601-fin-09fa

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E frqrplfv 601 1 Final Examination Answers Answer seven (7) of the following nine (9) questions in the exam booklets provided. Number each question carefully so that the instructor can f nd your answer to any question easily. All questions are of equal weight. 1. Textbooks introduce various kinds of systems of demand equations for con- sumers (e.g. Walrasian and Hicksian demands) and f rms (e.g. inputs demands based on pro f t maximization or on cost minimization). How are the various consumer demand systems related to the various producer demand systems? If a particular consumer (producer) demand system has no counterpart in producer (consumer) the- ory can you design a “new” demand system that would f ll this gap? Explain your answer carefully. In the context of consumers assume two goods; in the context of producers assume one output and two inputs. ANSWER Marshallian demands derive from the problem Max x 1 ,x 2 u ( x 1 2 ) such that w p 1 x 1 p 2 x 2 =0 which yields x i ( p 1 ,p 2 ,w ) . (1) Hicksian demands derive from the problem Min h 1 ,h 2 p 1 h 1 + p 2 h 2 such that u ( h 1 2 ) u 0 which yields h i ( p 1 2 ,u 0 ) . (2) Input demands of a pro f t-maximizing price taking f rm arise from the problem x 1 2 pf ( x 1 2 ) w 1 x 1 w 2 x 2 (3) which yields x i ( w 1 2 ) . Input demands of a cost-minimizing f rm derive from the problem x 1 2 w 1 x 1 + w 2 x 2 such that f ( x 1 2 ) y 0 which yields x i ( w 1 2 ,y 0 ) (4)

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E frqrplfv 601 2 Problems (2) and (4) are clearly the same and thus the associated demands func- tions h i ( p 1 ,p 2 ,u 0 ) and x i ( w 1 ,w 2 ,y 0 ) have much in common. The only di f erence is that utility cannot be measured in the same sense as output. Problems (1) and (3) are di f erent. The analogue of (1) in producer theory would be a f rm that maximized sales subject to a constraint on the total costs of its inputs. The problem faced by this kind of f rm would be Max x 1 ,x 2 pf ( x 1 2 ) such that C 0 w 1 x 1 w 2 x 2 =0 which would yield x i ( w 1 2 ,C 0 ) , which are much like the Marshallian demands of consumer theory. One could produce the analogue of (3) in consumer theory by using the concept of the marginal utility of money - the extra utility yielded by one more dollar of expenditure. Denote the marginal utility of money by λ . The inverse of λ is the “price” of utility - the number of dollars it takes to buy one unit of utility.
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