In our earlier posts, we explained the production function and law of variable production. If you have yet to read them, you can find them here – meaning of production function and the law of variable production. Now, here in this post, we are going to explain the law of returns to scale, which is a long-run theory of production in which all factors of production – especially capital & labor – are variable. We employ the modern form of production function with two variable factor inputs, i.e., Q = f(K, L), to analyze the whole story.
What does the term ‘returns to scale’ refer to?
Before understanding this law, it is good to understand the meaning of the term ‘returns to scale.’ The term returns to scale means what happens to returns when the scale of production changes. Here, returns refer to output under production, and scale refers to the size of employment of factors—labor and capital—for ease of exposition. That is, the term implies what happens to output when labor and capital are increased in the same proportion.
As oppose to the term diminishing returns, which explain short-run change in output due to change is variable factors of production given the fixed factor (law of variable proportion), returns to scale explain the long-run change in output due to proportionate change in factor inputs.
What are the basic assumptions?
Mainly, this law rests on following two assumptions:
- All factors can be used proportionately in production, i.e., in fixed proportions (say, the ratio of capital to labor equals the ratio of labor to land because proportion is the equality of rations). This is the one important feature of the classical production function.
- The production technique remains constant; if changed, it causes output to change more than the scale or size effect.
Statement of law
Employing factor inputs proportionately, i.e., increasing the production scale, it is likely that output may increase more than proportionately as the inputs, increase at the same proportion as the inputs, or increase less than proportionately as the inputs (not assumed to decrease). This is what the law of returns to scale says about. This argument indicates three possible cases of returns to scale: increasing returns to scale, constant returns to scale, and decreasing returns to scale.
Increasing returns to scale
Output increases more than proportionately as the inputs. In other words, doubling or trebling the inputs more than doubling or trebling the output. For instance, output increases by 110 percent when inputs increase by 100 percent. The main factor behind the IRS is the emergence of economies of scale. More specifically, factors contributing to IRS are the indivisibility of factors that they are available in a lumpy style, specialization of labor and use of specialized machinery possible as the scale of production increases, and dimensional economies (e.g., doubling the sides of a cube more than doubles the volume).
Constant returns to scale
Output increases at the same percentage as the inputs, i.e., doubling or trebling the inputs double or trebles the output. For example, output increases by 100 percent when inputs increase by 100 percent. The leading cause of the emergence of CRS is the balance between economies of scale and diseconomies of scale.
Decreasing returns to scale
Output increases less than proportionately as the inputs. Put another way, doubling or trebling inputs less than doubles or trebles the output. For instance, output increases by 90 percent when inputs increase by 100 percent. The leading cause of the DRS is the emergence of the diseconomies of scale as the scale of production remarkably increases. More specifically, the causes of the DRS are: an entrepreneur is considered the fixed factor of production and accordingly the operation of the law of diminishing returns; dis-management regarding coordination, communication, and control; and depletion or exhaustion of natural resources.
Final note on law of returns to scale
In a nutshell, there are both economics and diseconomies of scale that simultaneously operate in the production activities no matter what the size of production is. When economies of scale outweigh diseconomies of scale, the IRS emerges. On the contrary, DRS emerges when diseconomies of scale more than offset the economies of scale. Of course, CRS appears when these opposite forces are equal. Empirical studies regarding the law of returns to scale have found the operation of IRS at the initial stage or small-scale operation, CRS at the medium scale of operation, and DRS at large-scale operation. Amongst them, CRS was found to exist for more extended periods of scale of operation than others.
Some economists argue that the entrepreneur is the fixed factor and cannot be used in a fixed proportion with other factors. This view contends the law of returns to scale is a special case of the law of variable proportion because the entrepreneur is a fixed factor, and the rest of the others are variable. This argument has posed a challenge in operating the law of returns to scale. But, if we take entrepreneur as the human effort rather than a number, this law seems logical and operational because entrepreneurial effort directly varies with the scale of operation irrespective of the number of entrepreneurs.