The concept of capacity can be quite difficult to define and even more cumbersome to understand. There are numerous definitions of capacity, and several bases upon which to define it. The most widely used concept of capacity is the maximum potential production of an output or group of outputs by a producing unit, firm, or industry, given technology, capital stock and other factors of production. By definition, capacity is a short-run concept, since at least one input (usually the capital stock) and technology are held fixed at some level. There are at least three bases upon which to consider the concept of capacity.
First, there is an engineering concept of capacity. This concept of capacity defines a theoretical maximum rather than a real world, practical maxima (e.g. the name plate rating on an electric power generator or the maximum power rating on an engine) (Coelli, Grifell-Tatje, and Perelman, 2001). The engineering concept, however, is not a particularly useful concept for managers of fisheries and is not further considered in this Technical Report.
Another notion of capacity is the pure physical or technological notion of capacity. The physical or technological concept of capacity is the maximum potential output a producing unit, firm, or industry could produce, given technology, capital stock and other factors of production, but without any limits on the factors of production that can be changed (e.g. labour and energy) in the short run.
A third concept is the economic concept of capacity. As broadly interpreted, the economic concept of capacity is the output level that would be produced in order to satisfy some underlying economic behavioural objective, such as profit maximization or cost minimization (Morrison, 1985; Coelli, Grifell-Tatje and Perelman, 2001). This notion defines capacity as an economically-derived optimum level of output.
Regardless of whether or not capacity is defined according to an engineering maximum, a technological or purely physical maximum, or an economic optimum, capacity refers to a potential output level (e.g. the maximum potential number of automobiles a car manufacturer could produce, or the number of automobiles that must be produced in order to maximize profits). Even though all of the concepts of capacity refer to potential output, the various interpretations can be confusing to understand.
To help explain these concepts of capacity, we introduce the concept of a production function and some basic notation. Let Y be a single output; X, a variable factor of production; and Z, a fixed factor of production. A variable factor of production is an input whose level may be varied or easily changed in the short run (e.g. fuel and labour). A fixed factor is an input that cannot easily be changed in the short run (e.g. capital such as equipment and machinery). The production technology or production frontier, g, defines the maximum output attainable from a given set of economic inputs. The technology may be specified in mathematical form as Y = g(X,Z).
The production function or technology may exhibit various relationships between inputs and output. Of particular concern is how the level of output changes in response to changes in the levels of variable inputs. In general, it might be expected that output would initially rise at an increasing level given increases in the variable input (Figure 1). The rate of increase in output, however, would likely reach a maximum (point A), because output would start to be limited by the fixed factor and increases in variable input use would only modestly increase total output. At some level of production, output would be as high as possible and increasing inputs would actually decrease the level of output.
Figure 1 - The classic production function
The technological concept of capacity, as proposed by Johansen (1968), can be understood by viewing Figure 1. Johansen defined capacity as the maximum possible output that could be produced given technology, fixed factors and no limitations on the availability of variable production factors. The maximum output occurs at Point A in Figure 1. At the maximum or capacity level of output, inputs are fully utilized (i.e. they are used at levels yielding maximum output).
Also of particular concern is whether or not the technology exhibits increasing, decreasing, constant, or variable returns to scale. Returns to scale, however, are a long-run concept as it implies that there are no fixed inputs (i.e. the levels of all inputs can be changed). Technology is said to exhibit increasing, decreasing, or constant returns to scale if a proportional increase in all inputs results in a more than, less than, or same proportional increase in output (Figure 2). Variable returns to scale exist when returns to scale changes with input levels. For example, smaller units may experience increasing returns to scale, while larger units experience decreasing returns.
Figure 2 - Returns to scale
Färe (1984) considered Johansens definition of capacity a strong definition of capacity. This technological maximum, however, is not likely to be a particularly useful concept of capacity, since it would likely not be produced under customary and usual operating procedures. Färe subsequently offered a weak definition of capacity, which is similar to Johansens definition, but only requires that output be bounded as opposed to requiring the existence of a maximum (Figure 3). In Figure 3, capacity output, YC, is produced using XC units of the variable factors of production; the fixed inputs, however, bind or limit output to YC. This weaker concept of capacity output explicitly recognizes restrictions on production and may better indicate customary and usual operating procedures.
Figure 3 - Capacity output for the weak definition of capacity
The various technological concepts of capacity output, while being useful concepts of capacity, can be misleading. Most important is that these technological concepts may suggest capacity output levels for which profits are negative or lower than they could be, given some alternative level of production. As a consequence, economists have attempted to develop more economically meaningful measures of capacity (Coelli, Grifell-Tatje and Perelman, 2001). Explaining these various economic concepts of capacity output, however, requires a considerably different framework. First, rather than defining capacity output in terms of a physical or technological maximum, it must be defined in terms of an output level that satisfies some underlying behavioural objective (e.g. the output level produced when total cost is minimized, or the output level produced when profit is maximized). Second, rather than deriving capacity output directly from production relationships, it is derived relative to economic relationships (e.g. cost, revenue, or profit relationships).
Klein (1960) and Berndt and Morrison (1981) developed economic concepts of capacity based on the short-run cost function. Klein defined capacity output as the level of output corresponding to a tangency between short-run and long-run average cost curves. Berndt and Morrison defined capacity output as the level of output corresponding to the minimum point of a short-run average cost curve. Coelli, Grifell-Tatje and Perelman (2001) offer a definition of capacity output based on static profit maximizing behaviour; they define capacity output as the level of output corresponding to profit maximization. Färe, Grosskopf and Kirkley (2000) offer definitions of capacity output based on revenue maximizing and cost minimizing behaviour. More recently, economists have developed economic measures of capacity output assuming dynamic profit maximization (Fousekis and Stefanou, 1996; Fagnart, Licandro and Portier, 1999).
Static economic concepts can be easily illustrated in graphic form. Consider Figure 4, which depicts short- and long-run average cost curves, the short-run marginal cost curve and the price level facing a firm or producing unit. The short-run average cost curve is the cost per unit of production given the presence of fixed inputs. The long-run average cost curve is the cost per unit of production when all inputs are variable. Marginal cost equals the change in cost associated with increasing production by one unit. The usual distinction between short run and long run is related to the feasibility of adjusting input levels. The short run pertains to a period during which the level of one or more inputs cannot be changed (Ferguson, 1975). The long run pertains to a period during which the levels of all inputs can be changed.
In Figure 4, four concepts of capacity output are depicted. Capacity output as defined by Klein is YK; the capacity output of Berndt and Morrison is depicted by YBM; the Johansen concept of capacity output is given by YJ; and the static, short-run, profit maximizing capacity concept of Coelli, Grifell-Tatje and Perelan equals YCGP. The Johansen concept of capacity output is a technological concept and represents the highest level of output. The profit maximizing capacity output occurs at the point at which price equals marginal cost. Capacity output as defined by Klein is lower than the other concepts. Capacity output as defined by Berndt and Morrison is higher than the capacity output defined by Klein; the two concepts are equal, however, when technology exhibits long-run constant returns to scale.
Figure 4 - Economic concepts of capacity output
(YK = Klein; YBM = Berndt and Morrison; YCGP = Coelli, Grifell-Tatje and Perelman; and YJ = Johansen)
An important concept related to capacity is capacity utilization (CU), or the amount of productive capital and inputs being utilized to produce a given output, relative to the level of output that could be produced if the capital stock, other fixed inputs, and variable inputs were fully utilized. Alternatively, capacity utilization is a measure of the actual utilization of the capital stock, other fixed inputs, and variable inputs relative to some desired or maximum potential utilization. Most often, CU is defined and measured as the ratio of observed or actual output (YO) to capacity output (YC). If the technological notion of capacity output is assumed, CU is always less than or equal to one in value. If the technologically-based CU is less than one, excess productive capacity exits; that is, either production could be increased with no change in actual fixed and variable input usage, or fixed and variable input levels could be reduced with no change in the production level. If CU equals one, productive capital, other fixed inputs and variable inputs are fully utilized. If the economic concept of capacity is considered, CU is not restricted to being less than or equal to one in value; in this case, CU can be greater than one in value. That is, actual output can be larger than desired economic output. If the economic concept of CU is less than one in value, excess capacity exists, or the input base is said to be under-utilized. If CU is greater than one in value, there is an inadequate utilization of capital, other fixed inputs, and variable inputs, or the input base is said to be overutilized. If CU equals one, capacity is fully utilized and all production inputs have reached their full equilibrium levels.
