Law of Returns to Scale : Definition, Explanation and Its Types
In economics, a production function gives the technological relation between quantities of describes a boundary or frontier representing the limit of output obtainable . By definition, in the long run the firm can change its scale of operations by In the Cobb–Douglas production function referred to above, returns to scale. Economies of Scale refer to the cost advantage experienced by a firm when it increases its level of output. Effects of Economies of Scale on Production Costs. Economies of scale bring down the per unit variable costs. Describe the relationship between an individual consumer's .. Distinguish between increasing returns to scale, decreasing returns to .. Macroeconomic Objectives (Some Topics HL Extension, Plus One Topic HL Only ).
In Stage 1 from the origin to point B the variable input is being used with increasing output per unit, the latter reaching a maximum at point B since the average physical product is at its maximum at that point.
Because the output per unit of the variable input is improving throughout stage 1, a price-taking firm will always operate beyond this stage. In Stage 2, output increases at a decreasing rate, and the average and marginal physical product both decline. However, the average product of fixed inputs not shown is still rising, because output is rising while fixed input usage is constant. In this stage, the employment of additional variable inputs increases the output per unit of fixed input but decreases the output per unit of the variable input.
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In Stage 3, too much variable input is being used relative to the available fixed inputs: The output per unit of both the fixed and the variable input declines throughout this stage. At the boundary between stage 2 and stage 3, the highest possible output is being obtained from the fixed input. Shifting a production function[ edit ] By definition, in the long run the firm can change its scale of operations by adjusting the level of inputs that are fixed in the short run, thereby shifting the production function upward as plotted against the variable input.
If fixed inputs are lumpy, adjustments to the scale of operations may be more significant than what is required to merely balance production capacity with demand. For example, you may only need to increase production by million units per year to keep up with demand, but the production equipment upgrades that are available may involve increasing productive capacity by 2 million units per year.
Shifting a production function If a firm is operating at a profit-maximizing level in stage one, it might, in the long run, choose to reduce its scale of operations by selling capital equipment. By reducing the amount of fixed capital inputs, the production function will shift down. The output measured at time 2 is greater than the output measured at time one for both of the components of growth: The portion of growth caused by the increase in inputs is shown on line 1 and does not change the relation between inputs and outputs.
The portion of growth caused by an increase in productivity is shown on line 2 with a steeper slope. So increased productivity represents greater output per unit of input. The growth of production output does not reveal anything about the performance of the production process. Because the income from production is generated in the real process, we call it the real income.
- Theory of production
- Law of Returns to Scale : Definition, Explanation and Its Types
- Production function
The real income generation follows the logic of the production function. Two components can also be distinguished in the income change: The income growth caused by increased production volume is determined by moving along the production function graph. The income growth corresponding to a shift of the production function is generated by the increase in productivity.
The change of real income so signifies a move from the point 1 to the point 2 on the production function above. When we want to maximize the production performance we have to maximize the income generated by the production function.
The sources of productivity growth and production volume growth are explained as follows.
Economies of Scale
Productivity growth is seen as the key economic indicator of innovation. The successful introduction of new products and new or altered processes, organization structures, systems, and business models generates growth of output that exceeds the growth of inputs. This results in growth in productivity or output per unit of input. Income growth can also take place without innovation through replication of established technologies.
With only replication and without innovation, output will increase in proportion to inputs. They show that the great preponderance of economic growth in the US since involves the replication of existing technologies through investment in equipment, structures, and software and expansion of the labor force.
Further they show that innovation accounts for only about twenty percent of US economic growth. In the case of a single production process described above the output is defined as an economic value of products and services produced in the process.
When we want to examine an entity of many production processes we have to sum up the value-added created in the single processes. This is done in order to avoid the double accounting of intermediate inputs. Value-added is obtained by subtracting the intermediate inputs from the outputs.
It is widely used as a measure of the economic growth of nations and industries. Absolute total and average income[ edit ] The production performance can be measured as an average or an absolute income.
Expressing performance both in average avg.
