Bargaining. It is November 1st, and Angus and Bronwen are arguing over how to divide the remainder of their left-over trick or treat candy. They decide on the following rules. On Nov 1st, Angus will make Bronwen an offer (sA(1), SB(1)] where sa (1) + 5B (1) = 1. If Bronwen accepts then Angus gets a share s(1) of the candy and Bronwen gets sb (1). If Bronwen refuses, however, then no-one gets any candy on Nov 1st. In this case, on Nov 2nd, Bronwen gets to make Angus an offer (sa(2), sb(2)] where sa (2) + SB (2) = 1. If Angus accepts then Angus gets a share sa(2) of the candy and Bronwen gets sb (2). If Angus refuses, however, then no-one gets any candy on Nov 2nd. In this case, on Nov 3rd, Angus gets to make Bronwen an offer (sA(3), SB(3)] where sa (3) +SB (3) = 1. If Bronwen accepts then Angus gets a share sa(3) of the candy and Bronwen gets sb (3). If Bronwen refuses, however, then no-one gets any candy on Nov 3rd. In this case, on Nov 4th, Bronwen gets to make Angus an offer (sa(4), SB (4)] where sa (4) +SB (4) = 1. If Angus accepts then Angus gets a share sa(4) of the candy and Bronwen gets sb (4). If Angus refuses, however, then all the candy is thrown away by their parents. There is a catch. Both Angus and Bronwen are hungry and impatient for candy so they discount candy tomorrow. For Angus, each day, one candy tomorrow is worth only da candy today where da < 1. For Bronwen, each day, one candy tomorrow is only worth only dB candy today where 8B < 1. It is commonly known that Angus and Bronwen are rational and that they are not interested in distributive justice. You may also assume that each of Angus and Bronwen accepts an offer whenever he or she is indifferent. (a) What do you expect to happen, and what allocation of candy would arise if SA = ? Explain your reasoning carefully. (b) Compare your answer when da=dB=x, and when da = Intuitively, why is the impatience of both good for one and bad for the other. (c) Now suppose that Angus becomes more impatient so that da < SB. Does this change increase or decrease Angus's share of the candy relative to what it was when 8A = dB. Give an intuition.