section handout # 2_StudyGuide - (e) U(x,y) = max{2x+y,...

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Section Handout 2 (Econ310) 1. Consider the population of New York City and the relations (a) “at least as tall as” (as in “Jane is at least as tall as Jack) (b) “strictly taller than” (c) “in love with” Are these relations reflexive? Are they transitive? Are they complete? 2. A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete? 3. If both pepperoni and anchovies are bads, will the indifference curve have a positive or a negative slope? 4. Explain why convex preferences means that “averages are preferred to extremes.” 5. Use separate graphs to sketch two indifference curves for people with each of the following utility function (a) U(x,y) = x + 2y (b) U(x,y) = min {x, 2y} (c) U(x,y) = max {x, 2y} (d) U(x,y) = min {2x+y, 2y+x}
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Unformatted text preview: (e) U(x,y) = max{2x+y, 2y+x} In which of these cases are preferences convex? 6. Suppose there are only two alternatives x and y for Ali, i.e., X = {x, y}, and Ali strictly prefers x over y (a) suggest a utility function for Ali (b) Suggest another one (c) Is the utility function you suggested in (b) a monotonic transformation of the function you suggested in (a)? 7. Consider the following utility function u(x 1 , x 2 ) = min{x 1 , x 2 }, x 1 , x 2 0 (a) Let x 2 = 1. Write an algebraic expression for MU 1 as a function of x 1 . Sketch the graph of MU 1 (b) let x 1 = 4. Write and algebraic expression for MU 2 as a function of x 2 . Sketch the graph of MU 2 (c) Compute the value of MRS at (x 1 ,x 2 )=(4,1) directly. Is MRS = MU 1 /MU 2 at that point? 8. (from another universitys problem sets) 9. (previous prelim in Econ301)...
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section handout # 2_StudyGuide - (e) U(x,y) = max{2x+y,...

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