401-cbapproach

# 401-cbapproach - E frqrplfv 401 1 The Choice-Based Approach...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E frqrplfv 401 1 The Choice-Based Approach Consider a three-good 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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

401-cbapproach - E frqrplfv 401 1 The Choice-Based Approach...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online