Hicks - Example Suppose p2 = 2 and Y = 2. Lets nd the Hicks...

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Example Suppose p 2 = 2 and Y = 2 Expenditure function. At the old price of p 1 = 1 , the consumer bought the bundle q 1 ;q 2 = 1 ; 1 2 ± The utility of this bundle was U = 1 1 2 = 1 2 . We want to keep the consumer on the same indi/erence curve U ± 1 2 when the price p 1 changes. How much income do we have to give her (Expenditure function) and what will be her demand (Hicks demand function)? U = 1 2 at minimal cost X ( q 1 ;q 2 ) . X is a function in two arguments. We solve this problem by using the constraint to substitute for q 2 : U = q 1 q 2 ± 1 2 ) q 2 ( q 1 ) = 1 2 q 1 . Now the cost X is a function of only one variable X ( q 1 ;q 2 ( q 1 )) = q 1 p 1 + 2 1 2 q 1 ± . q 1 d dq 1 X ( q 1 ;q 2 ( q 1 )) = 0 which is 0 = p 1 ² 1 q 2 1 and rewriting shows that the cost minimizing quantity is q 1 ( p 1 ) = 1 p p 1 and from q 2 = 1 2 q 1
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Hicks - Example Suppose p2 = 2 and Y = 2. Lets nd the Hicks...

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