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 A symmetric Constant Elasticity of Substitution (CES) utility function is defined by us (21, 202) + where 8 * 0 is a fixed constant, which may be positive or negative

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 A symmetric Constant Elasticity of Substitution (CES) utility function is defined by us (21, 202) + where 8 * 0 is a fixed constant, which may be positive or negative. Also, when 8 = 0 we define uo (X1, X2) = 122 As the parameter o varies, the utility function represents different de- grees of complementarity or substitutability of the two goods. Note that the cases o = 1, 8 = 0 are examples we have seen before: perfect substitutes and Cobb-Douglas, respectively. (a) For the case S = -10, draw the three indifference curves through (1, 1), (3, 3) and (3, 6). (Use a calculator or computer to help with this.

(c) For a ?xed 3:1 and 232, what happens to the MRS as 6 —> —00? (The answer will depend on $1 and 3:2; how?) Based on this answer and your graph for 6 = —10, state which preferences (among those ‘ we have studied in class) resemble the case of extremely negative 6. (d) For 6 < 1, these preferences are convex, and you may assume there is an interior solution satisfying the tangency condition. Solve for the consumer’s choices ($1,132) in terms of y, phpg and 6. A correct formula will be valid for all 6 < 1. (It is not valid when 6 2 1, because for these values there is a corner solution.)