the fishery industry

The cost of operating a plant at lower capacity can easily be estimated if the cost structure of a plant operating at full capacity is known. In Table 5. 1, the relationship between the unit cost of production for a plant operating at a certain capacity and the costs of the same plant operating at full capacity, have been calculated for different cost structures. Values are given in the lower part of the Table 5.1 for fish plants, in accordance with the cost structures in Table 4.16 (Chapter 4).

Table 5.1 Production Costs as a Percentage of Operating Capacity

 % Structure of Annual Costs at 100% of Capacity Relationship of Relative Unit Cost with Capacity Indicated with Respect to Unit Cost at Full Capacity % Operating Capacity Plant Type Variable Fixed 20 40 60 80 100 A 90 10 1.40 1.15 1.07 1.03 1.00 B 80 20 1.80 1.30 1.13 1.05 1.00 C 70 30 2.20 1.45 1.20 1.08 1.00 D 60 40 2.60 1.60 1.27 1.11 1.00 E 50 50 3.00 1.75 1.34 1.14 1.00 F 40 60 3.40 1.90 1.41 1.17 1.00 G 30 70 3.80 2.05 1.48 1.20 1.00 H 20 80 4.20 2.20 1.56 1.23 1.00 I 10 90 4.60 2.35 1.63 1.26 1.00 FISH PLANTS Canned Products 78.0 22.0 1.89 1.33 1.15 1.06 1.00 Salted Products 81.5 18.5 1.74 1.28 1.12 1.05 1.00 Frozen Products 82.0 18.0 1.72 1.27 1.12 1.04 1.00 Fishmeal 86.0 14.0 1.56 1.21 1.09 1.03 1.00

Fish plants clearly have a high incidence of variable costs. These are specifically raw material and intensive labour. This simplified treatment relates the variation of all variable and semi-variable costs with the utilization of the plant, although, as stated previously, semi-variable costs do not necessarily vary linearly with production in the short run. However, the low proportion of these costs on total costs allows for this estimate (Zugarramurdi, 1981a).

Values are shown in Figure 5.4 where the curves for cost structures A and I have been drawn as broken lines and those for fish plants as continuous lines. Figure 5.4 Variation of Relative Unit Cost (RUC) for Different Levels of Production in Fish Plants (A and I cost structure defined in Table 5. 1)

## 5.4 Average Cost Curve in the Long Run

As fixed inputs no longer exist in the long run, the distinction between fixed and variable inputs disappears and there are no TFC or TVC curves. It is only necessary to look at the shape of the average cost curve in the LR. Suppose the technological restrictions allow a firm to choose between the construction of three plants of different sizes: small, medium and large. The sections of three short run average cost curves that identify the optimum plant size for a given level of production are shown as a continuous line in Figure 5.5. Figure 5.5 Average Total Cost Curve (ATC) in the Long Run for Three Possible Plant Sizes

The continuous line in Figure 5.5 is called the average cost curve in the long run (LRAC) and shows the minimal unit cost for any production when all the inputs are variable, and any size plant can be constructed. The dotted lines of the short run average cost curve (SRAC) curves always refer to greater costs at each production than what can be obtained with plants of other sizes.

The final selection will depend strongly on the market demand and the demand tendencies of the consumer, which generally favour large sized plants when planning for the future. On the other hand, the medium sized plant could be more attractive because of its smaller capital investment requirements. Usually, the firm will have more than three sizes from which to choose. When the number of options is large, the LRAC curve is tangent to the SRAC curves (see Figure 5.6). Figure 5.6 Average Cost Curve in the Long Run for Plants of Any Size

The most efficient of all possible plants is that whose SRAC curve is tangent to the LRAC curve at the lowest point. Figure 5.6 gives the optimum size plant on the SRAC4 curve.

### 5.4.1 Cost curves in the long run for actual plants

In practice, there are different shapes for LRAC and the reasons for that and how they relate to plant capacity should be analysed. The first possibility to be analysed is that of industries where the AC decrease steadily with Q. It can be seen that at high volumes of production there is a large sub-division of the productive process and a specialization in the use of inputs such as raw material, labour and supervision.

A direct consequence of this is an increase in efficiency and a reduction of costs. Also, large plants can, as a result of their volume of business, secure large discounts on the prices of raw materials and therefore offer their customers better conditions of sale, thus penetrating the market.

There are also advantages at company organization level, since administrative and managerial personnel are shared by different production units. A large firm, whether through vertical integration or by diversification, can deal with changes in the market such as sharp increases in prices, scarcity of raw material or technological innovation. These economies of scale are extremely important and cause the LRAC curve to decrease for the large production range. Examples are automobile, aluminum, steel, paper, aviation and farm machinery plants. In the food industries, some vegetable canneries, juice plants and fish canneries are cases in point (Figure 5.7). Figure 5.7 Average Cost Curves in the Long Run, with Optimum Plant Scale Case of Extended Economies

In some industries increases in size tend to create problems. This is because diseconomies of scale are created by growing difficulties at the managerial level, which consume more time and money, and produce problems concerning the inputs and their supply.

Figure 5.8 shows an LRAC curve for these businesses when dis-economies of scale occur at low production levels; for example, agriculture, printing, bakeries, electronics, instruments, and non-alcoholic drink bottling. Examples in the food sector where small-scale firms have cost advantages over large-scale enterprises, include frozen vegetables processing plants. Figure 5.8 Average Cost Curves in the Long Run, with Optimum Plant Scale. Case of Early Dis-economies.

