3. MEASUREMENT OF CAPACITY AND CAPACITY UTILIZATION

Several nations already have developed measures of capacity output based on the physical attributes of the fleet and implemented capacity reduction policies based on these capacity measures. See, for example, Kirkley et al. (2002) for an analysis of five United States-managed fisheries and Walden, Kirkley and Kitts (2003) for analysis of the United States Northeast Groundfish Fishery Buyback Programme. Of primary concern to most fisheries managers is the optimum utilization of the capital employed in the fishery (Kirkley and Squires, 1999). Fisheries managers need to know the fleet size and configuration that achieves the objectives defined by the management plans and policies of their respective nations. These usually equate (implicitly or explicitly) to some target level of output, which is often based on biological concerns. To this end, measurement of the capacity base and capacity output for a fleet or fishery is essential for comparison to these targets, representation of full capacity utilization, and management of capacity.

To provide an aggregate measure of capacity output or capacity utilization, it is necessary to deal with issues that arise for the aggregation of output, input, and stock measures, even if input-based measures are used that are not as dependent on the additional issues of scale economies and stock levels. The units are generally non-homogeneous, and restrictive assumptions may be necessary to aggregate or proxy them if characteristics cannot be measured and subsequently used to form aggregates. If the underlying simplifications and assumptions are not valid, and in most cases they are unlikely to be valid, the resulting aggregate measures may be distorted. In addition, there are serious theoretical issues related to aggregation. See, for example, Daal and Merkies (1984); Corns (1992); Dervaux, Kerstens and Leleu (2000); and Färe et al. (2000). It is therefore important to carefully consider how to measure the capacity base and input and output quantities in order to facilitate their applicability to management decisions.

3.1 Input stock or capacity and effort measures

Constructing capacity utilization (CU) measures based on either an input or output perspective requires representation of the fixed stock of inputs comprising capacity, or the capacity base. This typically involves measuring the number or characteristics of the vessels, or the capital stock, in which case the capacity utilization measures expressed in terms of inputs are equivalent to capital utilization measures.^[25] If other stocks also make up the capacity base and are assumed immobile and thus fixed (e.g. labour, which includes skipper and crew and the fish stock level, if capacity utilization is expressed for a given fish stock level), a broader interpretation of available capacity is implied.

For effective management, measures of the capacity base should take into account varying characteristics across vessels or fleet segments. That is, different productivities of alternative types of (fixed) inputs must be recognized and measured for appropriate capacity and capacity utilization analysis. This may be accomplished by identifying vessel characteristics that determine the overall “fishing power” of a given vessel and combination of vessels at the sub-fleet or fleet level. Estimation of capacity utilization may then be carried out separately for units with similar characteristics in terms of fishing activity (e.g. gear type used, fishing area, target species), or by explicitly controlling for (or taking into account) different productive contributions stemming from variations in such characteristics.

The application of variable inputs to the capacity base determines the potential output that may be produced from the existing capacity base. As presented above, this capacity output is compared to existing output levels to construct output-oriented capacity utilization measures, and the implied variable effort levels required to reach this potential output are compared to existing effort levels to generate input-based (but output-oriented) “variable input utilization” measures.^[26] Alternatively, the potential contraction in the capacity base that could still support existing catch or output levels may be imputed and compared to the existing capacity or capital level to construct directly input-oriented capacity utilization measures. Both of these input-based measures are sometimes referred to as capital utilization measures, although capital utilization may be expressed from either an output or input orientation; it just requires that only capital inputs comprise the capacity base.

Construction of capacity utilization measures, therefore, first requires defining and characterizing the inputs and outputs used for production, and then distinguishing between the inputs making up the capacity base (the fixed inputs) and those that could adapt to produce capacity or full-utilization output from this base (the variable inputs).

