MICROECONOMICS 1 – PRODUCTION THEORY We continue from where we left off, examining some concepts in production theory. As we saw earlier, the Marginal Rate of Technical Substitution (MRTS) measures the trade off between two inputs in production with output constant. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY A formal derivation of the formula for the MRTS is given below. Suppose our production function as generally specified is given by
y f ( x1, x2 ) Then if we consider the change in the use of factors 1 and 2 that keeps output unchanged, then we have: LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY y MP1 ( x1 , x2 ) x1 MP2 ( x1 , x2 ) x2 0, MP1 ( x1 , x2 ) x1 MP2 ( x1 , x2 ) x2
MRTS ( x1 , x2 )
x2 MP1 ( x1 , x2 ) x1 MP2 ( x1 , x2 ) LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY It is worth highlighting that the Marginal Rate of Technical Substitution (MRTS) is also the slope of the isoquant. That is, dx2 | x2 MRTS y y1 x1 , x2 dx1 x1
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Another closely related assumption about the nature of technology embodied in the production process is that of Diminishing Marginal Rate of Technical Substitution (MRTS). That is, as we increase the amount of one factor, say x1, and adjust
the second factor, say x2, so as to stay on the same Isoquant, the MRTSx1,x2 declines. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY It means that the slope of the MRTS must decrease in absolute value as we move East and must increase as we
move North Not to be confused with the law of diminishing marginal product (law of diminishing marginal returns). LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY K
MRTSL,K is high; labour is scarce so a little more labour frees up a lot of capital MRTSL,K is low; labour is abundant so a little more labour barely affects the need for capital
• •
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Diminishing MRTS and diminishing marginal returns are closely related but are not exactly the same. Diminishing marginal returns is an assumption about how the marginal product changes as we increase the amount of one factor, holding the other factor fixed. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY But diminishing MRTS is about how the ratio of the marginal products – the slope of the isoquant – changes as we
increase the amount of one factor and reduce the amount of the other factor so as to stay on the same isoquant.
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Elasticity of Substitution: the MRTS despite its insights has a serious defect, in that it is dependent on the units of
measurement of the factors. Hence a better measure of the degree of factor substitution is the elasticity of substitution. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Elasticity of Substitution: this is defined as the percentage change in the capital-labour ratio, divided by the percentage
change in the MRTS. Formally, the elasticity of substitution,
can be
represented by the following expression: LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Factor Intensity: the factor intensity of any process is measured by the slope of the line through the origin representing the
particular process. In other words, the factor intensity is the capital-labour ratio at
the particular point of interest in the production process.
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY
K
A 100
B 30 Q=12
50
200
L
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY In the figure above, what is apparent regarding points A and B are that:
That is, the upper part of the isoquant is more capital-intensive than the lower part, which includes more labour-intensive techniques LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY In general therefore, a production method that uses relatively more labour than capital is labour-intensive, while a method
that uses relatively more capital than labour is capitalintensive.
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Returns to Scale: now suppose that instead of increasing one input whilst the other is held unchanged, we increase both inputs
in the production process. In other words, let’s scale the amount of all inputs up by some
constant factor, e.g., use three times as much of x1 and x2 LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Returns to Scale describes the relationship between inputs and output when all factors of production vary. In other words, it describes the output response to a proportionate increase of all inputs. In general, if we scale all inputs by some amount, t, then three
possibilities can arise: constant returns to scale, increasing returns to scale and decreasing returns to scale. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Returns to Scale are easily defined for homogeneous production function. A production function is homogeneous of degree k if
f ( fx1 , tx2 ) t f ( x1, x2 ) k
where k is a constant and t is any positive real number.
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Constant Returns to Scale: this arises if we use twice as much of each input and we get twice as much output. Thus, in the case
of two inputs,
2� �1 ,�2 = �(2�1 ,2�2 )
�� �1 ,�2 = �(��1 ,��2)
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Why might we expect this outcome? It should be possible for the firm to replicate what it was doing before. Thus, if the firm has twice as much of each input, it can just set up two plants side by side and
thereby get twice as much output. But it is perfectly possible for a production technology to exhibit
constant returns to scale and diminishing marginal product to each factor. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Increasing Returns to Scale: this arises when we scale up all inputs by some factor, t, we get more than t times as much
output. Mathematically, this is given by
�� �1,�2 > �(��1,��2)
for all t > 1
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Decreasing Returns to Scale: this arises when we scale up all inputs by some factor, t, we get less than t times as much output.
Mathematically, this is given by
�� �1,�2 < �(��1,��2)
for all t > 1
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Returns to Scale: in general if both inputs are increased by the k
factor t, and output is increased by the factor t , returns to scale
are increasing if k > 1, constant if k = 1, and decreasing if k < 1.
LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Economies of Scale Vs. Returns to Scale
A production process is said to exhibit economies (constant
economies, diseconomies) of scale over a particular range of output per unit of time if the long-run average production costs fall (remains unchanged, increases) as output increases. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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MICROECONOMICS 1 – PRODUCTION THEORY Economies of Scale Vs. Returns to Scale
The term returns to scale refers to the effect on output of a
proportionate change in the level of use of all inputs. It is therefore important not to confuse the two concepts. LECTURE MATERIAL ON MICROECONOMICS 1: PREPARED BY DR. EMMANUEL CODJOE
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