Figure 5.9 shows a LRAC curve with a flat bottom, which implies constant returns to scale over a wide range of capacities. Examples are: home appliances, furniture, textiles, chemical industries, and meat, fruit and vegetable packaging. Figure 5.9 Average Costs Curve in the Long Run, with Optimum Plant Scale. Case of Constant Average Costs.

Example 5.1 Production Costs in the Short and Long Run for Industrial and Artisanal Fishmeal Plants

Calculate and compare the production costs in the short and long run for fishmeal plants: artisanal plants in Africa and large-scale plants in Europe.

A small plant is operating in Africa with a capacity of only 100 kg of raw material/day (with a 20% yield). This plant uses simple technology in order to adapt to the characteristics of the area in which it is located. Cooking is done indoors and drying is by solar energy (Mlay and Mkwizu, 1982). On the other hand, large scale plants are operating in developed European countries, working efficiently with large capacities, using technologies that include plants for concentrating stickwater (Atlas, 1975).

In general, when production costs are analysed, the concept of economy of scale would seem to indicate that the plant with the greatest level of production is the most suitable. However, some economic studies (Cerbini and Zugarramurdi, 1981b) show that in developing countries the level of productivity that is the norm in more industrialized countries could be assured even when the entire market is being supplied by a single factory.

These circumstances indicate the existence of a special technical problem in developing countries, which is the application of processes that permit improvement in productivity for smaller scale operations.

The application of these procedures, which are considered classical in developed countries, leads to excessive operating costs and lower production efficiency in countries with small markets.

Figure 5.10 shows the costs in the short and long run for both economies. Figure 5.10 (a) Production Costs in the Short and Long Run for Fishmeal. Plants; (b) Production Costs in the Long Run for Fishmeal Plants; (c) Relationship Between Investment and Raw Material Processing  Capacity (US\$/t RM)versus Production Capacity (t).

It is clear that use of appropriate technology in each country or region results in lower production costs and efficient use of local inputs. Operating costs behave in a manner consistent with the concept of economy of scale.

Artisanal plants can be installed with the technology best suited to a particular country in accordance with the availability of inputs. The result is considerably lower production costs. However, depending on the type of product and process, there could be technical and economic reasons that render these alternatives non-viable when production capacity should be increased.

For example, labour costs increase considerably when there are large volumes to be processed, as is the case with natural drying. It is not possible to control insect infestation efficiently, and raw material is lost, with a consequent increase in total cost of production. When all these factors are quantified, the actual cost curve for artisanal and industrial fish meal production would assume a shape like that drawn by a broken line in Figure 5. 11.

In this situation, both types of production - artisanal and industrial - could even coexist, as is the case in Tanzania with the production of fishmeal from Haplochromis spp. in Lake Victoria in the 1970s and 1980s (the industrial fishmeal production ceased when the Haplochromis fisheries collapsed following the introduction of Nile perch in Lake Victoria. Figure 5.11 Average Cost Curves in the Long Run for Artisanal and Industrial Fishmeal Plants

Example 5.2 Analysis of Average Cost Curves in the Long Run for Small Fishing Vessels in West Africa

Analyse the economies of scale for small fishing vessels of the west coast of Africa: (a) Ghana; (b) Côte d' Ivoire; and (c) Senegal according to the data provided by Frielink, 1987.

(a) Ghana. The sardine fisheries (Sardinella spp.)

Two types of fishing vessels are used for the exploitation of sardines in this region; some are less than 12 m long and others between 12 and 22 m. Thirty-two vessels, representing approximately 10% of the total fleet registered in 1983, were studied. They were categorized according to three different size groups: 0 m-9.9 in, 10.0 m-18.3 m and 18.4 m-30.5 m. The groups contained 7, 14 and 11 vessels respectively. Analyse the costs of fishing given in Table 5.2 for each group. Variable costs represent approximately 75 % of total costs; a result that holds true for many other fisheries. Fuel represents about 30 % of total cost.

Answer: It can be seen that the largest vessels (C) are the least profitable. Gross income, which is 13.5% greater for the (C) vessels when compared with the (B) vessels, does not compensate for the 19.6% increase in production costs.

Table 5.2 Catch, Income, Costs and Profitability of Fishing Vessels in Ghana

 Vessels Small (A) Medium (B) Large (C) Catch (t/year) 178 208 236 Gross Income (US\$/year) 33 820 39520 44 840 Investment (US\$) 47 150 58 720 65 675 Total Costs (US\$/year) 29455 34742 41 546 Average Costs (US\$/year) 165 167 176 Rate of Return (%) 5.67 4.77 1.6

The average cost values have been plotted in Figure 5.12. Note the occurrence of early dis-economies of scale. Figure 5.12 Average Cost Curves in the Long Run for Fishing Vessels in Ghana

(b) Côte d 'Ivoire. The sardine fishery in Abidjan

Sixteen vessels between 18.4 and 28.8 m long operated in the Côte d 'Ivoire in 1983. They were wooden motorized boats built in Abidjan, with no refrigeration system. For the purposes of this study, they were divided into two categories: small boats, about 240 lip; and large boats 450 hp.

As there were large differences in the performance of the individual boats in each group, average values were selected, instead of using typical boats. The total number of trips in 1983 was 110 and 122, respectively, with total catch of 1425 and 1723 t. The costs and profits of this fishery are shown in Table 5.3.

