501PS02 - ECON501 Advanced Microeconomic Theory 1 Fall...

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ECON501 Advanced Microeconomic Theory 1 Fall Semester 2007 Problem Set 2 The due date for this problem set is Friday October 19. 1. Solve the UMP of a consumer whose preference relation over the consumption set X = R 3 + can be represented by the utility func- tion.: u ( x 1 ,x 2 ,x 3 )= Ax α 1 x β 2 x 1 α β 3 where A> 0, and α , β and α + β are all in (0 , 1). Find the indirect utility function, the minimum expenditure function, and the Hicksian demand function. 2. Let x ( p, w )=( x 1 ( p, w ) ,x 2 ( p, w ) ,...,x L ( p, w )) be a demand func- tion. (a) Show that P L k =1 p k ∂w x k =1. (b) ∂p l x l ( p, w ) / ³ x l p l ´ is called the price elasticity of demand for good l (with respect to its own price). Show that the consumer will spend less on good l as p l (marginally) goes up if and only if the price elasticity is more than one. (c) If ∂w x l ( p, w ) 0 , good l is said to be normal at ( p, w ). A good is called a normal good if it is normal at any (
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501PS02 - ECON501 Advanced Microeconomic Theory 1 Fall...

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