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Unformatted text preview: E frqrplfv 401 1 The ChoiceBased Approach Consider a threegood example of Proposition 2.F.1 in MWG (p. 30) and the discussion that follows it. Let x 1 (a 3 by 1 column vector) denote quantities demanded at prices p 1 (another 3 by 1 vector). Now let prices change to p 2 and adjust wealth w so that x 1 is just a f ordable at prices p 2 . Let x 2 denote the bundle purchased at prices p 2 with adjusted wealth. The required change in wealth is ∆ w = ¡ p 2 1 − p 1 1 ¢ x 1 1 + ¡ p 2 2 − p 1 2 ¢ x 1 2 + ¡ p 2 3 − p 1 3 ¢ x 1 3 . Now ( ∆ p ) ¡ ∆ x ≡ ¡ p 2 − p 1 ¢ ¡ ¡ x 2 − x 1 ¢ = ¡ p 2 ¢ ¡ x 2 − ¡ p 1 ¢ ¡ x 2 − ¡ p 2 ¢ ¡ x 1 + ¡ p 1 ¢ ¡ x 1 Now, by construction, the cost of bundle 2 at the 2 prices and the cost of bundle 1 at the 2 prices are the same (note that this means that bundle 2 is revealed preferred to bundle 1), so the f rst and third term in the last line cancel each other leaving ( ∆ p ) ¡ ∆ x = − ¡ p 1 ¢ ¡ x 2 + ¡ p 1 ¢ ¡ x 1 IF this term were positive it would say that bundle 2 was a...
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 Fall '08
 Burbidge,John
 X1, AirTrain Newark

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