Table 5.3 Catch, Income, Costs and Profitability of Vessels in Côte d 'Ivoire

 Small Vessels Large Vessels Capture (t/year) 1 425 1 723 Gross Income (US\$/year) 422716 513 853 Average Costs (US\$/t) 229.5 256.2 Rate of Return(%) 15.8 7.4

The difference between sizes (A) and (B) is not great in terms of profitability, but the medium-size vessel is probably a better investment as it is supposed that it will have more possibilities and a wider range of action (Frielink, 1987).

Answer: Figure 5.13 shows that average costs present early dis-economies, and demonstrates that profit for large vessels is 35 % lower than for small vessels. Figure 5.13 Average Cost Curves in the Long Run for Fishing Vessels in Côte d 'Ivoire

As in other fisheries, variable costs represent about three-quarters of the total. There are no great differences in the cost structure of either class of vessel, except for fuel and lubricants, and interests. In large vessels, fuel costs are relatively high and, due to a larger investment, must support substantially higher interest payments.

Historically, the costs of large vessels have been almost double those of smaller vessels. Production and income per fisherman are 10% lower for large vessels, indicating a decrease in productivity as motor power - common in this activity - increases. Also, the aggregate value per fishing vessel is higher for the large vessels, due mainly to the high interest paid. The rate of return is acceptable for small fishing vessels and more than the bank rate. This is also true for large fishing vessels, although 7.4% is too low for the risk involved in the activity (Frielink, 1987).

(c) Senegal. The small pelagic fishery in Dakar

The purse seiners of the Dakar fleet are composed of different types and sizes of fishing vessels. The sizes vary from 22 to 256 t gross weight, with motors ranging from 110 to 600 hp. The old fishing vessels are made from wood and the newer ones of fibreglass. Table 5.4 shows the composition of the fleet, with the vessels grouped into four classes.

Table 5.4 Characteristics of the Purse Seiners Fleet in Dakar (Senegal)

 Class Construction Material Catch 1983 (t) Catch per Trip (t) No. of Trips Per Year Members of crew Investment(US\$) C1 Fibreglass 392 3 140 10 157480 C2 Fibreglass 1 370 5.5 249 16 289000 C3 Wood 1 159 6.1 190 20 525000 C4 Wood/Steel 2200 11.0 200 24 630000

Table 5.5 shows the costs and income of the four types of boats for 1983.

Table 5.5 Catch, Costs and Profitability of Fishing Vessels in Senegal

 Type of Vessel C1 C2 C3 C4 Catch (t/year) 392 1370 1159 2200 Gross Income (US\$/year) 55559 194173 164268 311811 Average Costs (US\$1t) 169.4 117.0 188.6 141.9 Rate of Return - 8.4 - -

Answer: The cost structure is somewhat different from the other fisheries. Total variable costs are less than 75% of the total. The main reason is that the fishing effort is unusually low. The fishing vessels must operate 250-280 days/year. Also, due to the short trips, fuel costs as a percentage of the total are 11-18%, instead of the 25-30% observed in other fisheries. The salaries are relatively high as they are partly fixed. An analysis of Table 5.5 shows that only the C2 vessels operated profitably in 1983. The other vessels, e.g., C3 reported sizable losses.

The main reason for the high profitability of the C2 vessels in relation to the other type of vessels seems to be the number of trips made. C4 vessels suffered losses in spite of their high catches, probably due to their high depreciation costs. Figure 5.14 shows the average costs for the four types of vessels. Observe that the medium fibreglass boats are most suitable. Figure 5.14 Average Cost Curves in the Long Run for Senegalese Vessels

Example 5.3 Analysis of Economies of Scale in the Production of Fishmeal. and Fish Oil in Oman (Amesen and Scharfe, 1986)

A significant resource of mesopelagic fish with a high productivity rate has been found in the Gulf of Oman. Each trawler can catch an average of 60 t/day of fish, 250 days/year, for possible use as raw material in a reduction plant. These figures are conservative, as trawlers can land above average catches when fish is abundant. Analyse and choose the most suitable daily raw material capacity between two plants whose nominal capacities are 250 and 500 t/day.

Answer: A study was made of reduction plants with capacities of 250 and 500 t raw material per day. For this study, once the production process was selected, investment and production costs were calculated for different capacities in the short and long run, as indicated in Table 5.6

Table 5.6 Income and Costs for Fishmeal Plants

 Capacity 250 t/day 500 t/day Raw Material (t/24h) 100 175 250 200 250 350 500 Sales of Fishmeal and Fish Oil (US\$ '000) 3025 5294 7562 6050 7562 10587 15125 Variable Costs: plant & boats (US\$ '000) 799 1224 1647 1 405 1 688 2252 3100 Fixed Costs: plant & boats (US\$ '000) 3663 3663 3663 4855 4 855 4855 4855 Average Cost (US\$1t) 850 532 399 596 499 387 303

A plant with a 500 t/day capacity is much more flexible than one with a 250 t/day capacity, but the costs of a 250 t plant are not very different from a 500 t/day plant. Building an oversized plant is a safety measure, so that when trawlers supply up to 90 t/day during periods of high catches, it can be processed during the course of the day. A plant that produces at reduced capacity can produce fishmeal with a lower fat and higher protein content.