3.1.1 Vessel units: fixed inputs, or the capacity base

The key (fixed) input capacity indicator is some measure of the stock of capital. This might include, at the most basic level, the number of boats in the fishery. Kendrick (1961), however, demonstrated that the number of operating units (e.g. plants) is an inadequate indicator of the capital stock; Kirkley and Squires (1986) demonstrated this was also the case for fisheries. Other measures have been developed that capture not only the number of boats in the fishery, but also the size of these boats, including measures of total gross tonnage, hold capacity or total engine power in the fleet. These latter measures characterize the fixed input or capacity base in terms of their productive characteristics. These measures recognize that a small fleet of large boats may have the same, if not greater, harvesting potential than a large fleet of small vessels. The FAO Mexico City consultation developed a comprehensive list of major capacity characteristics by gear type, which illustrates the potential array of different possible characteristics (Table 1).

Table 1 - Major capacity characteristics by gear type

Source: FAO (2000).

Several nations have developed composite measures of capacity based on the physical characteristics of the vessels, such as boat size and engine power. These measures attempt to equate capacity to fishing power (Kirkley and Squires, 1999).^[27] An assumption of such measures is that fishers are able to substitute among inputs, and hence an appropriate measure of capacity requires the combination, rather than individual quantities, of inputs to be represented. For example, in the United Kingdom, input-based vessel capacity is measured using Vessel Capacity Units (VCUs). These are defined as follows:

VCU = l × b + 0.45kW

where l is the length of the boat (in metres), b is the breadth (in metres), and kW is the engine power (in kilowatts). This is essentially a simple hedonic formula relating “effective” capital units to their characteristics. This particular formula was derived from an econometric analysis of the Scottish North Sea trawlers, and was found to explain between 70 and 80 percent of the differences in earnings between boats (United Kingdom Fisheries Department, 1988).^[28] While derived on the basis of the North Sea trawlers, the formula has been applied to all boats operating in all United Kingdom fisheries regardless of the gear type or target species. VCUs are estimated for each individual boat in the fishery and aggregated to give a total (fixed or stock) input capacity, or “effective” capital capacity measure, at the national level. In Australia, a similar measure was developed for the purposes of capacity management. However, unlike the United Kingdom, the units are non-transferable between fisheries. While intuitively appealing, such a measure can create severe distortions if applied to all fisheries for capacity management, because the relative importance of the boat size and engine power varies from fishery to fishery and its estimated contribution may crucially depend on the available data.

A preferred measure of the capital stock in a fishery is the economic value of the capital stock (Bell, 1967; Kirkley and Squires, 1986). The economic value of the capital stock can greatly ease the problems associated with aggregating over different types of capital and equipment and over different capital platforms (e.g. vessels). In addition, shadow values or rental prices can be obtained for different attributes of the capital stock, which reflect differences in the productivity of the various attributes. An economic measure of the capital stock for a fleet can then be obtained by aggregating the market values, insurance values, replacement values, or the actual investment values of the vessels.^[29] In theory, these measures should capture the differences in fixed input combinations (including difficult to quantify inputs such as levels of technology) on the assumption that the market value or one of the other measures of the capital stock reflects the productive capacity. In practice, however, financial values of the inputs may provide misleading indicators, particularly since financial depreciation may not correspond to a reduction in the productive capacity of the input. Such measures also preclude the ability to distinguish among the contributions of different types of investments.

For many fisheries, however, information necessary for constructing an economic value of the capital stock is not available. In this case, it may be possible to consider the differential capital productivities by explicitly incorporating different capital characteristics into the analysis as individual production determinants, or inputs; that is, the components of (fixed) input capacity may be measured separately. The capacity base, therefore, is recognized to have different quality-adjusted or effective levels depending not only on total boat numbers, but also on total gross tonnage and total engine power and, perhaps, on other indicators of “power” if available. An alternative framework to adequately deal with quality differences and varying characteristics, while also constructing an economic measure of the capital stock, is to combine different types of capital goods by weighting each type by its average compensation (National Academy of Sciences, 1979; Kirkley and Squires, 1986). In this way, it is possible to develop an aggregate measure of the capital stock. The information necessary for developing this latter measure of the capital stock, however, is seldom available for fisheries. Measures based on the physical indicators of the capital stock and fishing power may be estimated as separate indicators of capacity either at the boat or the fleet level. However, aggregating to the fleet may be difficult to accomplish without direct estimation of the varying productivities of the capital characteristics, potentially through the empirical representation of the production function relationship required for direct capacity utilization measurement.

