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2.1 Background production concepts
2.2 Primal-based capacity and capacity utilization: traditional concept
2.3 Economic-derived capacity and capacity utilization
2.4 Capacity utilization versus capital utilization
2.5 Variable input utilization rate
2.6 Capacity and capital utilization in fisheries

There is general agreement among economists that capacity is an output-based measure. The capacity output is a potential output which may be equated to a maximal output or an economically-derived output given the stock of capital and state of technology. The former concept is a technologically-derived physical measure of capacity and the latter is an economic measure (i.e., an optimum level of output). Capacity and capacity utilization for conventional industries are strictly short-run concepts. The two are defined or measured conditional on a fixed stock of capital and state of technology.

The two basic notions of capacity discussed in the economic literature may be viewed as the following: (1) a primal technological-based concept, and (2) an economic-based concept. Both definitions are based on the notion of a potential or capacity output given the capital stock, other fixed factors, the resource stock, technically-efficient, full-utilization of the variable factors of production (e.g., energy, labour, and materials), and the state of technology. What distinguishes the two notions of capacity is how the underlying economic aspects are included to determine the capacity output. With a purely technologically determined primal measure, capacity is simply the maximum possible output which could be produced using the available technology, capital, and the full and technically efficient utilization of the variable inputs; economic responses by firms are ignored in the physical or primal-based measure. The economic measure, however, explicitly considers the economically optimum potential output which could be produced given the capital stock, the technology, inputs prices, output prices when outputs are not fixed, and technically efficient and fully-utilized factors of production as appropriate to achieve maximum profit or minimum cost. The economic capacity measure can be either primal, so that it is in terms of physical units of output (that gives the economically optimum or target level of output), or it can be dual, so that it is in terms of the firm’s costs, revenues, or profits. Appendix II provides additional discussion of capacity and capacity utilization.

In the case of fisheries, adopting the traditional economic concepts of capacity and capacity utilization poses several problems. Foremost among the problems is the need to consider the resource capital (i.e., the fish stock). The resource stock is unpriced and represents a type of capital which cannot be aggregated with the vessel capital. Moreover, the resource, regardless of the level of capital and expansion of variable inputs, imposes an upper limit on the total level which may be harvested in this stock-flow production technology. That is, regardless of the expansion of capital and increased utilization of variable inputs, output or catch cannot exceed some level determined by the resource.

Another major problem for measuring capacity and capacity utilization is the possibility of multiple products and multiple quasi-fixed factors. Berndt and Fuss (1989) have shown that in the presence of multiple products and multiple fixed factors, capacity and capacity utilization may be indeterminate. Most fisheries involve multiple-product production and definitely have more than one quasi-fixed factor (e.g., the capital of the vessel and gear and the capital of the resource stock). The only approach known to allow for the calculation of capacity and capacity utilization in fisheries in which there is more than one output and more than one fixed factor is that of Segerson and Squires (1990). Under this approach, the determination of capacity and capacity utilization is conditional upon the resource stock(s) and requires a single measure of the capital stock.

Perhaps of equal importance is that international concerns about capacity and capacity utilization in fisheries appear to be mostly related to capital and effort utilization (utilization of vessels and overall total maximum potential catch). This latter concern, although similar to concerns about capacity and capacity utilization, requires a considerably different emphasis on defining and measuring capacity and capacity utilization in fisheries. The major issues relating to this latter concept is the frontier output, associated input levels, and optimum configuration of a fishing fleet (e.g., number of vessels, type of gear, factors of production, days at sea, etc.)

2.1 Background production concepts

2.1.1 the production function
2.1.2 production and fisheries

2.1.1 the production function

Both the primal and economic concept require recognition of an underlying production function or technology. The production function or technology describes how service flows from the stocks of economic inputs are used to produce outputs subject to, if any, various technological constraints (e.g., weather and nondiscretionary inputs such as age of facilities or capital). In general, the production function or technology should depict the maximum possible physical output. In mathematical form, the production function may be specified as follows:

(1) Y = f(K,L,E,M,X,T)

where Y is output, K is capital, L is the services of labour, E is energy, M represents materials, X represents other inputs used to product Y, and T represents the state of technology. Other inputs could be nondiscretionary inputs (NDX); a nondiscretionary input is an input which is beyond the control of the plant or firm manager. In the short-run, capital is usually fixed; that is, plant size and equipment cannot be increased or decreased.