With two 8-hour shifts, the plant can consume up to 240 t of fish, production being interrupted one day/week in order to allow for a proper cleaning and maintenance programme. It is, however, impossible that a plant with a nominal capacity of 250 t/day can absorb this quantity for an average of 250 days/year, not even with highly trained workers. From experience, it has been determined that up to 70% of the nominal capacity can be used over the 25,0 days/year. This represents an average production of 175 t of fish/day. The reasons for reducing actual capacity are:

• The actual capacity of the plant and the quality of fishmeal are strongly dependant on the freshness of raw material. If raw material is too old there is an increase of losses and a decrease in fishmeal. quality. If fish is too fresh (e.g., in rigor mortis) there are working problems to grind and transport the raw material and the quality of the resulting fishmeal may not be acceptable for the customer.

• There are large oscillations in daily catches, around 60 t/day per trawler. Catches below average cannot be compensated by catches above average at a later date.

• A well-run factory usually stops production one day/week for cleaning and maintenance. A stop in production may occur in the best plant. The stops will reduce the nominal daily production average.

• An average production of 175 t/day of raw material is equivalent to 58.3 t/day per trawler, a value close to the design capacity (with a profit of US\$ 400 000/ year). However, if the plant is to be served by 4 trawlers, the catch per trawler must be limited to 43.75 t/day, and 250 days of production will give a loss of US\$ 530000.

In Figure 5.15, the results for the unitary costs have been plotted. Figure 5.15 Average Costs in the Long Run for Fishmeal Plants

If a minimum catch of 60 000 t of fish is anticipated, the average will be 60 t per boat, when four trawlers are used over 250 fishing days/year. This catch must be processed by a plant with a nominal capacity greater than 250 t/day. For these reasons, the 500 t/day plant has been chosen (Arnesen and Scharfe, 1986).

## 5.5 Micro-economics Applied to a Whole Fishery

The application of micro-economics to fish catching and processing was discussed above in a way that could be defined as the individual owner's or company's point of view. In particular, in the case of fish catching no biological conditions were imposed on calculations, e.g., level of availability of resources, although they were in practice affecting the estimates. However, as fish is a renewable resource depending on defined physical and biological conditions, they should be taken into account, in order to find out how a fishery as a whole (not just a given type of fish processing plant or fishing boat) can be operated in a sustainable way.

Micro-economics applied to fisheries is now a well developed branch of modern fish biology, where the interaction of biological knowledge and micro-economics has led to the development of mathematical models regarding the economics and sustainability of a fishery as a whole. This approach allows for the definition of useful limits and conditions in exploitation of a given single or multi-species fish resource and establishment of general fishery policies (to be enforced by Governments and/or self-enforced by fishermen and the fishery industry. It is for the single fisherman or company, to adjust his own micro-economic analysis to the general micro-economic analysis of the resource for his exploit (and the whole exploitation) to be sustainable. In practice, this is one of the main problems of today's fisheries.

The production function has been defined as the relationship between the quantity of inputs used and the resulting quantity of product. In terms of a fishery, the production function expresses the relationship between the fishing effort applied and the fish caught. A fishery is considered here to be a stock of a species exploited by a group of fishermen, boats or fishing units. In practice, conditions are as complex as the fisheries are varied. The production function in a fishery depends on the reproductive biology of the stock of fish. Most theoretical treatments of fisheries economics use the analysis originally defined by Schaefer (1954), where the growth of a stock of fish is assumed to be a function of volume, expressed in units of weight.

The biomass of an unexploited fishery resource will grow at different rates depending on its size, and will increase towards a maximum point which, once attained, will remain constant. This population size is known as the population size in the virgin state (Anderson, 1974). The physical and chemical parameters influencing the fish population size and the rate at which the resource reaches its maximum point, include salinity, temperature, prevailing currents, feeding habits of other species, rate of photosynthesis, quantity of radiated solar energy and rate at which mineral elements are replaced.

If these parameters are assumed to be constant, the three population components that will determine the growth of the resource are: recruitment (the biomass of fish that enters the population that can be caught in a period), individual growth (the biomass of each individual fish in the population for that period) and natural mortality (weight of biomass of fish of the population, lost due to natural death and predators during that period); the period is normally one year.

In the Schaefer analysis, it is assumed that the increase in the biomass of a fishery is a function of the population. It can be shown as a bell-shaped curve, as shown in Figure 5.16(a). The horizontal axis measures the size of the population, and the vertical axis the growth per period; both are given in terms of weight. Figure 5.16 (a) Growth Curve; (b) Population Equilibrium Curve as a Function of Fishing Effort

For example, when the population has a value of P3, the net increase in size or growth will be V3. For stocks of small size, the net effect of recruitment and individual growth is greater than natural mortality. The natural growth is positive and increases with the size of the stock. A point will eventually be reached where recruitment and individual growth will equal natural mortality, and the growth of the stock will cease. This struggle between different forces can vary with different species, but in general the growth curve maintains its bell-shape. In some cases, the right side of the curve can asymptotically draw nearer to the horizontal axis, in a more or less pronounced manner.

According to Figure 5.16, P* is the size of stock in which recruitment and natural growth are compensated for by natural mortality. Therefore, the population will not grow above this size. This point will be the natural population equilibrium. For any smaller population, growth will continue until it reaches size P*.

