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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 3D 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 isoquant curves (“iso” = same, “quant” = quantity) in two
dimensions: This isoquant curve
shows all
combinations
that will produce
the same level of
output The equation of the isoquant curve for a particular, arbitrary level of output is:
5 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. {
Notice that as
then
and vice versa so that for
graph below for the isoquant for }
the isoquant doesn’t have finite intercepts (see
): All
combinations
producing an output
of Here are some more 3D production surface plots and 2D isoquant curves – notice how the isoquant curves are similar
to indifference curves which means you can use the techniques from consumer theory to graph isoquant 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 20122013) 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 2D 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 20122013) 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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This document was uploaded on 01/19/2014.
 Fall '14

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