Consider a setting where L = 3 and a consumer whose consumption set is R (i.e.,...

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Consider a setting where L = 3 and a consumer whose consumption set is R³ (i.e., allowing for a negative demand). Suppose that the consumer's observed demand function is given by x₁ (p, w) = P2 P3 x₂ (p,w) = - P₁ P3 and x3 (p, w) = W P3 (a) Show that the observed demand x(p, w) = (x1, x2, x3) is homogeneous of degree zero in (p, w) and satisfies Walras' law. (b) Show that x violates the weak axiom of revealed preference (WARP). (c) Show that v¹ S(p, w)v = 0 for every v ER³, where S(p, w) indicates the Slutsky matrix. Consider a setting where L = 3 and a consumer whose consumption set is R³ (i.e., allowing for a negative demand). Suppose that the consumer's observed demand function is given by x₁ (p, w) = P2 P3 x₂ (p,w) = - P₁ P3 and x3 (p, w) = W P3 (a) Show that the observed demand x(p, w) = (x1, x2, x3) is homogeneous of degree zero in (p, w) and satisfies Walras' law. (b) Show that x violates the weak axiom of revealed preference (WARP). (c) Show that v¹ S(p, w)v = 0 for every v ER³, where S(p, w) indicates the Slutsky matrix.

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a Wal ras law states that the total demand for goods must equal the total income of the consumer We can calculate the total demand by sum ming the ind... View the full answer