5.1 Production Function in the Short Run
5.2 Basics of Returns to Scale
5.3 Basics of Cost Functions
5.2 Basics of Returns to Scale
5.3 Basics of Cost Functions
5.3.1 Total costs and unit costs
5.3.2 Cost curves in the short run in the fishery industry
5.4 Average Cost Curve in the Long Run
5.4.1 Cost curves in the long run for actual plants
5.5 Micro-economics Applied to a Whole Fishery
5.5.1 Mathematical models for evaluation of the fish resources
The production function appears in the micro-economic analysis as one of the two determining factors of the economic sustainability of the firm. A businessman aiming at a state of equilibrium in his business, trying to maximize his profits in the short run, must simultaneously consider the technological characteristics of his installations and possible ways of using them to produce. The cost of the production process must also be considered.
The first factor is formally expressed through a production function. In any given country, a specific production technique exists, based on existing installations in the various productive sectors, production processes, different forms of organization, business management and division of labour. This situation can be functionally represented by a relationship that links the value added during production, or the domestic product, to the quantities utilized from the different productive factors. These concepts constitute the aggregate production function for each sector, e.g., the aggregate function of frozen fish plants.
Knowing the production function of each sector of the fishery industry enables formulation of a response to future changes that might occur, such as: reduction of labour force, scarcity of a particular species, technological innovations. It can be utilized determine to which point it is possible to substitute one input for another. It can also be used to determine the level of operation of the plant that would constitute maximum production efficiency.Production is a series of activities through which inputs or resources used (raw material, labour, capital, land and managerial talent) are transformed into products (goods or services) over a specific period of time. Economists use the term production function to refer to the physical relationship between inputs utilized by the business and its products (goods and services) per unit of time (Henderson and Quandt, 1971). This relationship can be expressed symbolically as:
Q = f(Xa, Xb, Xc,… Xn) (5.1)
where Xa, Xb, Xc,… Xn represent quantities of different types of inputs and Q the total quantity of product per period of time, for specific combinations of these inputs. There is a production function for each methodology. A company can modify the quantities of the product it generates by varying the quantities of the resources that it combines according to a productive technique, changing from one technology to another, or using both operations. It is assumed that companies use the most efficient technique such that it achieves maximum production of each alternative combination of inputs.
Production Function in the Short Run
The following parameters, which are relevant to this analysis, are defined in the micro-economic treatment of the production function:
A fixed input (F1) is defined as that input whose quantity cannot be quickly changed in the short run, in response to the desire of the company to change its production. Inputs are not fixed in the absolute sense, even in the short run. In practice, however, the cost of implementing changes in a fixed input can be prohibitive. Examples of fixed inputs are: pieces of equipment or machinery, space available for production, management personnel.
On the other hand, variable-inputs (VI) are those inputs whose quantities can be easily changed in response to the desire to increase or reduce the level of production, for example, electricity, raw materials, direct labour. Sometimes variable inputs are limited in variation due to contracts (e.g., steady supply of raw material) or law (e.g., labour laws); in such cases it is possible to talk of semi-variable inputs (SVI).
The short run (SR) is the period in which the company cannot vary its fixed inputs. Nevertheless, the short run is long enough to allow variation of the variable inputs. The long run (LR) is defined as the period that is long enough to allow the variation of all inputs, none of which are fixed, not even the technology. For example, while in the short run a firm can increase its production by working extra hours, in the long run, the company can decide to build and expand its production area to install capital-intensive machines and avoid overtime.The principle of diminishing marginal returns is related to the quantities of product that can be obtained when increasing quantities of variable inputs per unit of time are incorporated into the production process and combined with a constant quantity of fixed input.
The principle establishes that a point will be reached where the resulting increases in the quantity of output will become smaller and smaller. When the average product is increasing, the marginal product is greater than the average. When the average product reaches its maximum point, it is equal to the marginal product.
Before reaching the inevitable point of decreasing marginal returns, the quantity of end-product obtained can increase at a growing rate, as shown in Figure 5. 1. Above the inflection point of the production function, a greater use of the variable input induces a reduction in the marginal product. A production function and the associated AP and MP curves can be divided into three stages, as illustrated in Figure 5. 1.
Figure 5.1 Production Function in the Short Run and the Corresponding Marginal and Average Production Functions
Stage 1 extends from zero units of variable inputs (VI) to the point where the APVI, is at its maximum (DAR). Stage 2 extends from the (DAR) to the point where the quantity of product is maximum and the MP is zero (DTR). In Stage 3, from (DTR) onwards, the total product is decreasing and the MP is negative.
These stages have a special significance in analysing the efficiency with which the resources are used. The maximum of (MP) vs (xVI ) defines the point DMR, from there onwards an increase in (V1) will mean a decrease in (MP). The first stage corresponds to the range in which the AP is increasing as a result of utilizing increasing quantities of variable inputs (raw material, labour, etc.).
A rational producer would not operate in this range, because (FI) (equipment) is being under utilized. That is, the production expected from the use of more man-hours, for example, is increasing through stage 1, which indicates that the same production could be obtained with a lower quantity of fixed input. Production is also impractical at stage 3. Additional units of VI actually reduce total production.
If the efficiency of the production process is measured by the average product, which indicates the quantity of product obtained per unit of input, the previous discussion reveals that stage 2 is the best from the point of view of efficiency. In stage 1, a very small proportion of (VI) is being used when compared with the (FI). Efficiency considerations will lead to a preference to produce around the border of stages 1 and 2.
Basics of Returns to Scale
The production function of the firm has been analysed in the short run, where a proportion of the firm's resources are fixed. The concept of returns to scale occurs when the company is producing during a period long enough to allow changes in any and all of its inputs, especially those usually fixed in the short run.
Returns to scale are defined for cases where all the inputs are changed in equal proportions. In the case of a firm using X, units of input 1 along with X2 units of input 2, and obtaining Q units-of product, the relation can be written as:
(5.2)
Now suppose that the quantities of inputs X1 and X2 are varied by an arbitrary proportion g . Total production obviously will change. The question is in what proportion will it change? If this proportion is called p , the result is:
(5.3)- If the change in production is more than proportional to the change in inputs (pg ), increasing returns to scale
- If p = g , constant returns to scale
- If p < g , decreasing returns to scale
For the same technology, it is usually certain that on expanding its scale of operation, the company will have:
- A short period of increasing returns to scale
- A long period of constant returns to scale, and,
- A period of decreasing returns to scale
A company can increase use of its inputs to the point of maximum production; further increases of. inputs can produce a stage of negative yield, where production actually decreases. However, if the concept of returns to scale is used to allow changes in the technological capacity of the firm, and its size increases, companies can be (and they certainly are) capable of applying all their tools and new technologies for expanding their scale of operations without ever reaching the point of decreasing yields.
Firms with a prolonged period of constant returns to scale are common in food and fish processing.
Basics of Cost Functions
A fundamental point in the analysis of costs is the functional relationship that exists between costs and the production for a period of time. A cost function presents different results when the plant works with different percentages of utilization. But, as previously indicated, production is a function of how resources are used.
Thus, as the production function establishes the relationship between inputs and product, once the prices of the inputs are known, the costs for a certain production can be calculated. As a result, the level and performance of the costs of a plant, as the level of production varies, are directly related to:
- The characteristics of its own production function
- The purchase prices of its inputs