It is important not to confuse capital utilization with capacity utilization. Too often, particularly in natural resource-based industries, policy-makers conclude that an industry has excess capacity because it is over-capitalized. That is, the existing stock of capital is higher than necessary to produce a given desired level of output. Capital utilization is defined as the ratio of the desired stock of capital to the actual stock of capital and measures the utilization of a given capital stock. Capital utilization also may be defined as the ratio of the services of capital to the stock of capital (Schworm, 1977). Capacity utilization refers to the utilization of all inputs and not just the stock of capital. Berndt and Fuss (1989) demonstrated, however, that the two concepts are equivalent if there is one and only one fixed input and production is characterized by constant returns to scale. Although constant returns to scale may be appropriate for many industries or firms, the existence of one and only one capital input is likely to be unrealistic.
A concept related to capacity and capital utilization is the variable input utilization rate. Färe, Grosskopf and Kokkenlenberg (1989) appear to have introduced this concept to the economics literature. They define the variable input utilization rate as the ratio of the optimal use of a variable input to the observed, or actual, use. The optimum may refer to a variety of objectives, such as cost minimization or profit maximization or even output maximization. The optimum equates to the levels required to produce the optimum from the variable inputs. If the utilization rate is greater than one in value for a particular variable input, it means that the firm or producing unit has a shortage of that variable input. If the utilization rate is less than one in value, the firm or producing unit has a surplus of the variable input.
Fisheries involve common-pool resources, where yields are rivalrous and use is only partially excludable because agents are unable to contract to exclude others. As a consequence, the market fails to properly allocate firms or vessels to a fishery, and excessive levels of inputs are employed to exploit it. The fishery is then over-capitalized and has too much harvesting capacity. Alternatively, fishing fleets end up with the capability to harvest well in excess of sustainable levels. Too high a level of capacity equates to over-investment in stock resources (e.g. vessels and gear) and variable inputs. Resources tend to be over-exploited or at levels that cannot be sustained, and profits and economic rents tend towards zero. This is the Tragedy of the Commons problem discussed in Hardin (1968).
The history of fisheries economics, starting as early as Jens Warming (1911), has stressed the likelihood that fisheries will, in general, suffer from overcapitalization and too high a level of capacity. Yet, there has been little research attention given to actually assessing the levels of overcapitalization and capacity in fisheries. Clark, Clarke and Munro (1979) and Conrad and Clark (1987) provide an exhaustive discussion on the derivation of the optimal capital stock in a fishery, which they equate to capacity. These two works, however, actually address the issue of overcapitalization and not capacity. This is because solutions are offered in terms of capital stock and ignore full utilization of other fixed factors and variable inputs.
Defining the concepts of capacity and capacity utilization for traditional industries is difficult enough, but for fisheries it presents a more daunting task. The complexity is compounded by the fact that production depends upon a natural resource stock (i.e. the biomass or abundance of fish), which has its own regenerative properties that must be considered when defining and assessing capacity in fisheries. The resource stock introduces a constraint to the capital stock, which is recognized as the basis for existing capacity rigidities. In addition, ill-structured, incomplete, or severely attenuated property rights, regulatory structure and other factors further exacerbate the complexity of defining and measuring capacity and capacity utilization in fisheries.
Clear definitions and measures of capacity and CU, however, are fundamental to facilitating an understanding of capacity issues, and eventually, to helping develop capacity reduction programmes. The Food and Agriculture Organization (FAO) and the United States National Marine Fisheries Service (henceforth referred to as the National Oceanic and Atmospheric Administration, or NOAA, Fisheries) have generally agreed upon two concepts of capacity in fisheries. One concept is excess capacity, which characterizes the potential output level relative to the observed output level in the short run. Alternatively, excess capacity is defined as the difference between the maximum potential output - given technology, current resource conditions and full and efficient utilization of capital stock, other fixed and variable factors - and the observed output. The definition, although appearing to be equivalent to the technological definition, does not preclude consideration of the economic concept of capacity. The other concept, and the one which appears to be of greatest concern to resource managers, is overcapacity. Overcapacity equals the difference between the maximum potential output that could be produced - given technology, desired resource conditions, and full and efficient utilization of capital stock, other fixed and variable input - and a desired optimum level of output (e.g. the maximum sustainable yield, MSY, or maximum economic yield, MEY). The concept of overcapacity is, therefore, a long-run concept. By definition, it also does not preclude consideration of the economic concept of capacity.
The distinction between the two concepts is quite important for fishery managers concerned about reducing capacity in fisheries. Excess capacity is a short-run problem which can possibly self correct. That is, excess capacity may occur when shifts in supply and demand cause disequilibrium in the market, and firms end up having the capability to produce too much, given input and output prices. In this situation, firms can adjust their capital and variable inputs to either increase or decrease production. In contrast, overcapacity usually occurs because the market fails to efficiently allocate inputs and outputs. Firms cannot prevent other individuals from harvesting the resource, and there are no incentives to conserve inputs or outputs. With overcapacity, there a level of excess capacity persists. In this Technical Report, both concepts are presented, because it may only be possible to estimate excess capacity or some modified concept of overcapacity. This is because the empirical data available on fisheries may not reflect production activities during periods of desired resource conditions. The major emphasis of this report, however, is overcapacity.
Overcapacity typically results in overexploitation of resources and the inefficient use of the resource, capital stock, and all productive factors involved in the fishing activity. From an economic viewpoint, the same - if not greater - catches could be taken using fewer inputs, and consequently, at a lower cost. Alternatively, a smaller fleet could land the same level of catch at a substantially reduced cost. Reducing economic waste would generate additional profits, which could be used to benefit the entire community.
Resource managers historically have emphasized reducing the capital stock (i.e. overcapitalization) and not really reducing capacity, per se. Concurrently, though, they have also been concerned about the optimum utilization of the capital stock, the corresponding level of fishing effort or variable inputs, and the gear types. Thus, they have been partially concerned about overcapacity. The historical emphasis on reducing the capital stock or number of vessels (i.e. overcapitalization), along with concerns about production costs, however, have resulted in managers also desiring to measure capacity in terms of inputs (e.g. the number of vessels that could harvest the MSY if the capital and variable inputs were fully utilized and the resource was at the MSY level). These concerns have, subsequently, resulted in an input-based concept of capacity for fisheries. The input-based concept of capacity is defined as the number of vessels, or gear, required to harvest the capacity output. Similar to the notions of short- (excess) and long-run (over) capacity, are definitions of input capacity. For the short-run case of excess capacity, input capacity would be defined as the difference between the actual number of vessels harvesting a given output and the number of vessels required to harvest the capacity output. For the long-run or overcapacity case, input capacity would be defined as the difference between the number of vessels harvesting a resource - given desired resource conditions - and the number of vessels required to harvest a desired optimum level (e.g. MSY). Both of these concepts require the assumption of full input utilization.
It also is possible to think of the two concepts of capacity - input- and output-based - as dual to one another. If one knows the level of either excess or overcapacity and the full utilization levels of capital stock and variable inputs, it is possible to determine the level of the capital stock (i.e. number of vessels or gear) required to harvest a specified level of output.
There remains another notion of input capacity. In this case, the emphasis is on the minimum level of capital stock or fixed inputs required to produce a given output (e.g. MSY). In general, this concept of input capacity may be referred to as a dual or input- (cost) based, versus an output-based, concept of capacity. This dual notion is not the same as that previously discussed. In this case, input capacity refers to the minimum number of vessels operating at full utilization of the capital stock and the variable inputs required to harvest a specified level of output. In the former case, input capacity simply referred to the number of vessels required to harvest the capacity output if capital stock and variable inputs were fully utilized.
The presence of excess or overcapacity may be quite costly to society in terms of foregone profits, inefficient production and loss of alternative opportunities. Reducing either excess or overcapacity, however, also may be quite costly, both in financial and social terms. The loss of employment in the short run through capacity reduction often counters many fisheries management plans, the objectives of which may be to maintain employment or viable fishing communities (Charles, 1989). The effective management of capacity, therefore, not only requires a measure or indicator of excess or overcapacity, but also careful consideration of its appropriate measurement and use for policy guidance in the context of target biomass stocks and output levels, or other objectives of fisheries management plans. In addition, implementation of any formal capacity reduction programme needs to be cognizant of developing an appropriate timeline for capacity reduction.
