Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w)...

 

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Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w) is differentiable. Show the following: If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and the indirect utility function (p, w) are homogeneous of degree one [and hence can be written in the form x(p, w) = wx(p) and v(p, w) = wõ(p)] and the wealth expansion path is a straight line through the origin. What does this imply about the wealth elasticities of demand? Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w) is differentiable. Show the following: If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and the indirect utility function (p, w) are homogeneous of degree one [and hence can be written in the form x(p, w) = wx(p) and v(p, w) = wõ(p)] and the wealth expansion path is a straight line through the origin. What does this imply about the wealth elasticities of demand?

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