Marginal Rate Of Technical Substitution

3 Key excerpts on "Marginal Rate Of Technical Substitution"

• 

  eBook - ePub

  Principles of Agricultural Economics

  • Andrew Barkley, Paul W. Barkley(Authors)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  Marginal Rate Of Technical Substitution (MRTS) . It reflects how well one input substitutes for another.

  • • Marginal Rate Of Technical Substitution [MRTS] = the rate at which one input can be decreased as the use of another input increases to take its place. The slope of the isoquant. MRTS = ΔX2 / ΔX1.

  A graph provides the best way to gain understanding of what the MRTS is all about.

  The slope of the isoquant in Figure 5.10 shows the MRTS between inputs X1 and X2 . In this graph, input X2 is on the y-axis, and X1 is on the x-axis, so the slope of the isoquant equals ΔY / ΔX = ΔX2 / ΔX1 . In the case of imperfect substitutes, as in Figure 5.10 , the slope becomes less steep in response to substituting X1 for X2 . The value of MRTS changes with moves along the isoquant. When moving from point A to point B, the firm keeps output constant by reducing X2 by one unit (from 3 to 2 on the vertical scale), and increasing X1 by one input (from 1 to 2 on the horizontal scale). This results in a calculated MRTS of negative one (−1):

  (5.5) MRTS(AB) = ΔX2 / ΔX1 = (2 – 3) / (2 – 1) = −1.

  The MRTS must always be a negative number, since isoquants based on two inputs that are imperfect substitutes must always be downward sloping for rational producers.

  Figure 5.10 Marginal Rate Of Technical Substitution between two inputs

  The move from A to B shows that the firm can select a wide variety of input combinations that will yield the same level of output. In fact, any point on the isoquant will, by definition, result in the same level of output. The movement from A to B represents a shift out of input X2 and into input X1 .

  A move from point B to C will yield a smaller MRTS, because the slope of the isoquant becomes less steep with the move. This new MRTS (relating to the move from point B to point C) is calculated as:

  (5.6) MRTS(BC) = slope of isoquant = ʔX2 / ʔX1 = (1 - 2) / (4 - 2) = -1 /2 = -0.5.

  The slope of the isoquant, or MRTS, is crucial to determining which combination of inputs a firm will choose. The isoquant describes input combinations that are technically feasible. Economic information (the prices of the two inputs) allows this technical information to determine the cost-minimizing levels of input use. The next section switches from the technical information relating to input productivity to relative prices of the inputs.

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  eBook - ePub

  Principles of Agricultural Economics

  • Andrew Barkley, Paul W. Barkley(Authors)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  1 . A graph provides the best way to gain understanding of what the MRTS is all about.

  The slope of the isoquant in Figure 5.10 shows the MRTS between inputs X1 and X2 . In this graph, input X2 is on the y-axis, and X1 is on the x-axis, so the slope of the isoquant equals ΔY/ΔX = ΔX2 /ΔX1 . In the case of imperfect substitutes, as in Figure 5.10 , the slope becomes less steep in response to substituting X1 for X2 . The value of MRTS changes with moves along the isoquant. When moving from point A to point B, the firm keeps output constant by reducing X2 by one unit (from 3 to 2 on the vertical scale), and increasing X1 by one input (from 1 to 2 on the horizontal scale). This results in a calculated MRTS of negative one (–1):

  (5.5)  MRTS(AB) = ΔX2 /ΔX1 = (2 – 3)/(2 – 1) = –1.

  The MRTS must always be a negative number, since isoquants based on two inputs that are imperfect substitutes must always be downward sloping for rational producers.

  Figure 5.10 Marginal Rate Of Technical Substitution between two inputs

  The move from A to B shows that the firm can select a wide variety of input combinations that will yield the same level of output. In fact, any point on the isoquant will, by definition, result in the same level of output. The movement from A to B represents a shift out of input X2 and into input X1 .

  A move from point B to C will yield a smaller MRTS, because the slope of the isoquant becomes less steep with the move. This new MRTS (relating to the move from point B to point C) is calculated as:

  (5.6)  MRTS(BC) = slope of isoquant = ΔX2 /ΔX1 = (1 – 2)/(4 – 2) = –1/2 = –0.5.

  The slope of the isoquant, or MRTS, is crucial to determining which combination of inputs a firm will choose. The isoquant describes input combinations that are technically feasible. Economic information (the prices of the two inputs) allows this technical information to determine the cost-minimizing levels of input use. The next section switches from the technical information relating to input productivity to relative prices of the inputs.

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  Intermediate Microeconomics

  A Tool-Building Approach

  • Samiran Banerjee(Author)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  TRS . It is given by the ratio of the marginal productivities:

  We now consider several technologies, some of which are the production counterparts of preferences familiar to us from Chapter 3 in the context of consumption.

  7.2.1 Linear technologies

  A production function of the form

  where a and b are marginal products of inputs x 1 and x 2 respectively results in linear isoquants so long as at least one marginal product is strictly positive. When both are positive, the TRS is a/b analogous to the indifference curves depicted in the left panel of Figure 3.3 . When a > 0 but b = 0, the isoquants look like the indifference curves in the left panel of Figure 3.4 , while for a = 0 and b > 0, the isoquants are like the indifference curves in the right panel.

  7.2.2 Leontief technologies

  A production function of the form

  (where a and b are non-negative and at least one is strictly positive) generates L-shaped isoquants with kinks along the ray from the origin with slope a/b , analogous to the indifference curves depicted in Figure 3.5 . Here, of course, there are no substitution possibilities between the inputs — they are complements in that

  the two inputs are always used in fixed proportions according to the ratio b : a

  .2

  Figure 7.1 Two Leontief technologies

  However, if a firm has access to two different Leontief technologies, e.g., two plants for producing the same good where the inputs are combined in different fixed proportions, then input substitution possibilities arise. To see this, let the inputs be labor ℓ and capital k , and (ℓ 1 , k 1 ) and (ℓ 2 , k 2

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