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?

Microeconomic Theory
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Chapter4: Utility Maximization And Choice
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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?
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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