Suppose that in a world with two commodities, the consumer’s utility function takes the form u(x) = [?1 x1^? + ?2 x2^?]^{1/?}. This utility function is known as the constant elasticity of substitution (or CES) utility function. (a) Show that when ? = 1, indifference curves become linear. (b) Let ?1 = ?2 = 1. Compute the Walrasian demand function for this utility function. (Let x(p,w) denote the Walrasian demand function, where p = (p1,p2) is a vector of prices, w > 0 is the consumer’s level of wealth.) (c) Verify that the Walrasian demand function you computed in part (b) is homogeneous of degree zero in (p,w), that is, x(?p,?w) = x(p,w) for all ? > 0.
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The MRS is the ratio of the marginal utilities of the two goods, which can be found by taking the partial derivatives of the utility function with respect to each good. The utility function is given by u(x) = [G1xf + 82+3]. Let x1 and x2 represent the quantities Show more…
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