Hatfield and McCoy hate each other but love corn whiskey. Because they hate for each other to be happy, each wants the other to have less whiskey. Hatfield’s utility function is UH(WH,WM) = WH−W2M and McCoy’s utility function is UM(WM,WH) = WM −W2H, where WM is McCoy’s daily whiskey consumption and WH is Hatfield’s daily whiskey consumption (both measured in quarts). There are 4 quarts of whiskey to be allocated.
(a) If McCoy got to allocate all of the whiskey, how would he allocate it? ____________ If Hatfield got to allocate all of the whiskey, how would he allocate it? ____________
(b) If each of them gets 2 quarts of whiskey, what will the utility of each of them be? _________ If a bear spilled 2 quarts of their whiskey and they divided the remaining 2 quarts equally between them, what would the utility of each of them be? ________ If it is possible to throw away some of the whiskey, is it Pareto optimal for them each to consume 2 quarts of whiskey? __________
(c) If it is possible to throw away some whiskey and they must consume equal amounts of whiskey, how much should they throw away?