The absolute income of performance is obtained by subtracting the real input from the real output as follows: With the aid of the production model we can perform the average and absolute accounting in one calculation. Maximizing production performance requires using the absolute measure, i. Maximizing productivity also leads to the phenomenon called " jobless growth " This refers to economic growth as a result of productivity growth but without creation of new jobs and new incomes from them.
A practical example illustrates the case. When a jobless person obtains a job in market production we may assume it is a low productivity job. As a result, average productivity decreases but the real income per capita increases.
Furthermore, the well-being of the society also grows. This example reveals the difficulty to interpret the total productivity change correctly.
Unfortunately we do not know in practice on which part of the production function we are. Therefore, a correct interpretation of a performance change is obtained only by measuring the real income change.
Production models[ edit ] A production model is a numerical description of the production process and is based on the prices and the quantities of inputs and outputs.
There are two main approaches to operationalize the concept of production function. We can use mathematical formulae, which are typically used in macroeconomics in growth accounting or arithmetical models, which are typically used in microeconomics and management accounting. We use here arithmetical models because they are like the models of management accounting, illustrative and easily understood and applied in practice.
Furthermore, they are integrated to management accounting, which is a practical advantage. A major advantage of the arithmetical model is its capability to depict production function as a part of production process. Consequently, production function can be understood, measured, and examined as a part of production process.
There are different production models according to different interests. Here we use a production income model and a production analysis model in order to demonstrate production function as a phenomenon and a measureable quantity. Production income model[ edit ] Profitability of production measured by surplus value Saari ,3 The scale of success run by a going concern is manifold, and there are no criteria that might be universally applicable to success.
Nevertheless, there is one criterion by which we can generalise the rate of success in production. This criterion is the ability to produce surplus value. As a criterion of profitability, surplus value refers to the difference between returns and costs, taking into consideration the costs of equity in addition to the costs included in the profit and loss statement as usual. Surplus value indicates that the output has more value than the sacrifice made for it, in other words, the output value is higher than the value production costs of the used inputs.
The table presents a surplus value calculation. We call this set of production data a basic example and we use the data through the article in illustrative production models. The basic example is a simplified profitability calculation used for illustration and modelling. Even as reduced, it comprises all phenomena of a real measuring situation and most importantly the change in the output-input mix between two periods.
In practice, there may be hundreds of products and inputs but the logic of measuring does not differ from that presented in the basic example.
In this context we define the quality requirements for the production data used in productivity accounting. The most important criterion of good measurement is the homogenous quality of the measurement object. If the object is not homogenous, then the measurement result may include changes in both quantity and quality but their respective shares will remain unclear. In productivity accounting this criterion requires that every item of output and input must appear in accounting as being homogenous.
In other words, the inputs and the outputs are not allowed to be aggregated in measuring and accounting. If they are aggregated, they are no longer homogenous and hence the measurement results may be biased. Both the absolute and relative surplus value have been calculated in the example. Absolute value is the difference of the output and input values and the relative value is their relation, respectively. The surplus value calculation in the example is at a nominal price, calculated at the market price of each period.
Production analysis model[ edit ] Production Model Saari Saari ,4 A model  used here is a typical production analysis model by help of which it is possible to calculate the outcome of the real process, income distribution process and production process. The starting point is a profitability calculation using surplus value as a criterion of profitability. The surplus value calculation is the only valid measure for understanding the connection between profitability and productivity or understanding the connection between real process and production process.
A valid measurement of total productivity necessitates considering all production inputs, and the surplus value calculation is the only calculation to conform to the requirement. If we omit an input in productivity or income accounting, this means that the omitted input can be used unlimitedly in production without any cost impact on accounting results. Accounting and interpreting[ edit ] The process of calculating is best understood by applying the term ceteris paribus, i.
Therefore, the calculation can be presented as a process advancing step by step. First, the impacts of the income distribution process are calculated, and then, the impacts of the real process on the profitability of the production.
The first step of the calculation is to separate the impacts of the real process and the income distribution process, respectively, from the change in profitability This takes place by simply creating one auxiliary column 4 in which a surplus value calculation is compiled using the quantities of Period 1 and the prices of Period 2.