Question: Consider a many-to-one matching problem between two firms {fi(large), fs (small)} and three workers {j(junior 1), 2(junior 2), s(senior)}. The pref- erences are given

Consider a many-to-one matching problem between two firms {fi(large), fs (small)} and three workers {j(junior 1), 2(junior 2), s(senior)}. The pref- erences are given by fi: s (J1, 2) 1 > 2 > , fs: 11 12 s> 0, 11,12 f1 fs, S: fs > fi. For example, the large firm fi has a large project that can be completed by either one senior worker, or two juniors working together. (a) Explain that the large firm does not have responsive preferences. (b) Verify that the following matchings are both stable. P = {(fi, 8), (fs, j1)}, H = {(f, ), (f1, 12), (fs, s)}. (c) Explain that Rural Hospital Theorem does not hold.

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