The concepts of excess and overcapacity in fisheries can perhaps be illustrated best using the simple but widely used surplus production framework of Schaefer (1954). It is offered that the Schaefer model or framework is extremely limited and probably not applicable to many fisheries (Hilborn and Walters, 1992). It is, nevertheless, a model that is very familiar to resource managers and fisheries scientists and is widely used to discuss economic aspects of fisheries. The Schaefer model will therefore be used throughout this Technical Report to discuss capacity and related fisheries issues.
Prior to introducing the Schaefer model, however, it will be helpful to introduce some basic notation. Let C equal industry-wide or fleet-wide catch; E equal fishing effort, which is a combination of the number of vessels or capital stock, K, and the level of variable inputs, V (e.g. days fished); B is the population or biomass of the resource (throughout this report, biomass is used to indicate the level of the resource population); and q is the catchability coefficient (a scalar measure of the proportion of the stock that is removed with each unit of fishing effort). For a given set of biomass a production technology (i.e. the short term), catch is determined by C = qEB.
The simple surplus production model of Schaefer (1954) is a long-run sustainable yield function, which is derived assuming the simple logistic growth equation and the short-run yield function, C = qEB. Under this surplus production framework, it is assumed that there is some annual rate of growth (G) of a population given an existing population biomass (B) (Figure 5). As population increases, growth also increases up to some limit, which is established by food availability and the area of the water body. After realizing this maximum, growth continues but at a reduced level. Finally, there is some population level at which growth becomes zero, and this is referred to as the environmental carrying capacity (k) (Cunningham, Dunn and Whitmarsh, 1985). The long-run sustainable yield or production model of Schaefer assumes a logistic growth model, which is of the form G = rB(1-B/k), where r represents the intrinsic rate of growth. Growth is maximized in such a model at half the environmental carrying capacity.
Figure 5 - The logistic growth curve
To derive the sustainable yield function, we introduce the short-run yield or production function, C = qEB. Assuming the logistic growth equation adequately depicts growth, a long-run sustainable yield function may be derived by equating growth to removals from fishing. We have the equilibrium relationship G = rB(1-B/k) - qEB, which will equal zero. Solving in terms of the sustainable yield or catch (CS) gives us the long-run sustainable yield function of Schaefer: CS = qkE(1-qE/r), or more conveniently, CS = aE - bE2, where a=qk and b=q2k/r. The sustainable yield function of Schaefer is then a parabola (Figure 6). The origin of the sustainable yield curve corresponds to the environmental carrying capacity level of the population. As sustainable yield increases, population decreases. Yield increases until it reaches a maximum, which is referred to as the maximum sustainable yield, or MSY. The MSY equals the maximum growth; it is the largest level of catch that can be harvested on average per period of time (e.g. per year). For catch levels to the right of MSY, growth and, subsequently, sustainable yield decline.
Figure 6 - The sustainable yield curve
Using the sustainable yield function of Schaefer, the concepts of excess and overcapacity can be illustrated (Figure 6). Assume that the fishery is unregulated (i.e. open access) and the level of the population (B) supports MSY. Also assume that the objective of management is a harvest level equal to MSY, and that EOA is the full utilization level of capital stock and variable inputs for the fleet. Allow the level of effort to equal EOA, and thus, the short-run catch equals COA. At this level of effort and catch, there is overcapacity equal to COA - CMSY. In contrast, assume that the fleet is not fully utilized and instead operates at E1 units of effort. The fleet lands C1 units of catch. The fleet could, however, catch COA at EOA units of effort; the difference between COA and C1 equals excess capacity. A primary distinction between overcapacity and excess capacity is the time domain and an underlying stated objective of management. Excess capacity is defined and assessed relative to the short run; overcapacity in this case is defined and assessed relative to the long-run sustainable yield function and the objective of MSY.
The previous discussion of excess and overcapacity, unfortunately, is a bit misleading in that it better illustrates issues associated with overcapitalization. Normally, excess capacity is defined relative to an existing capital stock and potential output; that is, the maximum potential output given technology, fixed factors, and no limits on availability of the variable factors. In our example above, the capital stock (i.e. the number of vessels) was assumed to be held constant, with only the variable inputs changing. Both our short- and long-run yield curves permit changes in number of vessels. We would thus have a capacity output level for each level of vessels. If we assume, however, that the number of vessels is constant for all levels of effort and only allow the level of the variable inputs to change, the above depictions of excess and overcapacity illustrate the two measures. Alternatively, if we ignore the rigorous theoretical definition of capacity, we can loosely interpret the concepts of excess and overcapacity as the differences between COA and C1 and COA and CMSY. This is but one of many problems encountered in defining and assessing excess and overcapacity in fisheries.
We also may consider excess and overcapacity in terms of the input base - E. In this case, excess capacity is the difference between EOA and E1; overcapacity is the difference between EOA and EMSY. This is basically the mirror image, or dual to the output measure. This is not the economic dual, however, relative to the definition of capacity consistent with dual specifications of technology (e.g. cost, revenue, or profit functions).
Excess and overcapacity are typically associated with economic waste. Simply put, more inputs are being expended than are necessary to harvest a given quantity of fish; cost is not minimized; profits are not maximized; and society is not receiving the maximum possible benefit. Remembering that excess capacity is a short-run concept and overcapacity is a long-run concept, and is defined relative to either a desired resource condition or level of production, we need to consider two different frameworks for illustrating the implications of excess and overcapacity.
In the case of excess capacity, we consider a slightly different short-run yield function, C = qEbBaE, where b is less than one in value and a is negative. We also follow the example of Coelli, Grifell-Tatje and Perelman (2001), which describes the notion of excess capacity relative to the behavioural objective of maximizing short-run profits. The technology, as depicted, has a maximum potential or capacity output of CC (Figure 7). It is further assumed that E is comprised of the level of capital invested in the fleet (e.g. the number of vessels), K, which is assumed to be constant, and the variable input per vessel, V, (e.g. number of days fished). For further simplicity, we assume that V is the same for all vessels, but can be varied (e.g. for a fleet of 100 vessels, V could be 10 days or 20 days, but would be the same for all vessels). We also assume that C* represents that catch which maximizes short-run profits. We let C be a level of production. The level of effort is assumed to change only through variable input usage.
If the objective of the fleet was to maximize short-run profits (output and input levels of C* and E*), but the fleet produced at the capacity output level (CC), it would be over-utilizing the variable inputs and would have excess capacity relative to the optimum production level. In this case, the fleet would not realize the maximum profit. If the fleet produced at C1, variable input and capital stock would be under-utilized, and short-run profits would still not be maximized. Alternatively, if we consider only the technological concept of capacity output, we would conclude that the fishery had excess capacity if actual production equaled C1, given that the fleet had a potential maximum output of CC.
Figure 7 - Excess capacity and variable input utilization
The potential waste associated with overcapacity may be explored and illustrated by considering the sustainable economic benefits from fishing associated with the costs of production, and recognizing that overcapacity also implies inefficient use of existing vessels due to short-run rigidities, most likely associated with regulations. For the purpose of illustration, we use the sustainable yield model of Schaefer to formulate a simple bio-economic model of a fishery. For additional simplicity, we assume a constant output (fish) price and a constant average cost of fishing. By multiplying the constant fish price by the sustainable output, we obtain a sustainable revenue curve, or as correctly titled in Cunningham, Dunn and Whitmarsh (1985), a revenue product curve (Figure 8). We next impose a total cost curve on the sustainable revenue curve. In so doing, we assume that total cost equals the product of the average price of a unit of fishing effort and the level of fishing effort. Such a model allows us to broadly conceptualize the relationship between economic waste and overcapacity.
In an unregulated fishery with free and open access, fishing boats will enter the fishery as long as the resulting profits - Revenue (R) less total cost (TC) - are greater than those that could be earned in the next best alternative activity. The foregone profits in the alternative activities are considered the opportunity cost of entering the fishery, and economic profits are said to exist when the profits are greater than the opportunity cost of fishing. Hence, boats enter the fishery up to the point where economic profits cease to exist. At this point, fishers are earning the same level of returns on their investment and labour as they might in the next best alternative industry with equivalent risk. This return is the normal profits that are the minimum level of returns required to keep capital in the fishery. If the returns were greater than these normal returns, additional investment (and therefore effort) flows into the fishery. Conversely, if returns fall below this level, investment (and effort) moves out of the fishery. The returns that can be earned elsewhere in the economy are considered the opportunity cost of staying in the fishery. Economic profits are those that are achieved over and above the opportunity cost, or the normal returns.
