Economics
Constant Returns to Scale
Constant Returns to Scale refers to a production situation where increasing all inputs by a certain proportion results in a proportional increase in output. In other words, if inputs are doubled, output also doubles. This concept is important in understanding the relationship between input and output levels in the production process.
Written by Perlego with AI-assistance
Related key terms
1 of 5
6 Key excerpts on "Constant Returns to Scale"
eBook - PDFMicroeconomics
Equilibrium and Efficiency
- Thijs ten Raa(Author)
- 2017(Publication Date)
- Red Globe Press(Publisher)
This completes the proof of the Constant Returns Proposition. The proof of this proposition is straightforward, but the proposition itself is illuminating because it frees the concept of Constant Returns to Scale from the requirement that production has only a single output. In general, we can define Constant Returns to Scale for a production possibility set Y by the condition θ Y = Y ( θ > 0). A production possibility set is a more general tool than a production function because it encompasses many situations, including the economy-wide model (8.7) and its variants, in which joint products are made (see Section 8.3; for example, copper and gold ore). Decreasing and increasing returns to scale also may be reformulated for pro-duction possibility sets, but we refrain from doing this for two reasons. First, it is important to distinguish between weak and strong returns. Our definitions of returns to scale, (7.15) and (7.17), and their counterparts, (7.16) and (7.18), fea-ture strong inequalities (that is, < and > ). Therefore, all these returns to scale are strong. For example, our definition of increasing returns to scale, (7.17), implies that output increases at a strictly higher rate than input. However, if we replace the strong inequalities with weak inequalities (that is, ≤ and ≥ ), the returns to scale are weak and, therefore, are more amenable for reformulation as production possibility sets. The second reason we do not define returns to scale for produc-tion possibilities has to do with our equilibrium analysis in the next chapter, which will assume Constant Returns to Scale (7.14). 8.5 The Law of Supply If the price of one particular output increases, the producer will probably reallo-cate her resources to produce more of that output – in other words, the supply of an output is an increasing function of its price. Similarly, if an input’s price goes up, there will probably be less demand for it. In the theory of the con-sumer, however, things are not so easy.
- Roberto Serrano, Allan M. Feldman(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
Somewhat more precisely, when returns are increasing, costs are falling, and vice versa. As we will see below, this is what we find for constant, increasing, and decreasing returns to scale. 9.3 Cost Minimization in the Long Run 161 1 MC = AC = C (1) C ( y ) $ y (output) C (1) Figure 9.5 Total cost C ( y ) (in blue) with Constant Returns to Scale. Suppose a firm’s production function satisfies Constant Returns to Scale . Let ( x ∗ 1 , x ∗ 2 ) be the cost-minimizing input combination that results in one unit of output. Then C ( 1 ) = w 1 x ∗ 1 + w 2 x ∗ 2 . Now, if the firm wants to produce an arbitrary y units of output, by Constant Returns to Scale, it can do so by multiplying by y both the input quantities that gave one unit of output. Moreover, as we saw above, scaling up both the inputs in this fashion will leave MP 1 , MP 2 , and TRS unchanged. Therefore, since ( x ∗ 1 , x ∗ 2 ) was a point of tangency between an isoquant and an isocost line, ( yx ∗ 1 , yx ∗ 2 ) will also be a tangency point. Therefore, C ( y ) = yC ( 1 ) is the least-cost way to produce y units of output. That is, for Constant Returns to Scale, the long-run cost function is a very simple linear function that makes C ( y ) directly proportional to output y . We show this kind of linear cost function in Figure 9.5 . Remember that average cost is total cost divided by quantity, or AC ( y ) = C ( y )/ y . For our Constant Returns to Scale case, average cost is constant. This is because AC ( y ) = C ( y )/ y = yC ( 1 )/ y = C ( 1 ) . Also recall that marginal cost is the derivative of the cost function, or, intuitively, the extra cost per additional unit of output. That is, MC ( y ) = dC ( y )/ dy . In the Constant Returns to Scale case, MC ( y ) = d ( C ( 1 ) y )/ dy = C ( 1 ) = AC ( y ) . In short, with Constant Returns to Scale, total cost is a linear function of y , and both average and marginal cost are constant, equal to each other, and equal to the cost of producing just 1 unit of output.
- Dudley Jackson(Author)
- 2018(Publication Date)
- Routledge(Publisher)
Thus, although the total requirement for each factor input increases as the scale of output increases, the ratio between the factor inputs does not change. In other words, the capital- intensity of production theoretically remains constant as the scale of annual output increases among plants, and full increasing returns to scale is a phenomenon which is, in theory, distinct from mechanization. However, we shall show in subsequent chapters that the two forces often accompany each other in a highly interdependent way and that this happens for strong and compelling economic reasons. In other words, while mechanization and economies of scale can, in terms of pure theory, be distinguished one from the other, in practice the two may be difficult to distinguish—for good reasons which we shall subsequently explain. 7.8 Minimum cost production under full increasing returns to scale We have shown that, under the condition of full increasing returns to scale, each unit factor input requirement (at the minimum cost position) decreases 198 Profitability, Mechanization and Economies of Scale as the scale of annual output increases. The proportionate decrease will be according to the elasticity (1 - a - b)/(a + b ). At constant factor prices, this equi-proportionate decrease in each unit factor input requirement (at the minimum cost position) means that the minimum unit labour and capital cost combined will decrease in the same proportion. This can be shown as follows. Let v* denote the minimum unit labour and capital cost combined. Then: The expression in brackets is a constant, and we may denote it as j. For the illustrative case we have been considering./ = ($2.40 x 0.07683527 + 0.2 x 0.30734108) = 0.245872864. Hence for this illustrative case: v* = 0.245872864 0-0166667 In the case of increasing returns to scale, the exponent on Q must be negative and so the minimum unit labour and capital cost combined decreases as the scale of annual output increases.