When man begins to exploit a fishery, he becomes a predator who disturbs the population equilibrium. A new equilibrium point will thus be reached, where the net increase in weight due to natural factors, will equal the net reduction due to the fishing mortality. At any point in time, the catch or fishing mortality will be a function of the size of the stock and the quantity of fishing effort that is applied to the fishery. For any population size, the greater the fishing effort, the larger the catch; and for any degree of effort, the larger the population the larger the catch. Mortality due to fishing can be shown on a graph as a function of the fishing effort if the population remains constant, or as a function of -the population if the effort remains constant.

Given that the catch varies with levels of effort, the equilibrium size of the population will differ for each level of effort (Figure 5.161). This is important as fishing effort is a variable defined by man and should be controlled by him. The catch is a function of the size of the stock and degree of effort, but as the size of the stock in the equilibrium is a function of effort, the yield of fish in the equilibrium (V) is a function of effort only. In Figure 5.16, four dotted curves have been drawn showing the fishing mortality by weight (catch) that will occur during a period for different population sizes, each exploited by a different fishing effort.

The catch obtained from a level of effort and its corresponding population equilibrium is called Sustainable or Sustained Yield. It is sustainable because the size of the population will not be affected by fishing, since catch is balanced by the natural increase of the stock. Therefore, the same level of effort will supply the same level of catch in the following period. The series of points which represent catches from sustainable yield for each level of effort, is called the Sustainable Yield Curve.

For the hypothetical fishery in Figure 5.16, Figure 5.17.a would be obtained. The vertical axis measures catch in weight and the horizontal axis measures the effort, as would occur for a typical production function in the short run, with effort as a variable input.

The concepts of average and marginal sustainable yield, whose curves are shown in Figure 5.17 b, are also important. These concepts are also comparable with the average and marginal products. Average sustainable yield, the sustainable yield per unit of fishing effort, Y/E, decreases continuously until it reaches the value zero, at the same point at which total yield is zero.

Marginal sustainable yield, the change in sustainable yield due to a change in fishing effort, or (D Y/D E), is positive, but declines and reaches zero at the level where the Maximum Sustainable Yield (MSY) is obtained. Then it becomes negative. This implies that additional levels of effort over the point of MSY will actually reduce catch. Figure 5.17 Total, Marginal and Average Sustainable Yield Curves

The sustainable yield curve can be considered the production function of a fishery in the long run; i.e., it will show the quantity of the resource that can be "produced" with a sustained base at different levels of fishing effort. Changes in fishing effort will produce a change in the equilibrium size of the population, but time will pass before the new equilibrium can be reached.

In cases where this delay is substantial, the yield curves for specific population sizes can be used as production functions in the short run, such as those shown by dotted lines in Figure 5.17 a (they are inverse to the catch and population curves shown in Figure 5.16 a. A different curve is necessary for each population size. Of the two curves shown, the higher one corresponds to the larger population (P2, and P3 are the same as in Figure 5.16).

### 5.5.1 Mathematical models for evaluation of the fish resources

In order to evaluate the state of a fishery resource, determine the volume of catch that can be obtained and estimate the effects of different fishing alternatives, the effects that fishing has on the fishery resource must be quantified, mathematically showing possible population changes that might occur as a result of the different exploitation alternatives (Csirke, 1988).

The general concept used to develop the models of population dynamics that are used to evaluate fishery resources and recommend management measures can be simplified by Russell's formula:

F2 = F 1 + (R + G) - (M + C) (5.16)

where F, and F2 represent the biomass of the population at the beginning and at the end of a specific period respectively; R, the quantity of recruits or of new individuals that have become part of the population; G, the increase in weight caused by the growth of the existing fish in the population; M, the quantity of fish that died from natural causes; and C, the quantity of fish caught or killed by fishing during that same period of time.

According to this model, the population is maintained in equilibrium when the natural increase of the population (R + G) remains equal to its decrease (M + C) as a result of natural causes and fishing. In other words, the population tends to increase or decrease according to whether the increases or decreases are greater.

Of all these parameters, the only one that can be controlled by man is catch (C), through which he can change the size of the population during successive periods (F2, F3, .... Fn). One of the preoccupations of each fishing community is the determination of the maximum level of catch (C) and the size of the population (St) that, once kept in equilibrium (that is, where M+C = G+R), will allow the maximum catch to be obtained.

The methods that are generally applied to estimate the size of a population and the possible relationship between the rate of natural increase and the intensity and conditions for exploitation (for example, rate of exploitation, age at first capture, etc.) can be grouped into analytical or structural methods and synthetic or global methods.

Analytical or structural methods are used to study population size and dynamics by examining its main components and the changes that they experience. On the other hand, synthetic methods, best shown by global production models, are those that treat the population as a closed entity where no notice is taken of changes that occur internally. Only the relationship between the stimulus, usually represented by the intensity (fishing effort), and the total catch and catch per unit effort (response) obtained, are analysed.

The following analytical methods will be examined:

- Yield by Recruitment Model

In the application of the yield by recruitment model (Ricker, 1975; Gulland, 1969; Csirke, 1980; Pauly, 1980 or 1982), information, data and samples collected from the commercial fishery, as well as from exploratory fishing where available, are used to estimate the parameters of the population. Of all the parameters, the only ones that can be voluntarily controlled by man are fishing mortality, which is assumed to be proportional to the fishing effort (number of boats, fishermen, etc.) and the size or age at which the fish can be caught (which can be modified by changing the size of the nets, avoiding spawning areas, etc.).