Figure 8 - Economic implications of overcapacity in a fishery
In Figure 8, normal profits are earned when total revenue equals total costs, at which point total revenue is ROA. The economic measure of total cost includes the opportunity cost, so economic profit is zero at this point. The resulting current fleet size is EOA, and we refer to this as the open access equilibrium fleet level. Also depicted in Figure 8, the open access equilibrium results in biological overfishing. If the total cost curve had intersected the revenue curve to the left of MSY, however, biological overfishing would not occur, but there would still be considerable economic waste in the form of technical and economic inefficiency.
The same level of revenue (ROA) could be realized at a lower cost, however. In fact, fleet size or effort could be reduced from EOA to EMEY with no change in revenue. Relative to the revenue level of ROA and the objective of maximizing profits, there is overcapacity of EOA - EMEY. A reduction of effort from EOA to EMEY creates the possibility for economic profit, which is given by the difference between the revenue and costs at EMEY. The potential increase in profit, however, requires that the resource stock regenerate. But in the absence of additional regulations, it is likely that the existing vessel operators will attempt to realize profit by increasing their effort per period, which will subsequently increase the total cost, until eventually total revenue equals total cost (Anderson, 1977). Decreasing fishing effort or capacity in the absence of other regulations, therefore, does not guarantee that profits will be positive.
In Figure 8, ROA also equals the revenue corresponding to maximum economic yield (MEY). Maximum economic yield is the level of output at which economic profit is maximized. The fact that revenue, ROA, equals the revenue corresponding to maximum economic yield is purely an artefact of the cost assumptions used in the figure. The point of maximum economic profits can be found where the slope of the cost curve (indicated by the line TC in Figure 8) is equal to the slope of the revenue curve. A higher or lower average cost per unit of effort (giving a steeper or flatter total cost curve) would have resulted in the revenue associated with MEY being lower or higher respectively than that at the open access equilibrium.
In Figure 8, MEY occurs at a level of effort equal to EMEY, which is below EMSY. If the objective of fisheries management was to maximize long-term sustainable profit, there would be overcapacity relative to the fleet size and input utilization levels required to harvest MSY. Fishing activity that produces the maximum sustainable yield is above that which produces maximum economic yield. This form of bio-economic overcapacity - from an economic perspective - can exist even when maximum sustainable yield is taken at least cost.
The preceding discussion, based on the bio-economic model, illustrated various notions or concepts of overcapacity. Overcapacity was illustrated or characterized relative to bio-economic and biological optimums and the open access equilibrium. In some sense, the situation characterized as overcapacity (the levels of capital and effort corresponding to the open access and maximum economic yield or maximum sustainable yield) could be misleading. This is because the discussion emphasized the determination of the optimum capital stock (fleet size required to harvest either MSY or MEY) over capacity, which requires consideration of full utilization of existing capital stock, other fixed factors and variable inputs.
In some sense, however, the extent of overcapacity can be measured in terms of the difference between the current fleet size (K, or the level of capital invested) and the fleet size that would generate maximum sustainable yield (KMSY), or maximum economic yield (KMEY), assuming full utilization of the variable inputs. The notion of overcapacity previously discussed, however, might better be called overcapitalization, since the emphasis is on determining the optimum fleet size required to harvest either MSY or MEY. Alternatively, if overcapacity is initially determined relative to output levels and the capital stock or number of vessels, and we assume full variable input utilization, it is possible to define and assess overcapacity in terms of the capital stock or number of vessels.
However, the issue of determining the optimum capital stock versus optimum capacity may only be of interest to economic theoreticians. Stock conditions, or the size of the fish population and long-run adjustments of resource conditions to varying levels of effort, pose considerable problems for assessing and reducing overcapacity. Alternatively, standard bio-economic models may pose limitations for determining overcapacity and providing a basis for formulating capacity reduction programmes.
Consider again Figure 8, which assumes long-run stock levels and no inefficient use of inputs or capacity for the current biomass stock. At levels of effort higher than EMSY, the fleet exerts enough pressure on the resource that the stock can no longer support the MSY harvest level. Both the cost of fishing and the level of effort are higher than necessary to realize the sustainable revenue, R. At the higher level of effort, EOA, the stock is sustainable but lower than its potential maximum level, which corresponds to the population size necessary to support MSY. The number of vessels, however, could be reduced in order to achieve either EMEY or EMSY, and the same or even a higher harvest level could eventually be realized. At EOA, though, too many boats are in the fishery and stock levels are too low relative to levels desired by management or society. If the total level of effort was reduced to EMEY or EMSY relative to EOA, stock levels would increase but overcapacity would remain until the resource regenerated itself to a level that supports either MEY or MSY.
Determining and reducing the level of overcapacity in a fishery also could easily be complicated by erroneous assumptions about the logistic growth model or short-run yield functions. Initially, assume that the simple logistic curve represents the true biological potential, and technology is the standard short-run model (C = qEB). Maximum economic yield is produced with a fleet size exactly 50 percent smaller than the fleet size corresponding to the open access equilibrium level (this is a feature of the standard surplus production model and the assumed form of the short-run production function). This conclusion, however, also requires the stock to rebuild to a level necessary to support maximum economic yield. Given assumptions about the logistic growth curve and the short-run yield function, managers would subsequently conclude that the fleet should be reduced by 50 percent to realize the MEY level of harvest. If the short-run yield function took a different form, however, (e.g. C = qE.0.7B or C = qE.0.4B0.3), the reduction necessary to produce MEY might be quite different than 50 percent. It is thus important that careful attention be given to the bio-economic framework used to assess overcapacity.
Reducing overcapacity also may be quite difficult if the price of fish is sufficiently high (assuming a constant price), or the cost of fishing is very low. In this case, the intersection of the total cost (TC) and total revenue (TR) curves could be far to the right of the sustainable yield curve. Fish stock could be seriously overfished, relative to desired target levels, or even pushed toward extinction, with E nearing a level that reduces sustainable yield to zero - the level of effort that also extinguishes the stock. This is often referred to as EMAX, but not the EMAX concept of fishing mortality (Cunningham, Dunn and Whitmarsh, 1985). This could imply a very large gap between E and either EMSY or EMEY, and very high costs of reducing the implied overcapacity by stock regeneration.
In general, the bio-economic model indicates that overcapacity would occur in the absence of appropriate regulatory strategies. Fishing effort would become excessive and the resource would eventually be over-harvested relative to desired stock levels. Even with such a simplistic framework, establishing the extent of the gap between the existing fleet level and a target level of E such as EMSY or EMEY would generally require information on current fleet size, current harvest, maximum sustainable harvest and associated minimum fleet size. In addition, the growth curve for the biomass must be known. For economic measures of excess capacity, information on the production and cost structure of the industry, as well as the price of the output, also would be required. Although simple assumptions such as those built into the logistic growth and linear cost and short-run yield curves may facilitate such analysis, they are unlikely to be realistic for any particular fishery.
Also, at the existing biomass stock level B, the scenario represented in Figure 8 by the generation of revenues, ROA, associated with fleet, EOA, does not imply that any additional catch (output) may be produced. That is, given the overfished stock, the fleet effort level E is required - being the least cost or efficient level - to harvest the corresponding biomass growth. The only time the smaller fleet implied by, say, EMEY, could produce the maximum economic yield level of catch, CMEY, is after regeneration of the stock. Representing the existence of overcapacity or non-optimal capacity utilization at a given stock level requires further consideration of the impacts of regulations or other restrictions upon competitive factors that cause production to be carried out at less than optimal cost levels.
In practice, fishing fleets are typically subject to a number of constraints that limit their level of activity. In particular, constraints include management-imposed restrictions on catch (e.g. total allowable, or TAC, controls), gear, nominal fishing effort, areas and seasons. In the former case, fishing must cease on the species once its quota has been filled. The more common types of seasonal and area restrictions, respectively, are seasonal limits on either effort or catch and restrictions on areas that may be fished. We may generally view such restrictions as command and control type regulations, which are imposed on either outputs or inputs, or both.
Output regulations, which directly restrict the amount of catch from the fishery, are usually imposed to allow the stock level to rebuild or to keep it from further decline. Output restrictions, however, also imply limits on how much F may be applied to catch fish, and thus, limit input utilization. Restrictions on the level of output may curb the excessive harvest of the stock, or overfishing, but at the same time they also may generate excess capacity at existing stock levels. This is because open access motivations remain for any individual vessel to expand fishing effort as long as positive profits are generated (average revenue exceeds average cost). If the bio-economic framework is used to determine overcapacity, the impacts of regulatory factors must be taken into account to further conceptualize and understand the concepts of overcapacity capacity and non-optimal capacity utilization.
