cvevmarch07

# cvevmarch07 - Finding CV and EV an example A consumer has a...

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Finding CV and EV, an example. A consumer has a utility function u ( x 1 ,x 2 )= x 2 1 x 2 . Utility maximization problem for this consumer: max x 2 1 x 2 s.t : x 1 0 ,x 2 0 and p 1 x 1 + p 2 x 2 = m. The demand for the goods is x 1 ( p 1 ,p 2 ,m )= 2 m 3 p 1 , x 2 ( p 1 ,p 2 ,m )= m 3 p 2 . The indirect utility function is the utility level at the optimal point as a function of the budget parameters: v ( p 1 ,p 2 ,m )= μ 2 m 3 p 1 2 × m 3 p 2 = 4 m 3 27 p 2 1 p 2 Suppose at f rst prices are p 1 = p 2 =1 and income m = 120 : x 1 =8 0 ,x 2 =40 , u =8 0 2 × 40 = 256 , 000 . Consider a price increase for good 1, now p 1 =2 ,p 2 =1 and m = 120 : x 1 =4 0 ,x 2 =40 , u =4 0 2 × 40 = 64 ,

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To f nd the CV, we need to f nd how much extra money to give this consumer so that he can get the old utility level ( u = 256 , 000 . ) when the new prices prevail p 1 =2 ,p 2 =1 . Let us f rst f nd f nd the amount of money needed to have a utility level u =256 , 000
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cvevmarch07 - Finding CV and EV an example A consumer has a...

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