Answer to Question #243171 in Microeconomics for de girl

Question

 Suppose that u(·) is strictly quasiconcave (so that Walrasian demand is single-valued) and differentiable and that the Walrasian demand x(p, w) is differentiable. (a) Show that if u(·) is homogeneous of degree one, then x(p, w) and v(p, w) are both homogeneous of degree 1 in w (with this, the two functions will take the form x(p, w) = wxˆ(p) and v(p, w) = wvˆ(p)). (b) What do the results of previous part imply about the Hicksian demand h(p, u) and the expenditure function e(p, u)? . (c) Show that when x(p, w) is homogeneous of degree 1 in w, for each ` = 1, . . . , L ∂x`(p, w) ∂w w = x`(p, w) (or in matrix form Dwx(p, w)w = x(p, w)). What does this imply about wealth elasticity of demand? (d) Show that when Walrasian demand x(p, w) is homogeneous of degree 1 in w, for each ` = 1, . . . , L X L k=1 ∂x`(p, w) ∂pk pk = X L k=1 ∂xk(p, w) ∂p` pk 2 (or in matrix form p · Dpx(p, w) = Dpx(p, w)p)).

Answer 1

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