401-t1-11wa

401-t1-11wa - E 401 1 Test 1 Thursday 27th January 2011...

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E frqrplfv 401 1 Test 1 Thursday 27th January 2011 Answer all questions. Each is worth 10 marks. 1. What are the two main approaches to consumer behaviour in economics? What elements do they have in common, and how do they di f er? What restrictions do they place on a two-good system of ordinary demand equations? x 1 ( p 1 ,p 2 ,w ) x 2 ( p 1 2 ) ANSWER The two approaches are the choice-based approach and the preference-based ap- proach. The f rst is founded on the weak axiom of revealed preference; the second on preference relations. Both approaches assume standard budget constraints in R n + and therefore are consistent with the implications of imposing such budget constraints. The CB approach assumes the consumer’s choices are consistent with the weak ax- iom. The PB approach assumes the consumer’s choices obey the many assumptions imposed on preference relations (re F exivity, completeness, transitivity, continuity, monotonicity or local non-satiation, convexity, etc.). The restrictions on the demand system include the following. Walras’s Law p 1 x 1 ( p 1 2 )+ p 2 x 2 ( p 1 2 )= w Homogeneity for all α > 0 ,x j ( α p 1 , α p 2 , α w x j ( p 1 2 ) ,j =1 , 2 Denoting the Slutsky substitution matrix by S , these identities imply ± p 1 p 2 ² ³ S 11 S 12 S 21 S 22 ´ = ± 00 ² and
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E frqrplfv 401 2 ± S 11 S 12 S 21 S 22 ²± p 1 p 2 ² = ± 0 0 ² 2. Let X be a choice set and ( B ,C ( · )) be a choice structure on X . (a) Using mathematics, de f ne the weak axiom of revealed preference (WARP). (b) Do each of the following satisfy WARP? Justify each answer. (i) X = { a,b, c } , B = { B 1 ,B 2 3 } 1 = { a, b } 2 = { b, c } 3 = { c, a } ( B 1 )= { a } ( B 2 { b } ( B 3 { c } ; (ii) X = { a, b, c } , B = { B 1 2 } 1 = { a,b } 2 = { a, b, c } ( B 1 { a } ( B 2 { a, b } ; (iii) X = { a, b, c, d } , B = { B 1 2 } 1 = { } 2 = { a, b, d } ( B 1 { a, c } ( B 2 { a, d } ; ANSWER (a) WARP can be de f ned as: (*) Assume B 1 B 2 B , { a, b } B 1 , { a, b } B 2 then a C ( B 1 ) and b C ( B 2 ) a C ( B 2 ) .
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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401-t1-11wa - E 401 1 Test 1 Thursday 27th January 2011...

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