1. INTRODUCTION

Capacity utilization is defined as the ratio of actual output to some measure of potential output given a firm’s 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, Y_{t}, 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 firm’s 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 firm’s 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 CU_{C}
=C^{*}/C, where C is the firm’s 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
CU_{C} > 1, the capital stock’s shadow price exceeds the rental
price and investment incentives exist. If CU_{C} < 1, the capital
stock’s shadow price falls short of the rental price and disincentive
incentives exist. When CU_{C} = 1, the capital stock’s 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 - CU_{0 }= Y/Y_{0} ; (2)
tangency between short and long-run total average costs - CU_{t} =
Y/Y_{t}; and (3) minimum short-run average total cost - CU_{m} =
Y/Y_{m}. 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) CU_{t} = CU_{m} for constant returns to
scale; (2) CU_{m} < CU_{t} for increasing returns to scale;
and (3) CU_{t} < CU_{m} 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.