solutionproblemset5 - UCLA Economics 11 Fall 2006 Professor...

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UCLA Economics 11 – Fall 2006 Professor Mazzocco Problem Set 5 Due by November 9 before 11:30am. 1) A consumer has utility: 5 . 0 5 . 0 y x U + = . The Marshallian demands are given by: ) ( ) ( y x y U y x x y U P P P PxI Y P P P I P X + = + = And that the Hicksian demands are given by: 2 2 + = + = y x x C y x y C P P U P Y P P U P X a) Find the Indirect Utility Function V . b) Find the Expenditure Function E . c) Using the Slutsky equation, find the expressions for the substitution effect and the income effect on X generated by an increase in P x . d) Derive the Slutsky equation for the good X for a change in the price P y . [Hint: follow the method that we used in class to derive the Slutsky equation for the good X for a change in the price P x . But instead of computing the derivatives of the starting equation with respect to P x , you have to compute the derivatives with respect to P y .] f) Using the Slutsky equation derived in part d) find the expressions for the substitution effects and the income effect on X generated by an increase in P y .
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