In fisheries, the production process is stock-flow, that is, a bundle of inputs is applied to the resource stock to yield a flow of output or catch. Hence, the resource stock could be added to Equation (1). Firms and industries, however, seldom produce only one product. They frequently produce multiple products. Multiple product production is likely to be the case for most fisheries of the world; many fisheries involve the harvesting of more than one species, and even in the case of single species fisheries, more than one product form is typically harvested (e.g., male vs. female shellfish or jumbo vs. large vs. small size finfish). There is thus a multiple product analog of the single product technology; we may express the multiple product analog as follows:

(2) g(Y1,Y2,...,Ym;K,L,E,M,X,T) = 0

where g is the multiproduct production function, Yi is the ith output, and there are m outputs, Y1,Y2,...,Ym. If there are technical or economic interactions among all m outputs, production is said to be joint, and Eq. (2) is the proper specification of the technology.

If there are absolutely no technical or economic interactions among the m outputs, production is said to be nonjoint in inputs. Alternatively, if changes in the output or price of one product does not affect the production or supply of another product, the technology is nonjoint in inputs. For the nonjoint-in-inputs case, the multiproduct technology consists of separate production functions for each output Yi:

(3) Yi = g(Ki,Li,Ei,Mi,Xi,T)

and the sum of Ki, Li, etc. equals K, L, E, M, and X.

There also are several potential modifications to Eq. (2). For example, if Eq. (2), or the technology, can be decomposed into a function of outputs, O(Y), and a function of inputs, I(K,L,E,M,X), the technology is separable between inputs and outputs and is referred to as input-output separable technology. If production is separable between inputs and outputs, there is no unique or specific interaction between any one output and any one input. If a mathematical function is separable in any of its arguments, composites or aggregates, consisting only of those arguments, may be formed without any loss of information. In addition, the production technology may be specified in terms of a single composite or aggregate output and a single or composite input:

(4) O(Y1,Y,...,Ym) = I(K,L,E,M,X)

2.1.2 production and fisheries

The concept of production in fisheries, while seemingly straightforward, is quite complicated. Unlike conventional industries, the concept of production in fisheries or the catch-effort relationship is void of conventional measures of inputs (e.g., labour, capital, energy, and materials). This need not be the case and, in fact, has not always been the case.

Fishing effort subsequently becomes a surrogate or proxy variable representing all inputs used to catch fish or all inputs used to actually engage in fishing. Resource managers seldom regulate the more traditional economic inputs such as fuel. Historically, fishery managers have probably most often regulated catch or outputs and various characteristics of fishing gear (e.g., mesh size or sweep). Managers do, however, typically regulate days at sea, crew size but not explicitly the services of labour, and gear and mesh but not the actual capital value.

There remains considerable uncertainty about how to adequately consider the concept of fishing effort: (1) is effort a measure of a composite input in which the technology is separable in all inputs such that decisions about input levels are completely independent of resource levels; or (2) is effort a measure of an intermediate product in which effort is produced in stage one of a multi-stage production process. There are also the associated issues of measurement and standardization. How does one develop measures of fishing effort relative to heterogeneous gear and vessel characteristics which can be compared?

For fisheries, there are two traditional catch-effort relationships. First, there is the short-run catch-effort model in which catch is specified as a multiplicative function of a catchability coefficient (q), fishing effort (E or often referred to as f), and resource abundance (N):

(5) Catcht = q E N

Variants of the traditional specification are well articulated in Cunningham and Whitmarsh (1980), Cunningham et al. (1985), and Hannesson (1983). Then there is the surplus production model framework of Schaeffer (1957) and Pella and Tomlinson (1969). The Schaeffer or what is now referred to as the Gordon (1954)-Schaeffer model is as follows:

(6) Catchs = ß1 E + ß2 E2

where catch subscripted with s indicates sustainable yield. The Pella and Tomlinson model is similar but does not require the symmetry of the Schaeffer model. Cunningham et al. (1985) and Hilborn and Walters (1992) provide an exhaustive summary of various forms of the surplus production model as well as numerous other possible concepts of the relationship between catch and fishing effort.