3.1.2 “Effort” units: variable inputs applied to the capacity base, or overall effort

Effort is an abstract concept that consists of many elements, including time fished, the level of inputs, level of technology and the skill of the skipper and crew. Effort is typically represented as a combined measure of fixed (vessel) and variable (crew, fuel, days) components.^[30] Effort may be viewed as an aggregate input (e.g. we combine labour and capital services with fuel and call it fishing effort). Alternatively, we may view fishing effort as an intermediate output in a two-stage, non-separable technology, in which factors of production (e.g. fuel, capital and labour) are used to produce an intermediate product (e.g. effort) in stage one, and then used as an input to produce a final product in stage two (Pollak and Wales, 1987). However, the fixed input stocks making up the capital base (capacity) must be distinguished from the variable inputs applied to this base (effort) to represent non-optimal utilization of capacity. These variable inputs are typically summarized simply as days fished or days at sea, which represents the combination of inputs applied to the capacity base to generate catch, assuming that they are applied in some constant proportion. This is often done since many of the actual inputs are difficult to quantify, both conceptually and due to limitations in available data. Effort is thus generally measured in terms of time spent fishing or days at sea (days or hours fished per boat, or nominal effort).^[31]

This measure is, however, often standardized to account for differences in relative fishing power, such as those due to differences in boat size, skipper and crew skill, and level of technology (effective effort). Such standardized measures of the relative performance of different boats compensate for heterogeneity in the fleet. Standardized measures of effort are often constructed by normalizing effort by multiplying the ratio of the catch per unit effort of an existing vessel to the catch per unit effort of a reference vessel or gear, although a range of methods have been used to calculate relative fishing power (Gulland, 1956; Comitimi and Huang, 1967; Pope, 1975; Ricker, 1975; Hilborn and Ledbetter, 1985; and Hilborn and Walters, 1992). Kirkley and Strand (1984) provide a discussion of economic approaches to standardizing effort (e.g. cost, revenue and technical efficiency measures are used to standardize nominal fishing effort).

While the measure of total effective effort in a fishery is generally equivalent to that of total nominal effort for the particular time period in which fishing powers were estimated, changes in the composition of the existing fleet will result in a divergence between the nominal and effective measure of effort. For example, if the least efficient boats (in terms of catch per unit of nominal effort) were removed from the fishery, effective effort would decrease by less than nominal effort. This notion of standardized effort, however, is also a combination of the variable (E, effort) and fixed (K, capital) inputs that determine overall productivity, and it is necessary to distinguish their contributions separately for direct evaluation of capacity and capacity utilization in a fishery.

An alternative version of a standardized unit of effort is one that is expressed in terms of vessel features, rather than time fished, and thus is based on fixed rather than variable inputs. In this case, performance is related to a particular feature of the boat, such as engine power, so that a standardized unit of effort can be derived, say, by multiplying the engine power by days fished to produce a hybrid measure (i.e. kW days fished).

Measures of fishing power based on a single feature to adjust for the “effectiveness” of the capital stock can generally be readily derived for all fleet segments and fisheries, and thus provide a relatively easy foundation on which to aggregate across boats. However, while such a measure is likely to be related to the harvesting capacity for similar types of vessels, it may not be readily comparable across fleet segments (Ricker, 1975). For example, larger trawlers use bigger engines and are likely to catch more per day than smaller trawlers with smaller engines (i.e. some proportionality may be assumed between relative engine power and catch rates). In contrast, vessels using similar engines but different gear may achieve significantly different catch rates when operating in a given fishery. Measures of fishing power based on a single feature are, therefore, less accurate when comparing fleet segments within a fishery than standardized effort units based on more inclusive measures of fishing power. This also makes them less representative of the true mix of a variety of vessel characteristics. It seems that such characteristics might better be measured and represented in terms of their specific productivities (catch rates), to distinguish their individual impacts on catch for both specific vessels and the fleet as a whole.

