Print this page out. Use the space below and the back to write out and clearly i
ID: 1149396 • Letter: P
Question
Print this page out. Use the space below and the back to write out and clearly indicate your answers. Do not use this sheet as scrap paper, but use it to neatly present your work. There are three commodities available for con- sumption. In week 1, the prices of these commodities are (p1,p2,ps) = (4,2,2), and you observe Antwan con- sume quantities (x1, X2, X3) (6,3,2). In week 2, the prices of the commodities are (p1,p2, p.) = (3,4,1), and you observe Antwan consume quantities (x1, x2, x3) = (2,4,6). In week 3, the prices of the commodities are (p1,p2, p.) = (1,5,2), and you observe Antwan consume quantities (x1, x2, x3)-(42.8). You may assume that Antwan has monotonic preferences. Show that Antwan's choices satisfy the Weak Axiom of Revealed Preference (WARP). Do Antwan's choices satisfy the Strong Axiom of Revealed Preference (SARP)? Assum- ing that Antwan's choices do not change, is there an alternative price of commodity 1 in week 1, such that his choices violate WARP? Please explain your answersExplanation / Answer
Bundle 1: (6,3,2)
Bundle 2: (2,4,6)
Bundle 3: (1,5,2)
Week 1 :
Total Expenditure on Bundle 1 (6,3,2) at prices (4,2,2) = 6*4 + 2*3 + 2*2 = 34
Total Expenditure on Bundle 2 (2,4,6) at prices (4,2,2) = 2*4 + 4*2 + 6*2 = 28
Total Expenditure on Bundle 3 (4,2,8) at prices (4,2,2) = 4*4 + 2*2 + 8*2 = 36
Hencen when Bundle 1 was purchased Bundle 2. Bundle 3 was not affordable.
Week 2 :
Total Expenditure on Bundle 2 (2,4,6) at prices (3,4,1) = 2*3 + 4*4 + 6*1 = 28
Total Expenditure on Bundle 1 (6,3,2) at prices (3,4,1) = 6*3 + 3*4 + 2*1 = 32
Total Expenditure on Bundle 3 (4,2,8) at prices (3,4,1) = 4*3 + 2*4 + 8*1 = 28
Hence when Bundle 2 was chosen, bundle 1 was not affordable. Hence Bundle 1 is revealed preferred to Bundle 2.
Week 3 :
Total Expenditure on Bundle 3 (4,2,8) at prices (1,5,2) = 4*1 + 2*5 + 8*2 = 30
Total Expenditure on Bundle 1 (6,3,2) at prices (1,5,2) = 6*1 + 3*5 * 2*2 = 25
Total Expenditure on Bundle 2 (2,4,6) at prices (1,5,2) = 2*1 + 4*5 + 6*2 = 34
When Bundle 3 was purchased bundle 2 was not affordable. Hence Bundle 2 is revealed preferred to Bundle 3
Expenditure matrix:
When price 1, bundle 1 is chosen though bundle 2 was available. When price 2, bundle 2 is chosen, but then bundle 1 was not affordable. Hence bundle 1 is revealed preferred to bundle 2
When price 2, bundle 2 is chosen though bundle 3 was available. When price 3, bundle 3 is chosen, but then bundle 2 was not affordable. Hence bundle 2 is revealed preferred to bundle 3
This implies that Bundle 1 is indirectly revealed preferred to Bundle 3
SARP implies that transitivity must be true.
For SARP to satisfy bundle 1 must be directly revealed preferred to Bundle 3. However,
When price 3, bundle 3 is chosen though bundle 1 was available. When price 1, bundle 1 is chosen, but then bundle 3 was not affordable. Hence bundle 3 is revealed preferred to bundle 1. This violated SARP.
Changes in week 1 pricing that would violate WARP
Suppose the price in Week 1 is (8,2,2)
Total Expenditure on Bundle 1 (6,3,2) at prices (8,2,2) = 6*8 + 2*3 + 2*2 = 58
Total Expenditure on Bundle 3 (4,2,8) at prices (8,2,2) = 4*8 + 2*2 + 8*2 = 52
Hence when Bundle 1 was chosen bundle 3 was affordable. But When Bundle 3 was chosen bundle 1 was also affordable. Hence this violated WARP.
Please give a thumbs up if the answer was helpful to you.
Bundle 1 Bundle 2 Bundle 3 Price 1 34 28 36 Price 2 32 28 28 Price 3 25 34 30Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.