If these parameters are known, a rather complex equation proposed by Beverton and Holt (1957) or some modified version proposed by other authors, can be used to estimate the average catch that each recruitment can yield, for a certain combination of fishing mortality values and age at first catch. If the recruitment is known, it will also be possible to estimate the total potential catch of the entire year class and of the population.

- Virtual Population Analysis (VPA)

The method of analysing virtual population allows the history of an entire year class to be reconstructed (which when added to other year classes allows the history of the entire population to be reconstructed) from the catches and estimated natural mortality of that year-class during the time that it was exploited and the fishing mortality and abundance during the last year or fishing season. In this way, with a retrospective analysis of the catch of each year class over time, an estimate can be made of the number of individual fish that were present in the population in the past.

To apply this method, the total catch and the natural mortality in each year, for each group of a certain age needs to be known, in addition to the fishing mortality or abundance for the last fishing season. Then a series of equations (presented and discussed in detail in the works of Gulland, 1971; Pope, 1972; and Cadima, 1978) are applied to estimate the size of each year class and the population that existed in the past. Other methods are used when the time series values for catch and effort are not available (Garcia et al., 1989).

Analysis is made of the global method of production based on the law of population growth in the natural state and which follows a sigmoid shaped curve. Schaefer (1954) proposed a method for estimating the potential catch of a fish population, relating surplus production or sustainable yield to a measure of the population abundance or the fishing mortality.

This model rejects the assumption that under equilibrium conditions, the abundance or catch per unit effort (U) decreases in a linear form with increases in fishing effort (E). This relationship can be represented by the equation:

Ut = U00 - b x Et                     (5.17)

where: Ut is the abundance; Et is the fishing effort at a specific time; U00 is the index of the catch capacity or population size in the virgin state, and b is a constant.

Using this equation, and defining abundance as proportional to catch per unit effort (U = V/E), the following relationship between capture (V) and fishing effort (E), can be derived:

Yt = U00 x Et - b x Et 2                 (5.18)

which describes a parabola, where each point on the curve corresponds to a level of catch or equilibrium yield (V) according to the specific level of fishing effort (Et ). The highest point of the parabola is known as Maximum Sustainable Yield.

The simplicity of the fundamental theories and the fact that only data on catch and fishing effort are required (easily acquired statistical data which are also used for other purposes and by other users) resulted in production models and data collection on catch and effort, becoming the standard method for analysing and evaluating most fisheries. In many cases, this leads to erroneous conclusions, due to the lack of complementary information.

Pella and Tomlinson (1969) and Fox (1970) have proposed modified versions of this model in order to adapt it to specific applications and improve adjustments in particular cases. Csirke and Caddy (1983) proposed a modified version which allows this type of model to be applied to fisheries for which only data on catch or abundance indices, and estimates of total mortality are considered. This is particularly useful in cases where adequate data do not exist.

The conclusions drawn from an analysis of the characteristics of the dynamics of the fish populations must be expressed in terms which can be used by those who are not biologists, and have the responsibility of planning and managing fisheries development. Thus, models have been formulated such that the results can be expressed by relating equilibrium catches to the different values of fishing mortality which, for practical reasons, are normally shown by their corresponding value for fishing effort (for example, number of boats, trips, fishing hours, number of fishermen) (Csirke, 1985).

The advantage of expressing the results in terms of catch and fishing effort is obvious, since these are precisely the units with which those persons responsible for fishery management must deal continuously. The exact shape of the curves that relate catch to effort and catch per unit effort (apparent abundance) to effort can change according to the particular model used and the type of fishery being analysed. However, these two curves usually have the same shape as those in Figure 5.17.

The general conclusion that can be drawn, with respect to the relationship between catch and fishing effort, is that, Liking zero as a starting point, small increases in effort will be followed by an almost proportional increase in catch. However, the rate of increase in catch begins to decline at high effort values (catch per unit effort also decreases), reaches zero, and then becomes negative on the right side of the curve, entering what is known as a level of over-exploitation.

The point where the increase in catch with respect to the increase in effort is zero corresponds to the level of Catch or Maximum Sustainable Yield (MSY), which would be the optimal level of exploitation. if the aim of the fishery is to obtain the greatest sustainable catch possible.

Economic sustainability and social consideration are now receiving more attention and implications of these aspects are shown in Figure 5.18. Figure 5.18(a) gives the relationship between gross value of the catch (X-axis) and total costs of exploitation (Y-axis). Figure 5.18 Income and Total, Marginal and Average Cost Curves

The gross value of the catch is greatest at point B. At point A, the gross value of the catch is equal to operating costs at which profitability is zero. The maximum economic profitability (maximum net economic yield) is point C. From the economic point of view, this is the optimum catch level, but if other considerations are used (for example, maximizing total catch) the entry of new fishing units can be authorized, up to point B. Also, in the absence of a good policy for fisheries management, an equilibrium point can be reached where the value of the catch is equal to total costs (point A). In extreme cases the fishery can also stabilize at a more reduced level of catch (point D) where the value of the catch only serves to cover current costs (fuel costs, salaries, insurance, maintenance of vessels and fishing gear, etc.) and due to a lack of amortization and reinvestment, the fishery runs the risk of entering a process of gradual degradation.

Figure 5.18(b) shows other economic indices. The slope of the continuous line shows the marginal economic yield or net aggregate value added to the total catch with the entry of each new fishing unit (and corresponding increase in total fishing costs). The marginal yield shows the aggregate value for the entire fishery by the addition of one fishing unit (e.g., the entry of a new boat). The marginal yield starts off high, but begins to decline rapidly as fishing intensity increases. At a certain point, the marginal yield will be equal to the costs of the new fishing unit (point Q; that is, the level at which net economic yield is highest.