The concept of capacity utilization, even in fisheries, is relatively easy to understand. In its simplest form, it is simply the ratio of observed or technically efficient output to capacity output, where capacity output is defined in terms of either a maximum potential or economically optimum level of output. The concept may become a bit complicated to understand and calculate, however, because of related but different concepts of utilization. Almost from the beginning of FAOs initiative to define and assess capacity in fisheries, there has existed substantial confusion about the differences between capital utilization, capacity utilization, and variable input utilization. The three are related but not equivalent concepts. In this section, we attempt to illustrate the three concepts and related problems, again using the simple bio-economic model of Schaefer.
To begin, consider a fishery operating at the open access equilibrium level, which is characterized by a level of effort equal to EOA and revenue equal to ROA (Figure 9). Total cost (TC) for this initial situation is depicted by the total cost curve. This equilibrium is sub-optimal because the same level of revenue and catch could be realized with reduced fishing effort.
Figure 9 - Non-optimal capacity utilization with cost inefficiency
We now assume that regulations have been imposed to increase the stock to the MSY level. A total allowable catch (TAC) is set at the corresponding biomass growth rate. Competition exists, then, among boats to catch as much of this TAC as possible, but movement toward EOA is curtailed by regulation. Vessel owners, however, will keep investing in technology to remain as competitive as possible in order to catch a large share of the TAC. In this case, instead of moving toward EOA, the TC curve will shift upward so the TC* curve, including non-optimal use of capital inputs, intersects the revenue curve at the TAC level of RMSY (Figure 9). This short-run cost curve, incorporating non-optimal utilization of fixed inputs, is higher than TC due to cost inefficiencies from over-investment in fixed inputs that are not being used effectively to produce the allowed catch. Thus, costs are high and profits are negligible even at the maximum sustainable yield. Further development of this overcapacity concept requires a distinction to be made between variable (effort) input use, V, and the fixed capital component that is at sub-optimal levels, K, that make up the overall input base, E.
In this case, the TAC (CMSY) is being caught, although not at minimum costs because each boat could potentially catch more if it was able to use its capacity at full potential. No further investment is generated to compete more effectively, because no profit motive exists. Average revenue (AR) equals average cost (AC), or total revenue equals total cost, and again, more capital exists in the fleet than is necessary to catch the TAC. In terms of inputs, the extent of existing overcapacity can therefore be represented as the difference in effective E (or capital, K), implied by the gap between TC and TC*. In actuality, however, this situation depicts capital, and not capacity, utilization. Determining the level of excess capital in the fishery requires imputing the capital or fleet level associated with TC (the proportion that would contract 0-RMSY or 0-TC* to 0-TC (gap A), thus reaching minimum input costs). If we seek to directly determine the reduction in capital stock required to eliminate overcapacity, which also incorporates full utilization of the variable inputs and capital stock, we need an input-oriented or dual measure of capacity utilization. Alternatively, we need a measure of capacity utilization expressed in terms of the possible contraction of fixed capital inputs (vessels and power characteristics) but still capable of harvesting the current output level.
In contrast, determining potential catch if the current fleet was fully utilized would require adding the potential product from efficiently using this overcapacity for fishing purposes to the output or catch currently generated. This loosely implies (depending on scale economies and boat productivity, as elaborated below) addition of the TC-TC* gap above the revenue curve, which implies a full capacity utilization harvest level and, thus, revenues (RC) that would greatly exceed TAC=CMSY, or RMSY (gap B). The difference between the implied potential catch, CC, and CMSY, provides an output-oriented or primal measure of capacity utilization, which is consistent with the traditional concept of capacity utilization. This, in turn, implies a level of (variable) effort applied to the existing capacity base (or vessels) that exceeds what is currently exhibited in the fishery but would be consistent with full use of existing capacity. The difference between these two effort levels represents a capacity utilization indicator that is input-based, but output-oriented-a variable input utilization measure. The potential level of catch, however, would not be sustainable over the long run, and the stock would likely decrease. Nevertheless, the concept of capacity output can provide valuable information about the level of capital stock that should be removed from the fleet so that management goals and objectives are realized.
These three measures - the dual input-oriented measure, the primal output-oriented measure, and the variable input-based measure corresponding to the capacity output level - result in different utilization (CU) indicators. The dual input-oriented measure indicates how much the existing fleet could be contracted to a level of capital, KC, from the observed level, K, and still generate the same level of harvest, CUK=KC/K, assuming the full utilization level of the variable inputs. The output measure implies how much more output could potentially be produced with the given fleet if regulations - or other motives for producing at inefficient cost levels - were removed, and variable effort levels were correspondingly increased. This potential or capacity output level, CC, can be compared to observed (or target) catch, C, to construct a capacity utilization measure CUC=C/CC. The input-based measure of full utilization of the existing capacity indicates how much (variable) effort, E, would have to be increased to reach CC, EC, resulting in the capacity utilization measure CUV=E/EC, where V (and E) denote variable inputs.
Of the three concepts of utilization, only the output-oriented concept is actually a measure of capacity utilization. The dual input measure, while providing useful information, is actually a measure of capital utilization. Berndt (1990) defines capital utilization as the ratio of the desired stock of capital to the observed or actual stock of capital, which is the same as CUK=KC/K because desired could be equal to either the maximum potential output or the output level desired by management (e.g. the MSY level of output). The variable input utilization measure also is not a measure of capacity utilization. It is simply the ratio of the level of variable input usage required to produce the capacity or target output level, to the observed usage of a given variable input.
Differences among these measures arise not only in terms of perspective, and thus interpretation, but potentially in terms of magnitudes. The magnitudes of these ratios depend on the prevailing stock level, scale economies and the (marginal) productivity of boats (or their characteristics such as horsepower and technology). Importantly, it is these differences that have generated considerable confusion among resource managers and researchers about capacity utilization and capacity output in fisheries. The present emphasis of management is on reducing overcapacity in fisheries. Reducing overcapacity requires reducing the capital stock or number of vessels in a fishing fleet. To determine the potential reduction in the capital stock, however, requires information about the full utilization of the variable inputs by the existing capital. There has been a tendency by managers and fisheries scientists to focus only on the level of the capital stock (usually number of vessels) that must be reduced, without realizing that the desired level of the capital stock reduction is determined by the capacity or potential output and full utilization of the variable inputs. Thus, a key requirement to implement or quantify measures implied by the above analysis is an explicit link between inputs (V and K, or E overall) and output (C), particularly for estimating long-term sustainable yields. This requires knowledge or estimation of the underlying production relationship.
Estimation of capacity and capacity utilization requires recognition of constraints that fundamentally underlie the problem of excess and overcapacity, since the deviation between TC* and TC arises due to short-run rigidities and resulting non-optimal use of fixed inputs. That is, the existence of overcapacity, or lack of full capacity utilization, requires some restrictions or constraints on production or activity levels. In addition to the regulatory constraints raised as a motivating factor for the existence of excess and overcapacity, other constraints also may affect excess and overcapacity and capacity utilization. For example, onshore processing constraints may limit the level of fishing activity. If processors are unable to process more than a given quantity of fish per unit of time, this places a limit on the ability of the fleet to sell the fish they catch. In turn, this effectively limits the level of fishing activity and possibly results in higher costs of production than necessary for a given catch level.
At the individual boat level, breakdowns and subsequent repairs reduce the time available for fishing. In all cases, very few boats would be able to operate on every available day of the fishery, due to maintenance and repair requirements, unloading and re-provisioning, and rest and family commitments of the skipper and crew. This emphasizes the importance of distinguishing the maximum possible production from a given fleet, or capital stock, K, from the optimum or feasible production resulting from customary and usual operating procedures.
Older boats also may be subject to more breakdowns and therefore operate for fewer days than newer boats. Similarly, older skippers may fish for fewer days than younger skippers. This raises the issue of how to consider fleet heterogeneity, which must be recognized to effectively impute the impacts of K reductions, when assessing capacity and CU. These impacts will depend upon different boat characteristics and, thus, vessel or capital productivity. If licenses were transferred to newer boats with younger skippers, total fishing activity and subsequent catch could increase. These variations in productivity for different components of the capital stock should be taken into account or controlled for when estimating capacity levels and utilization, and particularly when guiding capacity reductions.
