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CHAPTER 11 PROFIT MAXIMIZATION Problems in this chapter consist mainly of applications of the P = MC rule for profit maximization by a price-taking firm and some examination of the firm’s derived demand for inputs. A few of the problems (13.2-13.5) ask students to derive marginal revenue related ideas, but this concept is not really used in the monopoly context until Chapter 14. Comments on Problems 11.1 A very simple application of the P = MC rule. Results in a linear supply curve. 11.2 Easy problem that shows that a tax on profits will not affect the profit- maximization output choice unless it affects the relationship between marginal revenue and marginal cost. 11.3 Practice with calculating the marginal revenue curve for a variety of demand curves. 11.4 Uses the MR-MC condition to illustrate third degree price discrimination. Instructors might point out the general result here (which is discussed more fully in Chapter 13) that, assuming marginal costs are the same in the two markets, marginal revenues should also be equal and that implies price will be higher in the market in which demand is less elastic. 11.5 An algebraic example of a profit function with one input. The problem asks the student to derive the supply and input demand functions from this profit function using Shephard’s lemma. 11.6 A problem in the theory of supply under uncertainty. This example shows that setting expected price equal to marginal cost does indeed maximize expected revenues, but that, for risk-averse firms, this may not maximize expected utility. Part (d) asks students to calculate the value of better information. 11.7 A simple use of the profit function with fixed proportions technology. 11.8 This is a conceptual examination of the effect of changes in output price on input demand. Analytical problems 11.9 A CES profit function. A very brief introduction to the CES profit function. Deriving the function involves a lot of algebra, but seeing how the parameters of the underlying production function enter this profit function is quite instructive. This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 87
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88 Chapter 11: Profit Maximization 11.10 Some envelope results. This problem describes some additional mathematical relationships that can be derived from the profit function. 11.11 More on derived demand with two inputs. This problem shows how an industry’s demand for an input can be computed and why that demand will depend on the elasticity of demand for the good being produced. This is a nice problem therefore for tying together input and output markets. 11.12 Cross-price effects in input demand. This is a continuation of Problem 11.11 to consider cross-price effects. The problem attempts to clarify how input cost shares enter into input demand elasticities.
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This note was uploaded on 06/09/2010 for the course AP 4010 taught by Professor Anam,mahmudul during the Fall '10 term at York University.

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