If the traditional catch-effort model of equation (5) is related to the traditional economic concept of production presented by equation (1), fishing effort or E represents the notion of a composite input or the input function f depicted in equation (1). Moreover, equation (1) is modified to reflect the importance of the resource stock. The catchability coefficient of equation (5) is a measure of the level of catch corresponding to a one unit level of fishing effort. For an economic specification, q equates to the technical efficiency parameter.

2.2 Primal-based capacity and capacity utilization: traditional concept

A technologically determined primal-based definition of capacity is simply the maximum potential output (Y*) attainable given the capital stock, the state of technology, and the efficient and full utilization of all factors of production. Hence, for a given plant size, the firm produces the output level for which the plant was “designed”. This notion of capacity is a technological one, so only technological and resource constraints and input levels determine the maximum potential output, no economic factors. Given the stock-flow production process in fisheries, capacity depends upon the level of the resource stock, where the resource stock abundance also sets an upper bound on capacity.

Capacity may be easily obtained from the frontier output of the production schedule. For example, if we consider the maximum possible output subject to capital being a limiting factor, the maximum or capacity output is depicted in Figure 1 as the maximum output level.

Figure 1: Capacity - Physical Measure

Capacity utilization (CU) is then simply the ratio of observed output (Y) to maximum potential output (Y*): Y/Y*. Interpretation of this technologically-derived physical measure, however, does pose some problems. There is a tendency to classify producing firms with primal CU values less than one as having excess capacity or as being overcapitalized. This is simply not the case. A primal CU value less than one simply means that firms have the potential for greater production, given the capital stock, without having to incur major expenditures for new capital or equipment (Klein and Summers, 1960). When capacity utilization is less than one, some of the capital stock is not fully utilized while full capital utilization and technical efficiency would yield Y*. CU cannot exceed one in value for a primal-based measure.

Measuring or assessing the primal-based concepts of capacity and CU for a multiple-product technology is quite difficult. To do so requires the adoption and acceptance of the multiproduct frontier production function and technical efficiency. Unlike the rigorous multiple-product, multiple fixed factor dual economic definition of capacity, the primal-based concepts of capacity and capacity utilization may be defined and measured for a firm or industry producing multiple products and using multiple quasi-fixed factors. The measurement, however, must be done in a manner similar to that offered by Segerson and Squires (1990). The measurement must be done conditional on the levels of the quasi-fixed factors (e.g., the capital and resource stocks), nondiscretionary inputs, possibly nondiscretionary outputs, and the state of technology. That is, the measures of capacity and capacity utilization are conditional on the available capital stock, the resource stock, other quasi-fixed factors, and any nondiscretionary inputs or outputs. One of three approaches can be adopted to accommodate the multiple products: (1) aggregate all outputs into a single composite measure (assuming homothetic separability of outputs); (2) determine the frontier output of the producing agent relative to the entire vector of all outputs and relative to each output; or (3), evaluate capacity with outputs in fixed proportions.1

2.3 Economic-derived capacity and capacity utilization

An economic-based definition of capacity equates potential output with the economically optimal or target levels of output. The economic-based definition is the output given technically efficient and full utilization of the capital stock, quasi-fixed factors, the resource stock, the state of technology, and all variable factors of production necessary to achieve an economic optimum such as minimum or least cost production or maximum profit. In contrast, the previously discussed technologically-derived primal definition of capacity equates capacity with the maximum potential output given inputs and the resource stock abundance, including those fixed (such as capital) in the short run, without any economic optimization.