Fish stocks, or existing biomass levels, impose another constraint on production. In general, the potential catch from the existing fleet (or capital/capacity) will be greater at higher stock levels (at least at the levels observed for currently over-exploited stocks). The reduction in E (K combined with variable effort V), associated with a movement toward EMSY or EMEY, thus, requires the stock to regenerate in order to reach desired catch levels such as MSY or MEY. This implies both that current biomass stock levels will affect measured short-run potential capacity output or input levels, and that imputing these levels for more optimal long-run stock levels is important for determining long-run or overcapacity. Long-run adjustments to accommodate stock regeneration, and associated capacity reductions that do not yield short- run benefits, also must be taken into account when constructing and using capacity utilization measures to manage fisheries.
There are also potential issues related to uncertainty and time. Resource levels and market conditions typically change over time and, thus, it may be necessary to have sufficient harvesting capacity to take advantage of such changes. That is, in most fisheries stock sizes fluctuate from year to year. As a result, complete capacity utilization under all conditions is not possible. In poor years the capital could not be fully utilized, while in good years the capital would be insufficient to achieve an efficient level of catch, given resource conditions. Some underutilization of capital is desirable under average conditions to enable the fleets to efficiently exploit the fluctuating resource. This should be accommodated in the definition of customary and usual operating procedures, which emphasizes the importance of imputing an optimum rather than maximum utilization of capacity. The extent to which capacity underutilization is efficient, however, varies from fishery to fishery and depends to a large extent on economic factors (i.e. the costs of maintaining an under-utilized capital stock in average and poor years, against the benefits of fully exploiting the capital stock in good years).
In summary, full utilization of capacity for a fishery is determined by the potential catch or fleet levels if all fixed inputs (e.g. the boats and associated technological capital, or the capacity base) are utilized optimally, given prevailing stock and market conditions. The difference between these optimal or potential and existing levels depends on short-run constraints, which cause the existing total cost level, TC*, to exceed TC, because capacity or capital stock levels, K, are higher than required to produce prevailing (allowed) catch levels. Capacity utilization is, thus, essentially a short-term concept, measured as a ratio of actual to potential catch, given the level of fixed inputs. Capital utilization, which equals capacity utilization only if the technology exhibits constant returns to scale and there is only one fixed factor, is measured as the potential contraction of capital inputs from their actual level that could still catch the existing or target catch level, while allowing for variations in economic and environmental conditions due to customary and usual operating procedures and natural stock fluctuations. It is measured as the ratio of the desired capital stock to the actual stock of capital. Schworm (1977) provides an alternate definition or measure of capital utilization - the ratio of capital services to the stock of capital. Variable input utilization equals the ratio of the level of a variable input required to produce the capacity output to the observed or level of the variable input actually used to produce the existing output level. Recognition of the impact of constraints such as those associated with biomass stocks, and of the importance of both short-term fluctuations and long-run adjustment, is important to build into the construction, and also to the interpretation and use of resulting utilization indicators.
The three types of utilization concepts outlined above - output-oriented measures imputing full utilization of the given capital stock, input-oriented measures capturing the contraction of the capital stock possible to maintain production of existing output levels, and input-based measures representing the variable input use corresponding to capacity output levels - are only equivalent in magnitude under certain restrictive conditions. These restrictions involve scale economies (constant returns to scale - CRS), or input-specific economies or returns, given existing levels of other factors, a single fixed input, and an optimum capital output ratio that is constant over time (Berndt, 1990).
Deviation between the output- and input-oriented utilization measures depends on scale economies; they will only be equivalent if the industry is characterized by constant returns to scale (CRS), (i.e. doubling the quantity of all inputs doubles potential output). As presented earlier, let E represent the combination of vessel characteristics (i.e. technological capital, K) and the variable inputs (V) used to generate catch. Given constant returns to scale and our measure of E, the relationship between E and catch (C) must be proportional for a particular biomass stock level (B). The formulation of E implicitly requires that the combination of the capital stock (K, or the fixed inputs) and V underlying the measure of total effort, or E, is proportional, or that the contribution of each input to catch is the same for all scales of operation (Squires, 1987). This latter conclusion is related to aggregation theory, which stipulates that an aggregate input should increase by the same proportion as the components that make up the aggregate (e.g. if K and V both double, then E should double).
The difference between output- and (variable) input-based measures involves the returns to variable inputs, given the existing capital base, that result from an expansion in scale of production with the capital factors fixed. That is, both of these measures involve imputing the potential for expansion of output, given fixed inputs, but one is expressed in terms of catch and the other, in terms of (variable) effort levels (i.e. the full utilization level of inputs required to produce the capacity output). The measurement issue in this context is thus based upon returns to a particular input, rather than returns to scale, and the measures will only be numerically the same with constant returns to the variable input.
For many fisheries (and many other industries), the notion that these relationships are constant or proportional may be incorrect. Economies or returns to scale are likely to be variable and deviate across inputs. In addition, the returns to the variable inputs, which also can be measured by output elasticities, are not likely to be constant. In fact, the returns to the variable inputs are likely to be diminishing. For example, doubling boat size, engine power, and variable input usage in many fisheries would likely result in catch increasing by less than the rate of increase in all factors of production. In other fisheries, however, it is possible that a doubling of effort might more than double catch. In contrast, reducing the existing capacity base or fixed input level by half could decrease the potential catch by either less or more than 50 percent. The doubling of variable effort levels, given the existing capacity base, might be expected to result in less than a doubling of catch if fishers are operating economically. Diminishing returns would arise not only from the existence of fixed capital levels, but also from other fundamental constraints such as biomass stock levels. Diminishing returns also are implied by the existence of some optimal level of utilization, or application of variable effort to the existing capital stock in the fishery. But since production with excess capacity is, by definition, being carried out at non-optimal levels, increasing returns to variable effort could also prevail.
It also is likely that greater crowding in fisheries as overall effort levels rise will result in a less than proportional increase in the level of output, which implies diminishing returns to both capital and variable inputs. The notion of crowding is typically recognized as a congestion or technological externality. As a consequence, potential catch will not increase by as much as potential effort, particularly if the increased effort involves higher variable effort levels applied to a given capacity base. In this case, (variable) input-based measures of capacity utilization indicating the increased effort required to reach capacity output will imply a larger gap between existing and optimal levels than the corresponding output-based measures.
More specifically, the proportion that catch or output, C, can be expanded given the existing capital stock, K, is constrained by decreasing returns to (variable) effort. This particular primal concept of capacity output is based on Golds (1955) and Johansens (1968) definitions of capacity output, which are identical. Simply, the technology must be of such a form that a maximum level of production exists; Coelli, Grifell-Tatje and Perelman (2001) refer to this as the strong concept of capacity. Coelli, Grifell-Tatje and Perelman (2001) also note, however, that for some functional forms (such as the Cobb-Douglas or multiplicative form of the short-run yield function) having diminishing returns to scale, the weak concept of capacity offered by Färe (1984) must be used. This is simply because such functional forms do not experience a maximum. Rather, output asymptotically approaches a maximum as the levels of variable inputs approach infinity.
We use the weak concept of capacity output to illustrate the difference between an output-oriented and an input-oriented measure of capacity utilization. If we assumed that the production technology had a global maximum output, and output decreased for higher levels of effort, we might consider the strong definition of capacity output. We further assume, given the weak concept of capacity output, that for effort level E2, capacity output is bounded or limited by the fixed input base (Figure 10). In such a case, the level of variable inputs determines the overall level of effort.
Figure 10 - Returns to E and capacity utilization, output orientation
With diminishing returns to effort (E), let the capacity output equal C3; for constant returns to effort, let the capacity output equal C2. Given diminishing returns to the variable input, there is a gap between catch, C1, and the imputed potential or capacity output level, C3 that is smaller than that associated with constant returns to scale. The output-oriented capacity utilization measure, C1/C3, is closer to one than that based on the variable input or E, which equals E1/E2. If constant returns to E existed, the implied capacity output, C2, and the associated variable input use, E2, would result in identical capacity utilization ratios, C1/C2 = E1/E2.
A similar diagram can be used to illustrate the input-oriented measure of utilization implied by contraction of the existing capacity base, given current catch C=C1 (Figure 11). Note that this concept, however, really indicates capital utilization rather than capacity utilization. We consider the case of one fixed input to illustrate the potential differences between estimates of capacity output, when based on a measure of capital utilization, given different returns to scale. In this case, the input represented on the horizontal axis is the capacity base or capital stock, K. If the current level of capital is one of excess capital, the levels of K and C will not be consistent with economic optimization and catch C=C1 will be produced with a capital stock of K2. Imputing the contraction of K required to produce C at least cost, or optimally, thus reproduces point K1, which is on both the constant and decreasing returns frontiers. The corresponding capital utilization measure is thus K1/K2. Since this measure does not imply any change in output, no scale economy or returns to K impact is imbedded in the measure, so it is independent of the form of these economies. It will differ from the output-based measure, however, depending on the extent of decreasing returns.
