NicholsonMTAISECh9IM

NicholsonMTAISECh9IM - CHAPTER 9 PRODUCTION FUNCTIONS...

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CHAPTER 9 PRODUCTION FUNCTIONS Because the problems in this chapter do not involve optimization (cost minimization principles are not presented until Chapter 9) they tend to have a rather uninteresting focus on functional form. Computation of marginal and average productivity functions is stressed along with a few applications of Euler's theorem. Instructors may want to assign one or two of these problems for practice with specific functions, but the focus for Part 3 problems should probably be on those in Chapters 10 and 11. Comments on Problems 9.1 This problem illustrates the isoquant map for fixed proportions production functions. Parts (c) and (d) show how variable proportions situations might be viewed as limiting cases of a number of fixed proportions technologies. 9.2 This provides some practice with graphing isoquants and marginal productivity relationships. 9.3 This problem explores a specific Cobb-Douglas case and begins to introduce some ideas about cost minimization and its relationship to marginal productivities. 9.4 This problem involves production in two locations and develops the equal marginal products rule. 9.5 This is a thorough examination of most of the properties of the general two-input Cobb-Douglas production function. 9.6 This problem is an examination of the marginal productivity relations for the CES production function. 9.7 This illustrates a generalized Leontief production function. Provides a two-input illustration of the general case which is treated in the extensions. 9.8 Application of Euler's theorem to analyze what are sometimes termed the "stages" of the average-marginal productivity relationship. The terms "extensive" and "intensive" margin of production might also be introduced here, although that usage appears to be archaic. Analytical Problems 9.9 Local returns to scale. This problem introduces the local returns to scale concept and presents an example of a function with variable returns to scale. 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. 69
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70 Chapter 9: Production Functions 9.10 Returns to scale and substitution. Shows how returns to scale can be incorporated into a production function while retaining its input substitution features. 9.11 More on Euler’s Theorem. Shows how Euler’s Theorem can be used to srudy the likely signs of cross productivity effects. Solutions 9.1 a., b. function 1: use 10 k , 5 l function 2: use 8 k , 8 l c. Function 1: 2 k + l = 8,000 2.5(2 k + l ) = 20,000 5.0 k + 2.5 l = 20,000 Function 2: k + l = 5,000 4( k + l ) = 20,000 4 k + 4 l = 20,000 Thus, 9.0 k , 6.5 l is on the 40,000 isoquant Function 1: 3.75(2 k + l ) = 30,000 7.50 k + 3.75 l = 30,000 Function 2: 2( k + l ) = 10,000 2 k + 2 l = 10,000 Thus, 9.5 k , 5.75 l is on the 40,000 isoquant 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
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NicholsonMTAISECh9IM - CHAPTER 9 PRODUCTION FUNCTIONS...

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