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{"ops":[{"insert":"\u00a0Suppose that u(\u00b7) 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(\u00b7) 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) = wx\u02c6(p) and v(p, w) = wv\u02c6(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 \u2202x`(p, w) \u2202w 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 \u2202x`(p, w) \u2202pk pk = X L k=1 \u2202xk(p, w) \u2202p` pk 2 (or in matrix form p \u00b7 Dpx(p, w) = Dpx(p, w)p)). \n"}]}
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