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# ch08 - CHAPTER 8 COST FUNCTIONS The problems in this...

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CHAPTER 8 COST FUNCTIONS The problems in this chapter focus mainly on the relationship between production and cost functions. Most of the examples developed are based on the Cobb-Douglas function (or its CES generalization) although a few of the easier ones employ a fixed proportions assumption. Two of the problems (8.9 and 8.10) make some use of Shephard’s Lemma since it is in describing the relationship between cost functions and (contingent) input demand that this envelope-type result is most often encountered. Comments on Problems 8.1 Famous example of Viner’s draftsman. This may be used for historical interest or as a way of stressing the tangencies inherent in envelope relationships . 8.2 An introduction to the concept of “economies of scope.” This problem illustrates the connection between that concept and the notion of increasing returns to scale. 8.3 A simplified numerical Cobb-Douglas example in which one of the inputs is held fixed. 8.4 A fixed proportion example. The very easy algebra in this problem may help to solidify basic concepts. 8.5 This problem derives cost concepts for the Cobb-Douglas production function with one fixed input. Most of the calculations are very simple. Later parts of the problem illustrate the envelope notion with cost curves. 8.6 Another example based on the Cobb-Douglas with fixed capital. Shows that in order to minimize costs, marginal costs must be equal at each production facility. Might discuss how this principle is applied in practice by, say, electric companies with multiple generating facilities. 8.7 This problem focuses on the CES cost function. It illustrates how input shares behave in response to changes in input prices and thereby generalizes the fixed share result for the Cobb-Douglas.

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