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.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
December 2022
Categories |