Unformatted text preview: to the
in consumer
theory). This shortcut  for the slope of an isoquant curve is – the
“marginal rate of technical substitution” (also
sometimes known as the
, “technical rate of substitution”) which for a 2 input production function is:
( ) For example, suppose:
10
ECO 204 Chapter 11: Producer Theory— the Basics (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Then, with on the yaxis: That was easy! Here is another example: suppose a firm has the production function:
{ } By the way, notice that to produce positive amounts of output, labor is an essential input whereas capital is an optional
input. The slope of an isoquant curve at some bundle of inputs is: Notice that the isoquant slope is independent of : as such, when
the production surface plot is “pulled up” since
the firm can produce more from the same inputs, but the curvature of the isoquant curves stays the same. You should
use algebra to convince yourself that the isoquant curves look like: In Wolfram Alpha type plot(L + L*K)from L=0,3 K=0,3 11
ECO 204 Chapter 11: Producer Theory— the Basics (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ________________________________________________________________________________________________
[Optional] Proof of
formula.
Along an isoquant curve:
( ) Take total differentials:
{ ( )
} ( { )
} Along an isoquant there’s no change in output so that:
{ ( )
} { ( )
} Rearrange:
{ ( )
} { ( )
} Or: Notice that for all production functions, the isoquant slope is independent of : as such, when
the production
surface plot is “pulled up” since the firm can produce more from the same inputs, but the curvature of the iso quant
curves stays the same.
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While there are many parallels between consumer and producer theories, there is one major difference: while applying
“positive monotonic transformation” (PMT) on a utility function yields another utility function representing the same set
of preferences, applying a PMT on a production function does not yield another production function representing the
same “production process”. This is because “utility” is an ordinal number  used to rank bundles and is not a physical
measure of the amount of utility  whereas output is a cardinal number and literally a physical measure of output.
Scaling up” a production function literally produces a higher level of output from all input bundles in the production set,
so that the two production functions do not represent the same production process; in contrast, in consumer theory,
scaling up a utility function represented the same preferences because it preserved the order of utility preference 12
ECO 204 Chapter 11: Producer Theory— the Basics (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. rankings. Just to make sure, let...
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 Fall '14
 Economics, Microeconomics, Economics of production, producer, S. Ajaz Hussain, Sayed Ajaz Hussain

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