ajaz_eco_204_2012_2013_chapter_11_producer_theory_basics

Eco 204 s ajaz hussain do not distribute then with on

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Unformatted text preview: to the in consumer theory). This short-cut -- for the slope of an iso-quant 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 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Then, with on the y-axis: 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 iso-quant curve at some bundle of inputs is: Notice that the iso-quant 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. You should use algebra to convince yourself that the iso-quant 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 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ________________________________________________________________________________________________ [Optional] Proof of formula. Along an iso-quant curve: ( ) Take total differentials: { ( ) } ( { ) } Along an iso-quant there’s no change in output so that: { ( ) } { ( ) } Re-arrange: { ( ) } { ( ) } Or: Notice that for all production functions, the iso-quant 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. _________________________________________________________________________________________________ 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 2012-2013) 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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