1. Assume a consumer has as preference relation represented by u(x1, x2) x + x2 for a € (0,1), with x € C = R}. Answer t

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1 Assume A Consumer Has As Preference Relation Represented By U X1 X2 X X2 For A 0 1 With X C R Answer T 1 (185.36 KiB) Viewed 76 times

1. Assume a consumer has as preference relation represented by u(x1, x2) x + x2 for a € (0,1), with x € C = R}. Answer the following: a. Show the preference relation this consumer is convex and strictly monotonic. Are they strictly convex? b. Compute the MRS between good 1 and good 2, and explain why it coincides with the slope of an indifference curve. Using the MRS, show that the preferences are convex. c. Write down the consumer's Marshallian optimization problem, and con- struct the first order conditions for this problem for an interior solution for consumption (i.e., optimal consumption of both goods are strictly positive). d. (difficult question): for these preferences, are optimal solutions for both goods always strictly positive for all prices? 2. Assume a consumer has as preference relation represented by u(x1,x2) = axi + bx2 with x E C = R7, and a, b > 0. Answer the following: > = + > a. Show the preference relation this consumer is convex and strictly monotonic. Show these preferences are not strictly convex for this consumer. b. Graph the indifference curves for this consumer. Now, solve for an explicit expression for the indiffence curve (i.e., x (x1;ū) i constructed in class for an indifference curve with utility level ū.) C. Compute the MRS between good 1 and good 2, and explain why it coincides with the slope of an indifference curve.