ECON 446 - PROBLEM SET VI 1. Consider a marriage problem (M, W, R), where M = {a,b,c,d}, W = {E, F, G, H}, and preferences R = (Ra, Rb, Re, Rd, RE, RF, RG, RH) are as follows: . . . . Ra F Pa H Pa G Pa E Paa, : Re: HPF PC PG PE, RE: d PE b PE a PEC PE E, RG b PG a PG d PG c PG G, : Rb F PG PH P₁b P₁ E, Rd E Pa F Pa G Pad Pa H, RF d PF a PF b PF F PF C, : RH a PH b PH CPH d PH H. (i) Find the matching μW (R) that is the result of the Gale-Shapley's women proposing DA algo- rithm and show that it is stable. (ii) Find the matching μM (R) that is the result of the Gale-Shapley's men proposing DA algo- rithm and show that it is stable. μ (iii) Consider matching = {(a, H), (b, E), (c, G), (d, F)}. Is individually rational? Is μ stable? Is μ Pareto optimal? (iii) Consider matching ' = {(a, G), (b, F), (c, H), (d, E)}. Is ' individually rational? Is μ' stable? Is Pareto optimal?

ECON 446 - PROBLEM SET VI 1. Consider a marriage problem (M, W, R), where M = {a,b,c,d}, W = {E, F, G, H}, and preferences R = (Ra, Rb, Re, Rd, RE, RF, RG, RH) are as follows: . . . . Ra F Pa H Pa G Pa E Paa, : Re: HPF PC PG PE, RE: d PE b PE a PEC PE E, RG b PG a PG d PG c PG G, : Rb F PG PH P₁b P₁ E, Rd E Pa F Pa G Pad Pa H, RF d PF a PF b PF F PF C, : RH a PH b PH CPH d PH H. (i) Find the matching μW (R) that is the result of the Gale-Shapley's women proposing DA algo- rithm and show that it is stable. (ii) Find the matching μM (R) that is the result of the Gale-Shapley's men proposing DA algo- rithm and show that it is stable. μ (iii) Consider matching = {(a, H), (b, E), (c, G), (d, F)}. Is individually rational? Is μ stable? Is μ Pareto optimal? (iii) Consider matching ' = {(a, G), (b, F), (c, H), (d, E)}. Is ' individually rational? Is μ' stable? Is Pareto optimal?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter17: Long-term Investment Analysis

Section: Chapter Questions

Problem 3.2CE: Why has coal dominated as a fuel source for 24/7/365 electricity generation for so many decades?

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