Solution-Q1-Nov3-12-1 - Solution Q1-Nov-3-12 1 1 Demand...

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Solution Q1-Nov-3-12 1. Demand functions are derived from Y x p x p x x U 2 2 1 1 2 / 1 2 2 / 1 1 : S.t Max a) Make a pos. mon. transformation on the utility function and write the Lagrange function as follows. ) ( ln 2 1 ln 2 1 2 2 1 1 2 1 x p x p Y x x L . F.O.C. are ) 3 ( 0 ) 2 ( 2 1 0 2 1 ) 1 ( 2 1 0 2 1 2 2 1 1 2 2 2 2 2 1 1 1 1 1 x p x p Y L p x p x x L p x p x x L (1) and (2) are inserted into (3) which gives that Y 1 which in turn is inserted into (1) and (2). That give demand functions: 1 1 2 1 p Y x and 2 2 2 1 p Y x . b) Write 2 , 1 , 2 1 ) , ( i Y Y p x p i i i , where ) , ( Y p x i i are the demand functions. Now differentiation w.r.t price and income give 1 2 1 2 1 , 0 1 0 ) , ( i i i i i i i i i i i i i i i x Y Y x p Y Y Y x Y x p p x x p p x p Y p x . Rearrangement gives that price elasticities are -1 for both commodities and
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