ajaz_eco_204_2012_2013_chapter_11_producer_theory_basics

Below all combinations producing an output of all

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Unformatted text preview: he “marginal product of capital” ( ) for all input bundles in the production set ) is the change in output over a (small) change in capital: Notice that for all input bundles in the production set Since at interior bundles in the production set, in a 2-D iso-quant curves map, output increases in a north easterly direction (see graph below): All combinations producing an output of All combinations producing an output of As with monotone preferences, the idea that more inputs yields more (or the same) output is a convenient assumption. In fact, there’s a real possibility of “more inputs less output!” (Remember the “too many cooks in the kitchen” example from ECO 100?). 8 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 often described a consumer’s preferences from the marginal utilities (which told us whether the consumer perceives the goods as “good”, “bad”, or “neutral”) and the slope of the indifference curve (or the marginal rate of substitution ( )) from which, for example, we could tell whether the consumer perceives goods as “imperfect” or “perfect” substitutes. The counterpart of in producer theory is the slope of an iso-quant curve, or the “marginal rate of technical substitution” which for a 2 inputs production process tells us the amount by which input #2 can be reduced in exchange for using (infinitesimally) more of input #1 and still be able to produce the same level of output as before. In the examples below, the iso-quant slope is (for illustrative purposes these graphs show large changes in inputs): Cobb-Douglas Linear One can calculate the either from first principles or use a “short cut” similar to how in consumer theory the was a short cut for calculating the slope of the indifference curve. First, here’s an example using first principles. Suppose a firm’s has the long run Cobb-Douglas production: With on the y-axis, the equation of an iso-quant curve for an arbitrary level of output { is: } The slope at a bundle on the iso-quant curve is (you should do this): 9 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. { Substitute } to get: { { } } That was painful. Before we see the short cut notice that the slope does not depend on (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); for the iso-quant curves are downward sloping; and the slope varies from bundle to bundle which means labor and capital are “imperfect substitutes”. In fact, as the absolute value of the iso-quant curve decreases (becomes flatter) as shown below: Rather than computing slopes from first principles, we could instead use a short cut (similar...
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This document was uploaded on 01/19/2014.

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