More formally and following Klein (1960) and Friedman (1963), the capacity output corresponds to the point at which the long-run and short-run average total cost curves are tangent at the minimum level for both short and long-run average total costs (Morrison, 1985; Nelson, 1989). The tangency between the short-run and long-run average total cost curves is the point at which a firm should be in long-run competitive equilibrium (Figure 2). (This tangency can lie at any point along the long-run average cost curve, not just its minimum.) When the firm is in long-run equilibrium with respect to its fixed factors, such as the capital stock, the firm does not face any incentives to invest or disinvest and thereby increase or decrease these fixed factors. The tangency point at the minimum long-run average total cost is also the point of maximum scale efficiency.

Intuitively, this economic notion of capacity means that for a given output level and state of technology, the firm is using the plant size that allows that output to be produced at the lowest average cost. Equivalently, for a given plant size, the firm is producing the output level for which the existing plant was designed.

Comparing the observed output Y with the capacity output Y* B giving the capacity utilization measure, shows that when Y > Y*, the firm is not in long-run equilibrium and faces economic incentives to disinvest. In this case, by reducing its capital stock, the firm can lower its average costs of production. Conversely, when Y < Y*, the firm is again not in long-run equilibrium and faces economic incentives to invest. By increasing its capital stock through investment, the firm again lowers its average costs of production.

It is common to associate movements along the long-run average total cost curve with plant expansion in the sense that all fixed inputs are increased. Chambers (1988) shows that this is clearly not the case. Movements along the average total cost curve indicate plant expansion activities only when there is a single fixed input. Thus, and as more formally demonstrated by Berndt and Fuss (1989), it may not be possible to determine the capacity output or rate of capacity utilization when there are multiple quasi-fixed or fixed factors. The indeterminacy problem is likely to be more severe in the presence of multiple products and multiple quasi-fixed factors.

Figure 2. Capacity: Economic Based Measure

[Note: Indeterminancy Problem with Multiple Products And Multiple Fixed Factors]
The economic approach, based on cost, profit, or revenue optimization, and a single quasi-fixed input, readily accommodates multiproduct production which is otherwise possible only under fairly stringent conditions with the primal approach (Segerson and Squires, 1990). The economic approach readily extends from the single-product to the multiple-product case, with a single quasi-fixed input, because the capacity utilization measure uses scalar measures of the shadow price and rental (services) price of the quasi-fixed input, to give a measure based on the ratio of shadow to total costs (or profit), so that scalar measures are still involved. But as discussed in greater detail in Berndt and Fuss (1989) and Segerson and Squires (1990), when there are multiple quasi-fixed factors in the economic approach, and/or multiple outputs in the primal approach, scalar measures are either not possible or are limited in some manner, and more limited measures must be applied to define and measure capacity and capacity utilization.

2.4 Capacity utilization versus capital utilization

In contrast to the concept of capacity utilization, capital utilization may be defined as the ratio of the desired stock of capital (given output quantity and input prices) to the actual stock of capital (Berndt, 1990). Fare et al. (1994) apply the same definition. Berndt and Fuss (1989) pointed out that these two measures of utilization coincide only if there is but one fixed input (capital) and if production is characterized by constant returns to scale. An alternative definition of capital utilization is the ratio of capital services to the stock of capital (cf. Schworm, 1977; Hulten, 1986; Hulten, 1990; Lee, 1995). Multiplying the stock of capital by the capital utilization rate gives the flow of capital services.

The distinction between capital and economic capacity utilization relates to underutilizing a given capital stock (or producing less than the maximum physical output, where CU is always less than 1) and to producing below or above the optimum output Y* (where it is possible to have CU > 1 or CU < 1). Thus capital utilization captures how much of the existing capital stock is being used and CU provides information about short-run vs. long-run equilibrium and economic incentives for investment and disinvestment.

Appendix I discusses the relationship between capital stock and capacity output, and in particular how capital input measures have been used to measure production capacity or potential output as well as capacity utilization. Appendix II provides additional discussion on capacity and capacity utilization. Appendix III provides additional discussion on capital utilization.