eBook - PDFA Reconsideration of the Theory of Non-Linear Scale Effects
The Sources of Varying Returns to, and Economies of, Scale
- Richard G. Lipsey(Author)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
As we will see later in this Element, when authors discuss the sources of favourable scale effects, such as more efficient capital or greater division of labour, they disagree in almost all cases as to whether the source causes an IRTS or an EoS. This should not surprise us in the light of our arguments both that the standard definition of returns to scale is deficient and that production actually takes place in multiple stages. Indeed, it is not obvious that there is any gain in distinguishing between these two concepts. However, if we wish to do so, the following definitions may suffice: returns to scale occur when there is a change in a firm’ s unit cost of production that would have occurred if all input prices had remained constant, while economies or diseconomies of scale occur if there are changes in a firm’ s unit cost including those that would not have occurred if input prices had remained constant. Thus, returns to scale are located in the relation between a firm’ s inputs and its output and these give rise to economies of scale which can also arise from sources such as input price changes due to changes in market power or upstream scale effects. For the rest of this study we use the type-1 definition where each different technique of production has its own PF, each one of which may differ from the others in the nature of inputs and the marginal rates of substitution among them at various scales of output. Those who wish to continue with the type-2 PF definition can think of returns to scale when we speak of efficiencies of design as defined below. Further Problems with the PF We note in passing that there are other serious problems connected with both of the definitions of a PF. To see these, consider the concept of technical effi- ciency, an engineering concept.
eBook - ePubEconomics of Tourism and Hospitality
A Micro Approach
- Yong Chen(Author)
- 2021(Publication Date)
- Routledge(Publisher)
On the long-run average cost curve there exists a strictly negative relationship between the average cost and output in the production range from zero to q E as shown in Figure 8.7, a phenomenon known as economies of scale. Due to economies of scale, the restaurant can enjoy increasingly lower average costs as long as it produces in large quantities until the output reaches q E. Note that economies of scale occur in the long run and thus differ from diminishing marginal cost in the short run. Figure 8.7 Long-run average cost and economies of scale Not only can the long-run average cost be driven down as output increases, but the minimum of average costs can also be sustained in a certain range of production. This is illustrated in Figure 8.7 by assuming that the restaurant continues to expand the premises, eventually rendering the long-run average cost curve flat between q E and q D. This means that the long-run average cost is invariant insofar as the restaurant produces any output between q E and q D. This phenomenon is referred to as Constant Returns to Scale. Constant Returns to Scale occur because relaxing the constraint of fixed costs in the long run can defer the increasing marginal cost that would otherwise arise in the short run. Nevertheless, as the level of fixed costs further expands, production efficiency could be undermined due to, for example, complicated coordination problems between different departments of a corporation as well as cumbersome bureaucracy in big corporations. This leads to an increase in average costs when the output exceeds q D as shown in Figure 8.7, which is referred to as diseconomies of scale. The existence of diseconomies of scale implies, on the one hand, that firm size is by no means infinite but has its limits
- Bhat, Anil(Authors)
- 2021(Publication Date)
- Daya Publishing House(Publisher)
Figure 2.2: Law of Increasing Returns In figure 2.2, along X-axis are measured the units of inputs applied and along Y-axis the marginal return is represented. PF is the curve representing the law of increasing returns. 2.1.1.3. Law of Constant Returns/Law of Constant Cost The law of constant returns is also called as the law of constant cost. It is said to operate when with the addition of successive units of one factor to fixed amount of other factors, there arises a proportionate increase in total output. The yield of equal return on the successive doses of inputs may occur for a very short period in the process of production. In the words of Marshall : “If the actions of the law of increasing and diminishing returns are balanced, we have the law of constant return.” Assumptions In actual life, the law of constant returns can operate only if the following conditions are fulfilled: 1. There should not be any increase in the prices of inputs required. This ebook is exclusively for this university only. Cannot be resold/distributed. 2. The prices of various factors of production should remain the same. 3. The productive services should not be fixed and indivisible. The law of constant returns can operate for a very short period when the marginal return moves towards the optimum point and begins to decline. If the marginal return, at the optimum level remains the same with the increased application of inputs for a short while, then we have the operation of law of constant returns. The law is represented now in the form of a table and a curve. Table 2.3. Total product, marginal product and average product in response to inputs application Fixed Input Input Variable Total Product Marginal Product 12 acres 1 labour 60 60 12 acres 2 labour 120 60 12 acres 3 labour 180 60 12 acres 4 labour 240 60 12 acres 5 labour 300 60 In the Table 2.3, the marginal product remains the same, i.e.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
