Assume that demand for three goods has been evaluated at the follow- ing three price vectors:...
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Assume that demand for three goods has been evaluated at the follow- ing three price vectors: p¹= (1,2,2); p² = (2, 1,2); p = (2,2,1); with income m= 12 in all cases. Consider two different data sets specifying r¹ r(p¹, 12), x² = x(p², 12), and z³ = x(p, 12). E (a) Suppose that x¹ = (4,2, 2), r² = (2, 4,2), and ³ (2,2,4). Show that there are no cycles in the affordability matrix. What does this imply for existence of a utility function rationalizing these choices? (b) Suppose instead that r¹= (2,3,2), (2,2,3), and 2³ (3,2,2). Show that there is a cycle in the affordability matrix. What does this imply for existence of a utility function rational- izing these choices? Assume that demand for three goods has been evaluated at the follow- ing three price vectors: p¹= (1,2,2); p² = (2, 1,2); p = (2,2,1); with income m= 12 in all cases. Consider two different data sets specifying r¹ r(p¹, 12), x² = x(p², 12), and z³ = x(p, 12). E (a) Suppose that x¹ = (4,2, 2), r² = (2, 4,2), and ³ (2,2,4). Show that there are no cycles in the affordability matrix. What does this imply for existence of a utility function rationalizing these choices? (b) Suppose instead that r¹= (2,3,2), (2,2,3), and 2³ (3,2,2). Show that there is a cycle in the affordability matrix. What does this imply for existence of a utility function rational- izing these choices?
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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