This is probably the point at which fishing should be maintained if net economic yield is to be maximized, as any increase in the fishing effort will cost more than the corresponding increase in total value produced by fishing, and would obviously be unprofitable if the fishery was considered as a whole. However, the criterion used to determine whether a boat should be built or a new one allowed to enter, is normally the potential catch of this boat and not the increase in total catch for the entire fleet. The catch by a new fishing unit can in fact be less, since the activities of a new boat could reduce the abundance of the population that is being exploited, and thus reduce the catch of the other boats. This is a very important aspect to consider when an increase in fishing effort and the development of a particular fishery are proposed (Csirke, 1985).

Just as it is possible to incorporate economic criteria into models of population dynamics, social criteria that tend to maximize the number of job positions, number of fishing units, etc., can also be incorporated. Models of population dynamics provide useful information on the limits for the development of a fishery and the consequences for the fish population and for man himself, if the number of fishing units are increased or reduced.

In an unregulated fishery, the level of fishing effort for equilibrium in the fishery will be E3, where total income equals total costs. It is also the point at which average revenue per unit effort is equal to average costs per unit effort. At this point, total revenue for the fishery to the left of E3 is greater than total costs. Therefore, each vessel will realize profits, i.e., average income per unit of fishing effort is greater than the average costs per unit of fishing effort. This situation will not only prompt the existing vessels to increase their effort, but will also motivate new units to enter the fishery. The opposite case is shown on the right of E3. Given that fishing effort tends to increase below E3 and decrease above this point, the fishing effort equilibrium level in an open access fishery will stabilize at this point.

This can also be called a bio-economic equilibrium point. The level of fishing effort will not change unless prices and costs vary. Fish population will also remain constant. The adequate use of a resource requires maximization of its net yield. This guarantees that production is maximized. In Figure 5.18, this situation is shown at point E1, where the annual profit of the fishery as a whole (difference between income and costs) is at its maximum. Any increase in effort above E, will reduce annual profits, as costs will increase more than income.

Income measures what the population is prepared to pay for the fish, and costs represent the value of the opportunity costs of those inputs required to produce the effort used to catch the fish. Therefore, when the marginal cost of effort is greater than the marginal income, the company is losing, as it is obtaining additional fish at a cost higher than its worth to the consumers. In other words, when fishing effort increases, inputs are being diverted from producing other goods that are more valuable to the company.

On the other hand, if the effort was reduced, profit would also decrease implying that income is decreasing faster than costs. Therefore, although the resources could be used in other types of production, the resulting goods would have a value lower than that of the fish that could have been caught with E,. This is called Maximum Economic Yield (MEY) of the fishery. What is important at the MEY point, is not the maximization of the profits of the fishery as a whole, but that the company's inputs not be used to exploit the fishery, unless they cannot be used more advantageously elsewhere.

The majority of small-scale, fishery resources can be exploited by anyone who wishes to do so. This natural open access to the fishery tends to lead to biological overfishing (beyond MSY) and to economic overfishing (beyond MEY), to the point where the total costs of fishing equal the total income obtained from fishing. While the MEY can, in rare cases, be found to the right of the MSY, the maximum economic profit for the country, resulting from fishery activity, is generally found to the left of the MSY. A point on the curve that relates yield to the size of the resource and the quantity of the fishing effort that is found on the right of the MSY, denotes additional fishing effort and a smaller population size; a point on the left of the MEY denotes less fishing effort, and a greater population size.

Similarly, the theory of sustained development can be applied to the case of a fishery or a natural,, renewable resource. This new concept of development will succeed if the biological, economic, political and cultural aspects are simultaneously accounted for. It can be defined as a collection of goals whose change with time must be positive. Some of the goals are increase of real income per caput, improvement of the sanitary and nutritional level of the population, expansion and extension of education, increase of resources, (natural or man-made), an equitable distribution of income, and an increase of fundamental freedom. The fulfilment of these goals is subject to the condition that the stock of natural capital must not decrease with time. A comprehensive definition of natural capital involves all the natural resources, from petroleum to the quality of the soil and continental waters, to the stock of fish in the oceans, and to the capacity of the planet to recycle and absorb carbon dioxide. If this theory is applied to the treatment of a fishery, the following equation is derived:

(dR/dX) x (l / p ) = P - C(X)                                                 (5.19)

where:

R = [P - C(X)] x Y(t), sustained revenue or profit of the activity
X = growth of stock = discount rate
P = price of natural resource
C = unitary cost of capture
Y(t) = capture

Its deduction and modifications when the price of the resource changes, are given in the References (Pearce et al., 1990). There are hardly any data on growth rates of the resources, which hinders the analysis of MEY. In order to study the income and costs of a fishery, three types of data are needed: (1) an estimate of the sustainable yield curve, (2) an estimate of the average costs of effort and (3) an estimate of the price of the resource.

From the Schaefer model, the sustainable yield curve can be mathematically expressed as:

Y = c x E - d x E2                                                             (5.20)

where:

Y = capture
E = fishing effort
c and d constants

Using standard mathematical techniques, it can be shown that the MSY will be equal to c2 /4d and will be obtained when the fishing effort is equal to c/2d.