The previously discussed standardization techniques have limitations.^[32] The standardization process is quite fishery-specific, so aggregation of standardized effort units across fisheries is seldom appropriate. It also does not readily allow for the application of production-oriented methods for constructing capacity measures. Such standardization may nevertheless be required for other purposes. In particular, estimation of fishing powers as a way of standardizing effort between different fleet segments within a given fishery is the basis for developing the biological or bio-economic models of fisheries that would be required for the estimation of target capacity levels. These methods may also be useful when data are especially limited. In particular, information on catch rates is necessary for the explicit estimation of fishing power but, in some cases, is not available at the individual boat or even fleet segment level. Measures of characteristics or even nominal levels of the fixed and variable inputs may also not be available. In these cases, the simpler standardized measures may be used to represent “effort,” and can be estimated at the fleet segment, fishery or national level without taking boat-specific characteristics into account. Results derived from this approach, however, would require careful interpretation. The qualifications above about the importance of representing a variety of specific input characteristics and their contributions to catch in order to more justifiably identify variations across boats or fleet segments must be taken into account when using such measures to guide policy.

The overall level of effort, E, for a fleet is a complex combination of variable “effort” in terms of days, crew, fuel, and other variable inputs (V), and the services of capital and equipment embodied in the vessels (K). Again, this presumes that the condition of separability, which is required for constructing an appropriate aggregate, characterizes the technology.^[33] This combination may not be expressed as a standardized measure for the representation of capacity and capacity utilization, since full capacity input-based measures are defined in terms of K, given catch levels, or in terms of E, given the capacity, or capital stock. And this distinction between fixed and variable inputs is necessary to generate total input measures for any level of aggregation - that is, for boat, sub-fleet, or fleet-level measures of inputs and resulting capacity and capacity utilization.

If appropriate data are available, output-oriented measures of capacity and effort may be developed and used instead to focus on the distinction between vessel characteristics comprising the capacity base, or fixed inputs, and effort or variable inputs applied to the base. Recognition of different boat, and ultimately fleet, characteristics, must be built into the process of capacity and CU estimation, in order to control for fishery-specific input relationships. This is important for identifying either the amount by which the capacity base could be reduced and still generate existing catch or TAC levels, or the output that the existing capacity base could potentially support. An output-oriented measure also facilitates justifiable aggregation of boat-level characteristics to analyze the potential power of the fleet as a whole, and to help determine the optimum fleet configuration when there are heterogeneous operating units.

The underlying productive relationships can be expressed in this case in terms of a production function relating output produced to the fixed and variable inputs applied (and their characteristics). For multiple output fisheries, these relationships may be expressed in terms of more general functions, such as a distance function, stochastic multiple output distance function, or polar coordinates (Löthgren, 1997). If the data are available to quantify these relationships, measurement methodologies that identify the specific contributions or productivities of capital stock and variable inputs may be applied, which is important for establishing the capacity level embodied in the capital stock. Analysis of the underlying production technology allows a detailed evaluation of the true power of the input stock, and the implications in terms of catch rates of reducing the physical capital stock, required for measuring and assessing capacity, capacity output and capacity utilization.

3.2 Capacity utilization definitions

Capacity utilization is defined more precisely in this section in relation to output, effort and input.

3.2.1 Output-oriented capacity utilization measures

The general definition of capacity output given in Section 1.1 can be modified to the specific definition of capacity output: the maximum amount of catch that can be produced in a given unit of time (e.g. year or fishing season) with existing plant and equipment under customary and usual working conditions, provided that the availability of variable factors of production is not restricted. In this case, the variable factors of production include days (or hours) fished, labour, quantities of gear, etcetera, which are separately identified from the capital or capacity base defined in terms of vessel characteristics. Hence, capacity output is fundamentally determined by the capacity base and is directly related to the corresponding full utilization level of variable inputs or “potential effort”, although the relationship is not necessarily proportional. This basic definition, however, is consistent with the strong concept of capacity output offered by Johansen (1968) and discussed in Coelli, Grifell-Tatje and Perelman (2001). The weaker concept, in which output is bounded or limited because of fixed factors, is generally used in this volume; this is especially the case when the primal or technological-economic concept of capacity output is used.