2.5 Variable input utilization rate

The variable input utilization rate measures the ratio of optimal use of a variable input to observed use (Fare et al., 1994). The optimum can refer to a variety of objectives, including the maximum possible output, an output quota (such as Total Allowable Catch), or an economic optimum, including profit and revenue maximization or cost minimization. The difference between variable input utilization and capital utilization is that the former refers to a variable input and the latter refers to a fixed or quasi-fixed factor.

Input capacity has been widely used in the data envelopment analysis (DEA) literature (Charnes et al., 1994) and the traditional agriculture literature (e.g., Heady and Tweeten, 1963 and Thompson et al., 1994). In the traditional agriculture literature, input capacity simply reflected the maximum number of hours a machine or labour could operate in a production cycle. More recent usage of the term connotes a matching between input levels and capacity output (e.g., Forsund and Hernaes (1994) measure capital service use in terms of the capacity of ferry to carry standardized vehicles).

2.6 Capacity and capital utilization in fisheries

The distinctions between capacity, capital, capacity utilization, capital utilization, and variable input utilization are quite important to fisheries. Most concerns raised about overcapitalized fishing fleets and excess productive (harvesting) capacity are actually concerns about capital and effort utilization. (Appendix II reviews capacity and capacity utilization in detail. Appendix III reviews capital utilization in detail.). Alternatively, the primary focus of these concerns relates to the optimum configuration of a fishing fleet and of a fishing industry relative to some maximum level which may be harvested (e.g., a total allowable catch (TAC)). The distinction also relates to two questions raised by Hannesson (1993a, page 107): (1) how much of a given capital stock to utilize in any given period (i.e. capital utilization) and (2) how large a productive (fishing) capacity to build and to maintain, which is an investment or disinvestment decision (i.e. economic capacity utilization).

The primary focus or concern for fisheries is, thus, the optimum utilization of capital. Resource managers desire to know the optimum number of vessels for a fishery and a nation, the optimum configuration, the gear types, and the optimum utilization of the vessels or the corresponding level of fishing effort. Optimum may be defined relative to the goals and objectives of the nation. Optimum may be equated to economic objectives such as minimum cost, maximum profit, and maximum net benefits or various socio-economic objectives. The resource or stock enter as a constraint to overall production.

Subsequently, in most instances, we may equate the terms “harvesting” or “fishing capacity” to optimal capital and effort utilization. Resource managers and fishery scientists appear to often equate the two terms to some underlying optimum rate of exploitation. In contrast, there is a tendency by managers and fishery researchers to equate the term “catch” or “catching” capacity to the more traditional economic concept of capacity. Relative to the various terms, physical or primal-based and economic characterizations are both possible. We seek a measure which allows us to determine the capacity output consistent with either the physical maximum or an economic optimum. The technologically derived, primal-based concept of capital utilization or “harvesting capacity” is simply the level of capital or number of vessels corresponding to the frontier output given full-utilization of the vessel, gear, and all variable inputs. The economic-based concept of capital utilization is the same except that the frontier output corresponds to an economic optimum output (i.e., maximum output as determined by input and output prices).

Given data typically available on fisheries, measures of capital utilization or “fishing capacity” will likely have to be determined using aggregate or fishery-wide data. The preferred orientation, however, is to determine “fishing capacity” or capital utilization at the vessel level and aggregate up to the fleet. The vessel level is preferred because it would help resource managers to better identify the actual vessels or types of vessels which should be purged from a fishery being downsized.

In Section V of this report, we present a wide variety of methods which may be used to develop measures of capacity or frontier output, capacity utilization, technical and allocative efficiency, and capital utilization or “harvesting capacity.” The focus of these measures is to assess the proportion of available capital or “harvesting capacity” which is currently utilized and which could be utilized given some upper allowable catch and goals and objectives of resource managers. We also provide approaches which provide measures of capacity and capital utilization subject to different types of available data (e.g., one only has data on effort and catch or has data on effort and catch plus extensive economic data).

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