Figure 11 - Returns to E and capacity utilization, input-orientation
The ratio, K1/K2, is equivalent to the output measure, C1/C2, that represents the (inverse of the) expansion of catch that could potentially (or optimally) be supported by K2, given constant returns to scale. However, with decreasing returns to scale, the output-based measure of capacity utilization is greater than the equivalent measure based on K: C1/C3 > K1/K2. This implies a smaller potential expansion of catch than if constant returns existed, and thus a greater adjustment of K than C to reach the potential or capacity input, KC (K1), or output levels, CC (C3). The deviation between these values may be measured only with information on the extent of returns to K and on scale economies if variable inputs adjust correspondingly. Such information may be generated through quantitative estimation, such as through a parametric model, although the resulting evidence of scale economies may be difficult to interpret since actual (variable) inputs are typically not well measured but instead broadly represented as effort.
It also is possible that output- and input-oriented measures of capacity output may differ because of their dependence on the state of the biomass. The biomass, or stock, is an underlying constraint or rigidity affecting potential catch. Imputation of potential or capacity catch and associated variable input levels therefore depends on existing biomass (B) levels, unless this potential is explicitly evaluated in terms of short-run potential, given the existing biomass. Over the long run, expanding catch levels implies changes in the stock.
Input-oriented utilization measures based on K contraction for a given C are independent of assumptions about the biomass, because assessment of capacity is made with existing output, and the associated stock, as a reference point. This is similar to the qualification raised for scale economies, since simulating potential catch levels may involve extrapolating catch and associated stock levels outside the range of existing observations, rather than evaluating relationships at existing scale (catch) and thus stock levels. This implies both that input-oriented measures reduce the difficulty of recognizing complex stock-flow issues associated with catch and both input and biomass stocks, and that to measure potential output we would not want to extrapolate beyond observed and, thus, feasible catch levels, particularly at the boat or trip level.
However, even though input-based measures reduce the potential for convoluting capacity and scale economy or stock issues and measures, identifying the input contraction that could be made and still support the existing level of output requires significant information about the productive process. In addition, the answer to this question also would differ if evaluated at different biomass stock levels. In particular, it requires information about the relationships among inputs and outputs (the production function, and resulting marginal and average productivities of inputs), the constraints imposed by biomass levels, and the potential future impact of technological progress (technical change or shifts in the production function).
Overall, output- and input-oriented capacity utilization measures are not directly comparable without corresponding estimates of scale economies and their input-specific components, and estimates of the dependencies of these relationships on the biomass. Output-oriented measures impute the potential or optimal output or catch possible to produce given the existing capital/vessel base, or capacity. Since this implies expansion of scale and harvest levels, it raises problems associated with scale economies and biomass dependencies. Input-oriented measures represent the potential contraction in existing capital or capacity that would still support production of existing catch levels. This requires recognition of varying vessel productivities, but does not imply changes in scale, and thus stock, if evaluated in the short run. Constructing either type of measure requires information to be generated about productive possibilities of inputs, and substitutability. However, since the different measures provide alternative complementary perspectives on the state of the fishery, they are all useful to construct to assess and manage capacity.
In practice (and as already evident from the qualifications presented in the previous two sub-sections), the conditions assumed in the simple illustrative examples presented in the previous sections were overly simplistic. They provide an adequate basis for illustrating concepts, but they would likely be too limiting for an empirical analysis and assessment of capacity output and capacity utilization in fisheries. Many of the issues alluded to relate to stock characteristics (heterogeneity), the form of the short- and long-run technology, and rigidities or expectations (short- as contrasted to long-run behaviour).
A fundamental issue, which should be addressed for construction, interpretation, and use of capacity and capacity utilization measures for micro-management, concerns the fact that boats are not homogeneous in cost structure and activity. Vessel operations typically involve different lengths of time, types of gear, technologies and cost structures, and often target a range of different species. As a result, the selection of boats to remove from a fishery must be based on appropriate criteria established by managers. A removal or capacity reduction strategy that does not adequately consider the heterogeneity of the fleet could greatly affect the level of output and the potential economic benefits that are generated. It is important to a capacity reduction programme, therefore, that overall measures of capacity utilization for the vessels in the fishery be generated, but also, individual boat measures of productivity, efficiency and utilization, calculated. This latter step, however, may be quite difficult since data may not reveal differences among vessels. For example, if boats are assumed homogeneous, removing the most economically efficient (i.e. least cost per unit of output, or largest level of output for given input levels) vessels could result in maximum sustainable yield being achieved with few economic benefits being generated. Similarly, removing the least technically efficient boats (in terms of catching ability) may result in a reduction in fleet size with either no change or only a minimal change in the potential output from the remaining fleet. The estimation and analysis of capacity should therefore consider boat-specific capital and other input characteristics relating to the efficiency of operations and catch.
Latent effort must also be considered when focusing on the overall fleet level. Individuals or firm owners may possess licenses to fish, but for various reasons they are not currently operating in a particular fishery. These vessel owners could, however, easily renew their activities in an existing fishery. Alternatively, individuals may own a permit to fish in a fishery, but the permit is for a vessel that has been destroyed. In this latter case, the holder of the permit may be able to purchase a new vessel and reactivate the permit for the fishery. In either case, the effective capacity base could increase. These possibilities also need to be considered when calculating capacity output and capacity utilization measures for a fleet.
Multiple species or multiple product fisheries also present problems for calculating and analyzing capacity and capacity utilization. Many fisheries of the world involve the capture of more than one species (i.e. a multispecies fishery), or the landing of more than one product (multiple product fishery). In the case of multispecies or multiple product fisheries, technical and economic interactions usually occur (e.g. the capture of one species affects the capture of another species, or the price level of one species affects the capture of other species). If these potential interactions are not adequately considered in an analysis of capacity, it may not be possible to determine the optimal or desired least cost or profit maximizing fleet. In order to adequately calculate and assess capacity in either multispecies or multiple product fisheries, it is very important to explicitly incorporate potential technical and economic interactions into the calculation and analysis of capacity.
Determining the respective adjustment period poses another potential problem for calculating a concept of capacity useful to resource managers. That is, should calculations be based only on the short run, or should more attention be given to determining capacity output over the long run? The presence of excess or overcapacity capacity implies that fisheries are not in a long-run equilibrium, or that short-run rigidities are driving observed costs. If a fishery is not in long-run equilibrium, it will not be possible to observe long-term catch rates. Managers, however, typically desire information on capacity relative to the long-run or desired resource levels. Methods for calculating capacity should, therefore, be capable of determining the potential long-run output expansion, or input contraction, using available or mostly short-term information. Implications for a long-run adjustment of the capacity base and biomass stock, as well as future technical change, also need to be considered in the calculation of capacity output, however. They have important ramifications for determining the capital stock or capacity base for a fishery.
For the purpose of estimating capacity output, it is also important to account for the impacts of short-run fluctuations and expectations on production and apparent excess and overcapacity. Excess capacity in the short term may actually be desirable, in terms of feasibly maximizing the benefits derived from fishing. Having excess capacity in the short run may permit cost efficient adjustments to the capacity base in the long run (i.e. it may be less expensive to purchase vessels in the present than it is to purchase them in the future). Fluctuations in either stock abundance or biomass are typical of many fisheries. Having seemingly excess capacity in one period when stocks are low may not actually equate to overcapacity in a period when stock abundance or biomass is high. Simply put, vessel operations with adequate capacity may be able to take advantage of high resource levels, even though they have excess capacity when resource levels are low. Harvesting at this higher level may yield higher net benefits to society than would be realized by harvesting levels corresponding to a lower capacity base. A measure of fisheries capacity also should recognize the existence of physical and motivational limitations; for example, required maintenance and personal choices considered to be part of customary and usual operating procedures.
One possible way to better consider the long-run notion of capacity, given various short-run issues, is to base the calculation and analysis of capacity output, capacity utilization and the capital base on information reflecting several years of operations. Alternatively, averages may be used to actually access capacity output and capital and capacity utilization, as was recently done in Walden, Kirkley and Kitts (2003). The use of information over several years should permit a calculation of capacity output that somewhat reduces the influence of stock fluctuations, while also better reflecting customary and usual operating procedures. The use of several years of information also should permit a distinction to be made between desirable excess capacity (that exists for economic reasons and accounts for fluctuations in stocks and market conditions, or normal physical limitations such as required maintenance) and undesirable excess capacity (capacity levels that are higher than the economically desirable or optimal level).