Determining capacity output requires imputing the catch that would be generated if all boats (available capital or capacity) operated at maximum potential effort levels (say, days or hours), given normal working practices (i.e. making allowances for repairs and other normal breaks in or constraints on fishing activity), and the state of the production technology (i.e. the technology required to convert inputs into outputs or produce a product). This requires taking a measure of the existing capacity (capital) and determining the most feasible catch from this capacity base, given the prevailing production technology and environmental/biomass conditions.

Capacity output can be measured at the species level or aggregate fishery level. For effective management of the fishery, measurement of capacity output should be undertaken at the species level where possible. This is important when identifying the extent to which individual species are being over-exploited, or face potential overexploitation.

Capacity utilization (CU), relative to capacity output, is the ratio of the current catch level to the capacity (or potential) catch level, which is interpreted as the extent to which the fixed inputs in the fishery (e.g. capital) are being utilized.^[34] That is, for the output (catch) oriented measure,

The measure of capacity utilization ranges from zero to one. Values of CU significantly less than one indicate the existence and extent of excess capacity in the fishery. That is, the current catch could be increased with no change in the fixed input base or capital stock, if operators fully utilized the variable inputs. The proportion by which a fleet could potentially contract and still produce the existing catch level is loosely implied by the CU measure. For example, a measure of 0.75 implies, very loosely, that reducing capacity by about 25 percent would allow the current output level to be produced in an economically optimal manner. As previously discussed, however, the actual magnitude of the measure will depend on scale economies and returns to individual factors.

As previously noted, however, CU measures should be carefully assessed relative to resource and economic conditions. One way to do this, particularly in the absence of detailed economic data, is to develop CU measures under average resource and economic conditions. Measures derived under average conditions should facilitate a better understanding of the severity of excess capacity and promote capacity reduction targets more consistent with the needs of management. Consider, for example, a period during which resource or economic conditions were favourable for increased exploitation. It is likely that an analysis of capacity would suggest a higher level of capacity output than would normally be realized by a fleet or vessel. If a subsequent capacity reduction programme was based on estimates of capacity output obtained during periods supporting high capacity output, the programme might remove too many vessels, particularly relative to customary and usual operating procedures. Similarly, if the capacity reduction programme was based on estimates of capacity output obtained during conditions supporting very low catches, it is possible that the programme would remove too few vessels from the fishery. In order to assess the extent to which capacity underutilization is excessive, it is important to compare CU measures over several years of observation, including periods in which fish stocks were considered “good” or above average, to distinguish stock from utilization fluctuations.

3.2.2 Potential effort and variable input utilization

Potential effort is the level of effort or levels of all variable inputs required to produce the capacity output, given the existing capital stock. More formally, we can define such a measure of potential effort as follows: the (variable) effort level corresponding to the maximum amount of catch that can be produced in a given unit of time (e.g. year or fishing season) with existing plant and equipment under customary and usual working conditions but with variable input use unrestricted.

In the case of fisheries, and because of limited data, days at sea or days fished, or some other measure of fishing effort is typically used to represent the influence of the variable factors of production. If additional data are available, such as person-hours of skipper and crew labour, these other variable factors also should be included in an analysis of variable input utilization. The corresponding input-based (but output-oriented) measure of capacity utilization is typically referred to as the variable input utilization (CU_V) (Färe, Grosskopf and Kokkelenberg, 1989; Färe, Grosskopf and Lovell, 1994). The measure provides an indication of the level of effort or levels of variable inputs required to produce the capacity output; it is therefore an input-based but output-oriented measure (i.e. it provides a measure of the proportion by which variable inputs should be expanded or contracted relative to capacity output, but the capacity output is a measure of the amount by which output could be expanded until reaching the maximum potential capacity level). It is formally defined as the ratio of the current to the potential level of effort:

The input utilization measures may be less than, equal to or greater than one in value. A CU_v < 1.0 implies a shortage of effort relative to the level necessary to produce the capacity output; a CU_v > 1.0 in value implies a surplus of effort relative to the level necessary to produce the capacity output. Färe, Grosskopf and Kokkelenberg (1989) use a somewhat different and possibly confusing terminology for CU_v > or < 1.0; they refer to the case of CU_v > 1 as over-utilized and CU_v < 1.0 as under-utilized.

