3.D.3B Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w) is differentiable. Show the following: (a) If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and the indirect utility function v(p, w) are homogeneous of degree one [and hence can be written in the form x(p, w) = wx(p) and v(p, w) = w(p)] and the wealth expansion path (see Section 2.E) is a straight line through the origin. What does this imply about the wealth elasticities of demand?
3.D.3B Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w) is differentiable. Show the following: (a) If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and the indirect utility function v(p, w) are homogeneous of degree one [and hence can be written in the form x(p, w) = wx(p) and v(p, w) = w(p)] and the wealth expansion path (see Section 2.E) is a straight line through the origin. What does this imply about the wealth elasticities of demand?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![3.D.3B Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian
demand function x(p, w) is differentiable. Show the following:
(a) If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and
the indirect utility function v(p, w) are homogeneous of degree one [and hence can be written
in the form x(p, w) = wx(p) and v(p, w) = w(p)] and the wealth expansion path (see Section
2.E) is a straight line through the origin. What does this imply about the wealth elasticities
of demand?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaa15c2a-5d73-4965-9b94-aa09fb474d04%2Fe9c16138-89b1-4bf8-a6ef-976dce404cb7%2F33hugr8_processed.png&w=3840&q=75)
Transcribed Image Text:3.D.3B Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian
demand function x(p, w) is differentiable. Show the following:
(a) If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and
the indirect utility function v(p, w) are homogeneous of degree one [and hence can be written
in the form x(p, w) = wx(p) and v(p, w) = w(p)] and the wealth expansion path (see Section
2.E) is a straight line through the origin. What does this imply about the wealth elasticities
of demand?
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