Question

Explain the 4 different capacity concepts (make sure to address how each concept determines capacity, what capacity is, the difference between supply and demand, etc.). Why does capacity matter when costing a product? Provide an example showing how a different capacity level may impact the cost of a product.

Answer 1

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 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 . 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.^[5]

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 Johansen’s 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 Johansen’s definition, but only requires that output be bounded as opposed to requiring the existence of a maximum (Figure 3). In Figure 3, capacity output, Y_C, is produced using X_C units of the variable factors of production; the fixed inputs, however, bind or limit output to Y_C. 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 Y_K; the capacity output of Berndt and Morrison is depicted by Y_BM; the Johansen concept of capacity output is given by Y_J; and the static, short-run, profit maximizing capacity concept of Coelli, Grifell-Tatje and Perelan equals Y_CGP. 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)

The capacity decisions within a company are very important because they help determine the limit of output and provide a major insight to determining operating costs

1. Low Utilization

If some of your production capacity is idle, your investment in the facilities and equipment is not generating any income and reducing your potential profit. Since additional production volume does not increase fixed costs, higher capacity utilization may result in lower per-unit product costs and higher potential profits.

For example, if your facilities have a capacity of 1,000 units per month and cost $10,000 per month to operate, producing 500 units with a variable cost of $20 costs 500 x $20 plus $10,000 for a total of $20,000, or a unit cost of $40. If you produce 800 units, your costs are $20 x 800 plus $10,000 for a total of $26,000, or $32.50 per unit. If you can sell 800 units at a reduced price of $35, your overall profit increases.

2. Peaks

Unless your planning compensates, peaks in capacity utilization can damage both product quality and profitability. When you see a demand peak approaching through an increase in orders for your product, you have to delay deliveries so that you can smooth the effect on your production schedule. Peaks that surpass the normal maximum capacity lead to problems in production that affect product quality and overtime that reduces profits. Managing your demand through price adjustments to reduce demand during peaks and increase demand during troughs balances your schedule and achieves maximum profitability.

3. Full Utilization

When your product is successful, you can reach full capacity utilization, leading to high profitability and a streamlined manufacturing plant that turns out high-quality products. If you want your company to grow, and if your planning has correctly forecast the trend toward the use of all your capacity, you can now expect to have new capacity coming online to take over new demand. Your profitability will drop as your total capacity utilization decreases temporarily, but increasing demand will bring profits back up to a higher level as you approach full utilization of the new capacity

4. Over-Utilization

When capacity utilization passes its maximum due to demand that exceeds your ability to supply the products, your costs rise and product quality decreases. To meet excess demand, you have to schedule overtime that results in higher costs and stressed workers who make more mistakes. There is less time for equipment maintenance, and employees cut corners to maintain high levels of production. You have to avoid over-utilization of capacity by acting to reduce demand with longer delivery times and higher prices