The variable input utilization measure has also been referred to as a measure of capital utilization, since it is a direct measure of the utilization rate of the physical inputs in terms of the application of variable inputs, whereas output-oriented measures of capacity utilization are represented in terms of potential output (catch) from the capacity base. However, any utilization measure where the capacity base is defined solely in terms of capital levels or characteristics may be termed a capital utilization measure. Also, as elaborated above, if the fishery is subject to diminishing returns to effort, the CU_V measure is likely to be less (further from one) than the CU_C measure of capacity utilization.

Determining potential effort requires imputing the catch that would be generated if all boats operated at the maximum number of days (or hours, etc.) given normal working practices. Alternatively, and for the weaker concept of capacity output, it would require determining the maximum number of days corresponding to utilization of the fixed factors, such that addition increases in variable input usage did not further increase output. The calculation of either notion of potential effort involves taking a measure of the existing capacity (capital), expressing the maximum feasible output producible from this capacity (given an existing production technology under customary and usual operating conditions), and determining the implied amount of variable inputs. This may in turn imply levels of effort, crew, or other variable inputs, but as noted above this is usually summarized in terms of days fished, with the idea that given amounts of crew and fuel are necessary per day to fish effectively.^[35] Although such measures ideally would be constructed at the individual boat or fleet segment level, to take specific vessel characteristics into account, fleet level measures also may be generated through aggregation.

In some cases, measuring potential effort may instead require subjective evaluation of how much input use might be feasible if regulations were removed separately from the impact of customary and usual operating conditions on the definition of “feasible” or “potential” catch or variable input use. This implies approaching the capacity output question initially from the input perspective.

For example, if the fishery has been regulated throughout the period for which data are available, (e.g. through TACs) the potential number of days may not be observed directly. Thus, estimating the number of days that a vessel could operate may require a subjective assessment rather than a simple representation of the maximum catch as that observed within the existing data for a vessel with particular characteristics, but “unrestricted” by variable inputs. To facilitate this, effort units must be expressed in terms of their optimal application to a given capacity base and thus, implicitly (but not directly), in terms of days adapted by a combination of capital characteristics (e.g. kW*days). Such a perspective helps to determine how many days a boat of a given size could potentially fish if the regulations restricting days at sea were removed; it facilitates representing the “marginal product” of days to determine how days fished might change if it were possible to do so. The potential number of days fished in an unrestricted environment is in this context based on a balance between the productivity of additional days and, potentially, some notion of the costs of the additional days if such an opportunity cost exists.

Generally, the assumption of normal working practices includes that existing gear type/use and engine size cannot be changed, even if restrictions are imposed. This is consistent with the idea that these are part of the capacity base and therefore considered as additional capital characteristics for representing the level of fixed inputs. Depending upon the specific fishery, however, gear use may be a variable input (e.g. change in number of traps or pots), and independent of the amount of overall effort summarized in terms of days. If the quantity of gear currently employed is restricted, possible changes in gear use will need to be reflected in the estimation of potential effort and catch, and further assumptions or subjective evaluations may be necessary. For example, effort in fisheries using static gear (e.g. nets, lines, and pots) could readily expand through increasing the quantity of gear employed, as well as the number of days the gear are employed.

At the fishery level, estimating potential vessel entry or the impact of latent capacity and thus implicitly the associated catch or use of variable input in an entire fishery, also requires consideration of vessels that operate in multiple fisheries. While this effort could, theoretically, be allocated fully to one fishery, it is possible that fishers could allocate their effort across several fisheries. The allocation of effort among fisheries may vary from year to year, based on environmental and economic conditions, and this could be accounted for to assess full utilization.^[36] Alternatively, the actual time spent in any one fishery could be considered to be the maximum time that multi-fishery vessels would operate in that fishery under normal working conditions and given existing environmental and economic conditions. In this case, the potential effort of these boats should not be expanded to equate to the potential effort of “full-time” boats, assuming that individual boat activity can be identified. Vessels switch according to opportunities or expectations. If they leave one fishery, conditions in the fishery they left should improve, while conditions in the fishery they entered will likely deteriorate. Estimation of capacity output and capacity utilization for such operations may thus be quite complicated. It may be best to consider the broader economic concepts of capacity and capacity utilization, or at least develop good measures of customary and usual levels of effort and capital stock. When these multi-fishery boats cannot be identified, potential effort is likely to be overestimated.

