![]() Since y = ex is a continuousfunction, it is sufficient to show that (tx1 + (1 t)x2, ty1 + (1 t)y2) S for anyparticular t (0, 1). For example, (0, 1) and(1, e) (x, y)|y = ex, but combination of the two vectors with t = 12not: (12, e+12) /(x, y)|y = ex.(b) (x, y)|y exThis set is convex.Proof: Let (x1, y1), (x2, y2) S = (x, y)|y ex. If it is notconvex, give a counterexample.Answer(a) (x, y)|y = exThis set is not convex.Any combination of points would be outside the set. ![]() 3011 Mathematical Appendix1 Mathematical Appendix1.1 Chapter A1A1.7 Graph each of the following sets. ![]() 62 Consumer Theory 122.1 Preferences and Utility. Solutions to selected exercises fromJehle and Reny (2001): AdvancedMicroeconomic TheoryThomas HerzfeldSeptember 2010Contents1 Mathematical Appendix 21.1 Chapter A1. ![]()
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