To apply the model's equation to a fishery, it will be necessary to obtain estimates of c and d. From the equation for sustainable yield, the average sustainable yield per unit of fishing effort can be expressed as:

Y/E = c - d x E             (5.21)

Therefore, using data on catch and total effort over a period of years, estimates for c and d can be obtained by using the minimum squares technique.

Example 5.4 Lobster Fishery in the Northern USA (1950-66)

This type of analysis was applied to the lobster fishery in the northern USA in order to obtain a rudimentary overview of the operation of open access fisheries and to recommend regulation policies (Bell and Fullenbaum, 1973; Fullenbaum and Bell, 1974). The following equation was estimated using data acquired for catch and effort between 1950 and 1966.

Y/E = - 48.4 - 0.000024 x E + 2.126 x °F                 (5.22)

According to this estimate, an increase of 100 000 traps would reduce annual catch per trap by 2.4 1b, and a temperature increase of 1 °F would increase catch by 2.126 lb. If 46 °F, which was the average temperature for 1966 and which is close to the average temperature for the past 65 years, were used, the result would be an MSY of 25 459 million pounds, that would have been caught by 1030 000 traps. This means:

Y = 49.4 x E - 0.000024 x E2                                     (5.23)

If the operating costs of a vessel are known, as well as the average number of traps that each carries, total costs (TC) can be expressed as a function of effort, in the following way:

TC = 21.43 x E                                                         (5.24)

and if this were divided by total yield, the average costs would be:

AC =21.43 x E / 49.4 x E - 0.000024 x E2             (5.25)

Solving the quadratic equation (5.23) to obtain E = f(y) and substituting it in equations (5.24) or (5.25), equations are obtained that are an exclusive function of Y. Similarly, marginal costs can be estimated in terms of yield, as the derivative of the total cost equation. If the results are analysed, it is observed that as the number of traps increases, total yield decreases, but average cost per pound continues to increase, as more money is being spent to obtain a lower yield.

To determine the equilibrium point, an examination must be made of the following demand curve by applying standard econometric techniques, with data on prices for landed lobsters, consumer income, population of the USA, consumer price indices, total consumption, total imports and total production of lobsters in the USA compared with production in the north.

Price = 0.9393 - 0.005705 x Y (5.26)

On analysing the demand Equation (5 * 26), it was observed that if the lobster catch increased by 1 million 1b, the price dropped by less than 0.5 cents/lb. The equilibrium point is found by making the demand equation equal to the average cost curve. At the point where they intersect, a price of US\$ 0.7952 and a total mass caught of 25.24 million 1b, were obtained. To obtain this yield 933 000 traps must be used. The actual figures for 1966 were: US\$ 0.762, 25.6 million 1b and 947 113 traps.

The MEY occurs at the intersection of the marginal costs curve and the demand curve. The equilibrium price was US\$ 0.833, with a total yield of 18.57 million 1b, using 490 000 traps. The average costs per pound, operating at this production level, was US\$ 0.571. Total income at this point, which is equal to the difference between sale price and cost multiplied by total yield, was US\$ 4 865 340.

Another conclusion could be the following: if the production of the fishery had to be reduced from 25.24 to 18.57 million 1b and the number of traps from 933 000 to 490 000, this would lead to a decrease in the average costs per pound, from US\$ 0.7952 to US\$ 0.571, with a combined decrease in total costs of US\$ 9 467 378. This reduction implies, when considered along with the concept of opportunity costs, that there are goods with this same value that can be produced in other parts of the economy.

At the same time, the reduction in total yield caused an increase in price and a reduction in the consumption of lobster, resulting in a loss of US\$ 4 602 038. Subtracting this amount from the increase in production of goods in other areas, it is found that moving to the MEY point allowed the company to obtain a net profit of US\$ 4 865 340, which is the same as the profit made by the fishery when it was operating at MEY (Anderson, 1974).

Fishing companies must have a sufficient understanding of the micro-economic management of the fishery as a whole, since their development and functioning over time depends on it. It is also essential that this knowledge be available to fishermen's associations and fishery industry in general, since it is a common problem.

Another example of the application of these concepts was the Cyprus fishery (Hannesson, 1988), where effort was measured in units of fishing days. Optimum effort was found to be 105 fishing days/mi2 for some fishing areas, and 175 fishing days for others. These levels are far below the actual levels of fleet operation, 67% of the average levels between 1983 and 1984 and 58% of the level in 1984. Similarly, the economic benefits have been calculated assuming optimum effort yields a total catch of 1 360 t'. This can be compared with actual catch in recent years in Cyprus, which ranges from 1 038 t in 1980 to 1952 t in 1984.

Several policies that can be used to reduce the level of fishing effort to optimum levels, have been analysed using these results. One of these methods is to gradually reduce the level of effort, after having first stopped the increase in effort. Obviously, alternative means of employment for those persons leaving the fishery will have to be considered.

This reduction in fishing effort can be achieved by dividing the total catch into individual quotas, limiting fishing licences, imposing a resource tax on fishing, excluding some occasional fishermen, and assigning specific zones for fishing permits. It has been proposed that fishing licences or quotas be granted to fishermen who are actively engaged in fishing when the regulation is introduced, and then quotas or licences be bought back, as needed, until the optimum fishing effort is reached.

The micro-economics of a fishery as a whole, and the various possibilities for its regulation, have been extensively studied (Csirke, 1985; Doubleday, 1976; Gulland, 1974; Gulland and Boerema, 1973).