hw8-06-2 - expenditure function, B = B ( p x , p y , U )...

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ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 8 Skip has the following utility function: U ( x, y )= x ( y +1) ,where x and y are quantities of two consumption goods whose prices are p x and p y respectively. Skip has a budget of B. Therefore the Skip’s maximization problem is x ( y +1)+ λ ( B p x x p y y ) a) From the f rst order conditions f nd expressions for the demand functions x = x ( p x ,p y ,B ) y = y ( p x ,p y ,B ) Carefully graph x and y . Graph Skip’s indi f erence curves. What kind of good is y? b) Verify that skip is at a maximum by checking the second order conditions. c) By substituting x and y into the utility function f nd an expressions for the indirect utility function, U = U ( p x ,p y ,B ) d) By rearranging the indirect utility function, derive an expression for the
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Unformatted text preview: expenditure function, B = B ( p x , p y , U ) Interpret this expression. Find B / p x and B / p y . Skips maximization problem could be recast as the following minimization problem: p x x + p y y s.t. U = x ( y + 1) e) Write down the lagrangian for this problem. f) Find the values of x and y that solve this minimization problem and show that the values of x and y are equal to the partial derivatives of the expendi-ture function, B / p x and B / p y respectively. (Hint: use the indirect utility function) 1...
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This note was uploaded on 09/13/2009 for the course EOCNOMICS Econ 331 taught by Professor Kelvinkwainger during the Spring '09 term at Simon Fraser.

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