Capacity utilization is defined as the ratio of actual output to some measure of potential output given a firms short-run stock of capital and perhaps other fixed inputs in the short run (Nelson, 1989). Capacity utilization captures the output gap between actual output and capacity output.
There are four different measures of capacity output (Morrison, 1985; Nelson, 1989). The four measures differ by the manner in which potential or capacity output is defined and whether or not the potential or capacity output is technologically determined, without an explicit economic foundation, or whether this capacity output represents the outcome of an explicit economic optimization process, such as cost minimization or profit maximization.
Capacity output defined by the economic approach can explicitly vary with changes in such economic variables as input prices, quantities of short-run fixed factors or outputs fixed by regulations or other reasons, overtime or added costs, and other factors (Morrison, 1985). The fundamental concept underlying the economic measures is that firms face short-run constraints, such as the stock of capital and other fixed inputs, and thus optimal short-run equilibrium output might differ from that in a long-run, steady-state equilibrium (Morrison, 1985).
The short-run constraints can include various existing regulations - which in fisheries could include constraints on mesh size or gear, and social objectives such as minimum employment levels. Total allowable catches are simply exogenously fixed output levels and hence fit into this framework. The economic capacity and capacity utilization literature was developed around firms that minimize the costs of producing exogenously fixed outputs. Hence, no distinction is made between capacity with and without constraints that may exist in addition to a fixed factor such as the capital stock.
2. PRIMAL-BASED CAPACITY AND CAPACITY UTILIZATION: TRADITIONAL CONCEPT
The engineering-technological approach defines the capacity output as the maximum potential output, Yt, which could be produced if all firms produced at maximum technical efficiency, full-utilization of all inputs, and produced the maximum output given variable inputs, the stock of capital, and the state of technology. The capacity output 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. Capacity utilization (CU) is simply the ratio of observed output (Y) to maximum potential output (Y*).
Interpretation of this physical measure, however, does pose problems. There is a tendency to classify producing firms with CU values less than one as having excess capacity or as being overcapitalized. This is not the case. A primal CU value less than one simply means that firms have the potential for greater production without having to incur major expenditures for new capital or equipment (Klein and Summers, 1960). 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 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, nondiscretionary inputs, and possibly nondiscretionary outputs. That is, the measures of capacity and capacity utilization are conditional on the available capital stock, other quasi-fixed factors, any nondiscretionary inputs or outputs, and state of technology. It is only necessary to determine the frontier output of the producing agent relative to the entire vector of all outputs and relative to each output. In fact, capacity utilization can be shown to equal the inverse of technical efficiency. That is, rather than examine the ratio of the distances (mathematical distance from point of observation to origin) of the frontier output to observed output as is done for technical efficiency, capacity utilization under a multiple product technology equals the ratio of observed output to the frontier output.
3. ECONOMIC-DERIVED CAPACITY AND CAPACITY UTILIZATION
There are three economic measures of capacity and capacity utilization. The first economic approach, proposed by Klein (1960) and Friedman (1963), defines capacity output as that output corresponding to the tangency of the long and short-run average or unit total cost curves (the average total cost curve includes the cost of the capital stock which is a fixed or quasi-fixed factor). The second economic approach, advocated by Cassel (1937) and Hickman (1964), defines capacity output as that corresponding to the minimum short-run average total cost. These first two economic measures may be deemed primal because capacity and capacity utilization are expressed in terms of physical output levels.
A third economic measure, proposed by Berndt and Morrison (1981) and Morrison (1985), may be deemed dual because it does not directly compare physical output levels. The third measure, a dual-based concept is defined in terms of the firms costs. The primal economic capacity utilization measures capture the output gap that exists when actual output differs from capacity output. The dual economic capacity utilization measure captures the cost gap when actual output differs from capacity (short-run optimal) output. However, this cost gap of disequilibrium is measured not by the differences in actual and capacity output levels, but by the difference between the firms implicit marginal valuation (shadow price) of its capital stock and the rental or services price of that capital stock.
The dual capacity utilization measure, thus, contains information on the difference between the current short-run (temporary) equilibrium and the long-run equilibrium in terms of the implicit costs of divergence from long-run equilibrium. It is defined as CUC =C*/C, where C is the firms actual cost and C* is its shadow cost. This shadow cost C* is defined as the cost of the variable inputs plus the shadow cost of quasi-fixed input equal to the shadow price of the quasi-fixed input multiplied by the quantity of its stock. When CUC > 1, the capital stocks shadow price exceeds the rental price and investment incentives exist. If CUC < 1, the capital stocks shadow price falls short of the rental price and disincentive incentives exist. When CUC = 1, the capital stocks shadow price equals the rental price and there are neither investment nor disinvestment incentives. The dual economic measure provides an equivalent measure to the primal economic approach (Morrison, 1985).
We refer to the first three measures, respectively, as follows: (1) engineering definition - CU0 = Y/Y0 ; (2) tangency between short and long-run total average costs - CUt = Y/Yt; and (3) minimum short-run average total cost - CUm = Y/Ym. The two primal economic measures of capacity utilization are higher than the engineering measure. The two primal economic measures depict the divergence between short-run equilibrium and long-run equilibrium output levels. The relationships between the two economic measures vary in accordance with returns to scale: (1) CUt = CUm for constant returns to scale; (2) CUm < CUt for increasing returns to scale; and (3) CUt < CUm for decreasing returns to scale.
4. DYNAMIC ADJUSTMENTS OF THE CAPITAL STOCK
Morrison (1985b) develops the notion of capacity and capacity utilization that allows for gradual movements in input stocks. This approach is based on costs of adjustment for quasi-fixed factors that induce slow adjustment by firms to optimal or desirable levels of the quasi-fixed factors. Within a dynamic framework, firms move along a given short-run average total cost curve but also shift their short-run average total cost curves by optimally investing in quasi-fixed inputs. This dynamic optimizing behavior has implications for movements in capacity utilization when capacity output Y* is determined by the position of the short-run average total cost curve. The dynamic approach could be extended to allow for changes in resource stocks over time. The capital stock would have to remain homogeneous or single-valued and capacity and capacity utilization in a given time period conditional on the resource stocks.
5. MULTIPLE FIXED INPUTS
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 maximum capacity output or rate of capacity utilization when there are multiple quasi-fixed or fixed factors. The indeterminacy problem is more severe in the presence of multiple products and multiple quasi-fixed factors.
The dual economic approach, which is based on cost, profit, or revenue optimization, economic duality, and a single quasi-fixed input, readily accommodates multiproduct production which is otherwise possible only under fairly stringent conditions with the two economic approaches developed in the primal form (Segerson and Squires, 1990). The economic duality approach readily extends from the single-product to the multiple-product case, with a single quasi-fixed input, because the capacity utilization measure uses a scalar measure of the cost gap that exists when actual outputs differ from the capacity outputs, 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.
6. MULTIPLE PRODUCTS
Segerson and Squires (1990) observe that a consistent scalar measure of output in multiproduct firms exists if all outputs are homothetically separable from inputs. In this case, a direct analogue of the single-product primal measure of capacity utilization can be developed for the multiproduct firm or industry. When the production technology is not homothetically separable, Segerson and Squires (1990) suggest two alternative ways of defining a primal capacity utilization measure. Both approaches of Segerson and Squires, however, required restrictive assumptions: (1) outputs must move along a ray (giving a ray measure of capacity utilization and essentially assuming Leontief separability of outputs), and (2) only one output can adjust (giving a partial measure of capacity utilization). Squires (1987) and Segerson and Squires (1993; 1995) suggest an alternative approach for profit and revenue functions.