Suppose we have a small inhabited island with three residents and a volcano that generates air pollution. Two people live upwind of the volcano and one person lives downwind. For \(\$ 21,000\) we can clean up the volcano with a patented "smoke guzzler." The two upwind people would pay \(\$ 1000\) each to get rid of the smoke whereas the downwind person would be willing to pay \(\$ 15,000\). Consider two plans to finance the "smoke guzzler." Plan A calls for a head-tax of \(\$ 7000\). Plan B calls for the affected party (the downwind person) to pay \(\$ 21,000\) and everyone else nothing. Compare each plan to the status quo and indicate society's choice using

(a) the Pareto criterion;

(b) majority rule;

(c) potential Pareto improvement.