Calculating concepts of capacity and capacity utilization, which will be useful for capacity reduction programmes, therefore may be quite complicated. It should be evident that the basic bio-economic framework presented in Sections 2.3 through 2.5 is too restrictive or simplistic for developing useful measures of capacity and capacity utilization. The purpose of presenting that framework, however, was to illustrate basic concepts related to capacity and capacity utilization. A considerably more complicated analytical framework needs to be developed; the framework or method to be used will, however, primarily depends upon available data. That is, if appropriate economic data are available, an economic concept of capacity should be calculated. These estimates should be based on economic measures presented in the literature (e.g. Morrison and Berndt, 1981; Morrison, 1985a, b; and Berndt, 1990) and more recent research developments, such as Fousekis and Stefanou (1996), Fagnart, Licandro and Portier (1999), Färe, Grosskopf and Kirkley (2000), and Coelli, Grifell-Tatje and Perelman (2001). If only primal (outputs and inputs) related data are available, then the technological economic concept of capacity is all that can be estimated. In the absence of any empirical data, it is likely that a survey will have to be designed and implemented to calculate capacity output, because it will likely be the most consistent measure.
In subsequent sections of these guidelines, we present concepts of capacity output and capacity utilization and methods for estimating these concepts when data are primarily limited to observations on input and output levels. It is recognized that several member states of the European Union, the United States, and other nations have initiated large-scale economic data collection programmes, but such data are not available for all fisheries and all nations. Methods requiring only primal data thus are likely to have the broadest current applicability. There is, however, an increasing body of literature on dynamic measures of capacity output using both cost and profit functions, or the assumption that producers maximize profit or minimize cost. An excellent treatment of ways to estimate and analyze the economic concepts of capacity and capacity utilization in fisheries when only data on output prices and levels and input quantities are available appears in Segerson and Squires (1990, 1993, and 1995). The approach, however, is quite complicated and requires an understanding of duality theory and virtual prices. For the most part, we ignore this more recent literature, and instead refer readers to the more recent references focusing on economic measures.
 The mathematical
specification of the production technology is not the most generalized
specification of the technology. For more general specifications, see Chambers
(1988) and Fare, Grosskopf and Lovell (1994).|
 The relationships discussed pertain to what is usually referred to as the classic production function. With this production function, there are three stages of production, which may be characterized in terms of the average product or the ratio of total output to the level of the variable input. There are numerous other specifications, which do not assume the three stages of production.
 Returns to scale depicted in Figure 2 assume extremely restrictive forms of technology. More complex forms are illustrated in Coelli, Rao and Battese (1998).
 Conrad and Clark (1987) and Hilborn and Walters (1992) present considerably more complex biological and bio-economic models. Alternative dynamic specifications appear in the literature on dynamic pool models. Brock and Riffenburgh (1963) and Clark (1976) have shown that the logistic model may be inadequate for many types of schooling fish.
 Alternative functional forms of the long-run sustainable yield function are possible. Different short-run yield functions or different growth functions yield different long-run sustainable yield functions. Pella and Tomlinson (1969) allow for raising the second-order term of the traditional growth function to some arbitrary power. Similarly, the use of a short-run transcendental or translog production function results in different long-run sustainable yield curves. Also, sustainable yield curves for some types of species, such as shrimp, may be characterized by sustainable yield curves with high sustainable yields over a wide range of fishing effort levels.
 As presently illustrated, excess capacity is defined relative to a level of landings interior to the long-run sustainable yield. It could just as easily be characterized relative to landings in excess of MSY but lower than COA.
 If price varies with output, the shape of the sustainable revenue curve would be quite different. A linear total cost function has been assumed, but it is possible for the cost function to be non-linear.
 The total cost curve has been drawn to intersect the sustainable revenue curve to the right of the MSY level. It is possible for total cost to intersect the sustainable revenue curve either to the left of the MSY level or exactly at the MSY level. In either case, the open access equilibrium level of profit would still be zero.
 This conclusion is based on the simplistic assumption of zero discounting, no uncertainty, the form of the technology and long-run sustainable yield curve, and price being constant. Clark, Clarke and Munro (1979), Charles and Munro (1985) and Conrad and Clark (1987) provide conditions for different conclusions. Conrad and Clark note, however, that the optimal level of fishing effort will at least be less than the open access level of fishing effort.
 An obvious exception to this conclusion, of course, would occur when the total cost curve intersects the revenue product curve (sustainable revenue curve) either at MSY or to the left of MSY.
 A wide range of alternative specifications or frameworks exist for constructing bio-economic models. See, for example, Deriso (1980), Conrad and Clark (1987), and Hilborn and Walters (1992).
 In the short run, capital and equipment are generally viewed as fixed or quasi-fixed inputs; that is, they cannot be increased or decreased. For example, a vessel size cannot be changed in the short-run. Over the long run, however, capital and equipment may be viewed as variable inputs. They can be changed. A vessel owner, for example, can purchase a larger vessel. From an economic perspective, the long-run competitive equilibrium for an industry occurs at the point of minimum long-run average cost. This occurs because firms enter an industry and eventually force the price received by producers to equal minimum average cost. At that point, there is no incentive for entry or exit.
 This does not mean, however, that there is no incentive to make new investments. Fishers will likely invest in technology that may allow them to more effectively harvest a share of the catch, and this will increase the level of capital in the fishery.
 This notion of capacity output, primal, is strictly a short-run concept. It assumes that the capital stock or fleet is given. It is a measure of the potential output that could be produced given resource conditions, technology, capital stock, and full utilization of the variable factors (the level of variable factors required to produce the capacity output level). Although it is a short-run concept, it provides a valuable reference point for management. If managers have information on the level of capacity output for a given capital stock, they can then determine the level of capital stock that must be reduced from the current fleet to achieve a desired harvest level (e.g. MSY or MEY).
 Färe, Grosskopf and Kokkelenberg (1989) refer to the measure as the optimum variable input utilization ratio. It is the ratio of the observed level of variable inputs to the level of the variable inputs required to produce the capacity output.
 This notion is explored in the context of excess capacity resulting from future expectations, as distinguished from that associated with disequilibrium or short-run rigidities, in Morrison (1985a).
 Färe (1984) and Färe, Grosslopf and Kokkelenberg (1989) introduce the notion that output is bounded by a fixed input. This can apply to either constant or variable returns to scale (i.e. diminishing returns to the variable input are not required). Coelli, Grifell-Tatje and Perelman (2001) provide additional discussion about the capacity concept of Färe; more formally, this concept of capacity is referred to as the weak concept of capacity, whereas the Johansen concept is referred to as the strong concept of capacity. With the Färe concept, production is bounded by the fixed input, and additional levels of variable inputs do not increase output. (In Figure 10, for example, once E2 was reached, assuming E2 equalled the full utilization level of the variable input, the output would remain unchanged regardless of the level of the variable inputs.)
 The returns to K here involve only the C-K relationship. However, assuming that variable inputs are not constraining the relationship, returns to K and to scale are essentially equivalent. That is, if variable input or effort use is represented in this diagram, decreasing returns would be expressed in terms of short-run returns rather than scale economies. The latter implies a movement along long-run cost curves, whereas, by definition, in a situation of excess capacity the relevant cost curve is short run.
 Gates, Holland and Gudmundsson (1996) demonstrated that it is critical to know the general level of efficiency of each vessel, particularly for buyback programmes. Buyback programmes in the United States generally have removed the least efficient vessels, and thus not substantially reduced capacity. Walden, Kirkley and Kitts (2002) provide an analysis of the level of capacity reduced in the New England groundfish buyback programme.
 A multispecies fishery is one in which more than one species is caught. A multiple product fishery may involve either multiple-species or a single species (e.g. many single species fisheries involve some level of price discrimination based on size or sex of the product being landed).
 Methods for estimating both static and dynamic economic concepts of capacity are discussed in Clark, Clarke and Munro (1979), Morrison (1985a,b), Conrad and Clark (1987), Grøn (1994a,b), Fousekis and Stefanou (1996), Fagnart, Licandro and Portier (1999), Higgins and Thistle (2000), and Coelli, Grifell-Tatje and Perelman (2001).