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ajaz_eco_204_2012_2013_chapter_11_producer_theory_basics

# One can plot these iso quant curves iso same quant

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Unformatted text preview: e the same level of output In Wolfram Alpha type plot(L^0.25)(K^0.75)from L=0,10 K=0,10 Each contour on the 3-D production surface plot traces the locus of labor and capital combinations with which the firm can produce a particular level of output. One can plot these iso-quant curves (“iso” = same, “quant” = quantity) in two dimensions: This iso-quant curve shows all combinations that will produce the same level of output The equation of the iso-quant curve for a particular, arbitrary level of output is: 5 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. { Notice that as then and vice versa so that for graph below for the iso-quant for } the iso-quant doesn’t have finite intercepts (see ): All combinations producing an output of Here are some more 3-D production surface plots and 2-D iso-quant curves – notice how the iso-quant curves are similar to indifference curves which means you can use the techniques from consumer theory to graph iso-quant curves in producer theory: In Wolfram Alpha type plot 2L + 3K, min(2L,3K) from L=0,10 K=0,10 6 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. In consumer theory, we assumed that the consumer either had monotone -- “more is better” – preferences ( )8 or had “more is the same” preferences ( ) over all bundles in her consumption set (i.e. we ruled out the case of “all goods are bad”). For a consumer with monotone preferences over all interior bundles in the consumption set, it implied that in the 2-D indifference curve map, utility increased in a north easterly direction (see graphs below for where at all interior bundles): However, if you remember, we assumed monotone preferences because it simplified the algebra of constrained UMP optimization (how?). In reality, a consumer may not have monotone preferences over all bundles in the consumption set, or for that matter, may have monotone preferences over some bundles in her consumption set, as the following ( ) ( ): examples show for and In the same way, for the sake of convenience we will assume that a firm’s production function is characterized by the property of “more inputs more output” (this is NOT the same thing as “increasing returns to scale” or “increasing 8 Be careful: monotone preferences is not the same thing as “increasing marginal utility” 7 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. returns”) or “more inputs same output”; put another way, we are ruling out the case of “more inputs less output” (alternatively, we are assuming the firm will never operate in the region of the production set where more inputs leads to less output). To check whether a production function has the “more inputs more output” and/or “more inputs same output” property we need to check whether the “marginal products” of each input -- the change in output due to a small increase in the input – are each . For example, suppose a firm’s production function is: defined over {( Then the “marginal product of labor” ( } ) is the change in output over a (small) change in labor: Notice that T...
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