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econ11_08_ps4 - Eco11 Fall 2008 Simon Board Economics 11...

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Eco11, Fall 2008 Simon Board Economics 11: Practice Problems 4 (Week 5) October 16, 2008 1. Expenditure Minimisation with CES demand A consumer has the utility u ( x 1 , x 2 ) = x 1 / 2 1 + x 1 / 2 2 . a) Find the Hicksian demand for x 1 and x 2 b) Find the expenditure function. c) Find the Marshallian demand for x 1 and x 2 . d) Find the indirect utility function. Depending on how you approach this question, you may find it useful to note that: p 2 p 1 1 / 2 + p 1 p 2 1 / 2 = p 1 + p 2 ( p 1 p 2 ) 1 / 2 e) Show that the Slutsky equation holds. 2. Consumption with Endowments: Labour Supply A particular household consists of two agents who are both potential workers and who pool their budgets. The households preferences are represented by a single utility function u ( x 0 , x 1 , x 2 ) = log( x 0 - α ) + log x 1 + log x 2 where x 1 is the amount of leisure enjoyed by agent 1, x 2 is the amount of leisure enjoyed by agent 2, and x 0 is the amount of the single composite consumption good enjoyed by the household. The two agents each have T
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