Marginal Rate Of Technical Substitution

4 Key excerpts on "Marginal Rate Of Technical Substitution"

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  Managerial Economics

  Problem-Solving in a Digital World

  • Nick Wilkinson(Author)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  Figure 6.5 shows an isoquant map, based on the data in Table 6.1. Points A, B and C correspond to the values indicated in the table. Thus it can be seen that the output of 80 units can be achieved either by using six machines and three workers (point B) or by using four machines and five workers (point C). On the other hand, in order to produce 100 units of output, it is necessary to use five machines and five workers (point A), although other combinations (involving fractions of inputs) can also produce the same output. It should be noted that the isoquant for the output of 100 units starts to curve upwards as more than seven workers are used; this is because it is not possible to produce 100 units with fewer than five machines. The maximum output from using only four machines is 90 units, no matter how much labour is used. 6.5.2 The Marginal Rate Of Technical Substitution The Marginal Rate Of Technical Substitution (MRTS) is a measure of the degree of substitutabil- ity between two inputs. More specifically, the MRTS of X for Y corresponds to the rate at which 6.5 The Long Run 293 one input (X) can be substituted by another (Y), while maintaining total output constant. It is shown by the absolute value of the slope of the isoquant; thus, in moving from point B to point C, the MRTS is one, meaning that, if two more workers are used, we can give up two machines and still produce 80 units of output. The slope of the isoquant is decreasing in absolute magnitude from left to right. This means that as more and more labour is used to produce a given output, the less easily the capital input can be substituted for it. The reason for this is the occurrence of the law of diminishing returns, explained in the previous section. Thus, as more labour is used and less capital, the marginal product of additional labour falls and the marginal product of the capital lost increases.

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  Intermediate Microeconomics

  An Intuitive Approach with Calculus

  • Thomas Nechyba(Author)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  For instance, while doubling all the values associated with a consumer indifference map leaves us with the same tastes as before, doubling the values associated with isoquants alters the production technology, with the new technology producing twice as much output from any bundle of inputs. Graph 12.3 Relatively More or Less Substitutability of Capital for Labour 0 (a) A 10 2 100 200 300 100 200 300 100 200 300 k ℓ (b) (c) 0 k ℓ 0 k ℓ TRS = –3 Why do you think we have emphasized the concept of marginal product of an input in producer theory but not the analogous concept of marginal utility of a consumption good in consumer theory? Exercise 12A.6 12A.2.1 TRS and Marginal Product While the economic interpretation of isoquants is in many ways dif-ferent from the economic interpretation of indifference curves, there is much that we have learned in our study of indifference curves that is directly applicable to our understanding of isoquants. We begin with the interpretation of the slope of isoquants, known as the marginal technical rate of substitution or just the technical rate of substitution . A slope of 2 3 on an isoquant as, for instance, in panel (b) of Graph 12.3, indicates that 3 units of capital could be traded for 1 unit of labour with overall production remaining roughly constant. The technical rate of substitution thus tells us at each input bundle how many units of the input on the vertical axis could be substituted for 1 unit of the input on the horizontal axis and maintain a constant level of output. Since it is a mouthful to say marginal technical rate of substitution, we will generally stick with just technical rate of substitution and abbreviate it to TRS . Furthermore, since we have adopted the convention of always putting labour on the horizontal and capital on the vertical axis in our isoquant graphs, we will call the slope of an isoquant the TRS without always having to add the phrase ‘of labour with respect to capital’.

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  Microeconomics

  Theory and Applications

  • Edgar K. Browning, Mark A. Zupan(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  This indicates that the marginal product of the second unit of capital is 12 units of output. Further raising capital from two to three units, assuming that labor employment is still held constant at L f , increases output from 30 to 40 units (from point H on IQ 30 to point F on IQ 40 along segment L f F). Since the third unit of capital has a lower marginal product (10 units of output) than does the second unit of capital (12 units of output), the law of diminishing marginal returns applies to capital over this range of capital use. MRTS and the Marginal Products of Inputs The degree to which inputs can be substituted for one another, as measured by the Marginal Rate Of Technical Substitution, is directly linked to the marginal productivities of the inputs. Consider again the MRTS, or slope, between points B and D in Figure 7.3. Between these two points one unit of labor can replace two units of capital, so labor’s marginal product must be two times as large as capital’s marginal product when the slope of the isoquant ( ) MRTS LK is two units of capital to one unit of labor. To check this reasoning, note that between points C and A in Figure 7.3 the slope of the isoquant is unity. Here the marginal products must be equal because the gain in output from an additional unit of labor (that is, labor’s marginal product) must exactly offset the loss in output associated with a one-unit reduction in capital (that is, capital’s marginal product). Thus, the Marginal Rate Of Technical Substitution, which is equal to (minus) the slope of an isoquant, is also equal to the relative marginal productivities (MPs) of the inputs: MRTS K L MP MP LK L K . ( ) / / (2) Note that the isoquant’s slope does not tell us the absolute size of either marginal product but only their ratio. • Production When All Inputs Are Variable: The Long Run 171 We can also derive this relationship more formally. In Figure 7.3, consider the slope of isoquant IQ 30 between points E and H, ΔK / ΔL.

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  Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

  • Toshiyuki Sueyoshi, Mika Goto(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  Chapter 23 on the classification of DTR.

  22.2.2 MRT and RSU

  Figure 22.2 depicts RSU among an input (x), a desirable output (g) and an undesirable output (b). As depicted in Figure 22.2 , for example, dg/dx measures the degree of MRT where d stands for the derivative on a functional form between g and x. In a similar manner, the degree of MRT is applicable to other relationships among x, g and b. It can be intuitively considered that the MRT measures the rate at which a DMU willingly exchanges an amount of a production factor for another one.

  FIGURE 22.2

  Marginal rate of transformation and rate of substitution

  The degree of (dg/dx)/(g/x) measures a magnitude of RSU that is considered as “scale elasticity” when the two vectors (X and G) have a single component. The analytical relationship is applicable to the other two cases (b and x; g and b) in the manner of (db/dx)/(b/x) and (db/dg)/(b/g).

  Here, it is important to note that RSU, explored in this chapter, is different from elasticity of substitution (ES) that serves as a fundamental concept of economics. Both measures have similarities and differences in many aspects. To describe the position of RSU more clearly, this chapter reviews ES and then compares it with RSU.

  Elasticity of Substitution (ES):

  The concept of ES has a long history in economics, dating back to the original concept proposed by Hicks (1932)6 . He used ES as a methodology for analyzing between capital and labor income shares in a growing economy, along with constant RTS and a natural technology change. Allen and Hicks (1934)7 and Allen (1938)8 extended the original concept of ES. Uzawa (1962)9 further analyzed the concept, becoming a dominant concept of ES, conventionally referred to as “Allen–Uzawa elasticity” in modern economics. Later, Morishima (1967)10 proposed an alternative to the Allen–Uzawa elasticity, referred to as “Morishima elasticity,” to which many economists (Davis and Gauger, 1996; Klump and de la Grandville, 2000)

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