3.2.3 Input-oriented capacity utilization measures

As emphasized in the preceding section, capacity, or the capacity base, is comprised of the fixed input stocks or vessel and vessel characteristics (fishing power) used for production in the fishery. Capacity output is then the level of potential catch, given this fixed input base, while “potential” effort, or full variable input utilization, is the amount of variable inputs (e.g. days) that would be applied to the capacity base to generate capacity output. Such a measure is sometimes called a (variable) input-based measure of full capacity utilization. An input-oriented, or dual, measure of capacity utilization is instead the amount that the (fixed) capacity base, or level of capital, may be contracted to produce the existing or target (e.g. TAC) level of output or catch.

The input-oriented capacity utilization measure may be formalized by first defining a measure of potential capital (K) as: the minimum amount of capital (vessel power) that, in a given unit of time (e.g. year or fishing season), produces the existing or target output under customary and usual working conditions, provided that the availability of variable factors of production is not restricted. In this context, therefore, we may define an input-oriented capacity utilization measure as follows:^[37]

where the subscript K indicates that it is a capital input-oriented measure of capital utilization.

A value of CU_K < 1 indicates the potential capacity or capital contraction that could be achieved and still maintain current (or target) output levels, since the numerator indicates the amount of K that would be necessary to produce the existing level of output at a full or optimal utilization level.

Any of these capacity utilization measures - CU_C (or CU, as usually specified), CU_V, and CU_K - can be considered indicators of the degree to which the excess capacity exists in the fishery. All three measures, however, basically relate to the short run. None of the three CU measures allows for full adjustment of resource conditions, capital stock, equipment, capacity output and variable inputs.^[38] All three are defined or calculated conditionally on existing values of some variables (e.g. capacity output is conditional upon no change in the fixed factors; variable input utilization is conditional on capacity output and no change in the fixed factors; and the input utilization for capital, CU_K, is conditional on no change in output). However, as noted above, they are not necessarily equivalent in magnitude since they are determined relative to different orientations and constraints. In addition, the relationships among output and capital and variable inputs are not likely proportional, which would be required for the three measures of CU to be similar. Thus, constructing any of these measures and identifying their variations in terms of magnitude requires knowledge or estimation of the underlying input-output relationships, which provides impetus to move toward estimating methods for computing such measures.

It also is important to emphasize before taking this step that the notions of “maximum”, “minimum” or “potential” catch, effort and capital used above must take into account customary and usual operating procedures, and fluctuations in economic and environmental - in particular, biomass stock - conditions over time. Consistent and excessive underutilization of capital may indicate excess capacity in the fleet, but this must be distinguished from capacity that is required to accommodate, or at least respond to, ideal or peak conditions. Ideally, a well managed fishery would have only sufficient latent effort and capital underutilization under normal conditions to allow for the efficient exploitation of the fishery under “good” conditions, which is what we wish to identify as the optimal or potential level of capacity and capacity utilization.

It should be stressed that construction of any of these measures also raises key issues about the level of analysis, at least in terms of fleet definition. Evaluation of capacity and utilization issues at the boat level, taking into account only the boats already in the fishery, provides an indication of optimal or full utilization levels for this main fleet component. Moving to the full fleet level, however, requires extension of the notion of “potential” output, variable input use, or the current capital stock, to include the latent capacity represented by increased participation of existing vessels in this fishery. Multi-fishery boats also must be properly accounted for in these estimates, so the measurement of latent effort allows only for a “feasible” transfer of effort into the fishery by these boats. While this may not be a problem under the explicit assumption of customary and usual practice, transfer of a license from a multi-fishery boat to a new ‘full-time’ boat may result in an increase in potential effort. Managers also may wish to produce an estimate of potential and latent effort assuming that all licenses are fully active in the fishery, which could provide a ‘worst case’ scenario of potential and latent effort.