Questions 1) Consider a world in which there are only two periods: period 0 and period 1 and three possible states of the world in period 1 (a good weather state, a fair weather state, and a bad weather state). Also, apples are the only product produced in this world, and they cannot be stored from one period to the next. The following abbreviations will be used PA -apple in the present period (i.e., present apple), GA- good weather apple in the next period. FA = fair weather apple in the next period, BA = bad weather apple in the next period Suppose that an apple tree firm offers for sale a bond and stock. The apple tree produces 80 GA, 50 FA, and 25 BA. The bond pays 20 GA, 20 FA and 20 BA. The stock pays 60 GA, 30 FA and 5 BA. The price of the bond is 18 PA, and the price of the stock is 22 PA. In addition, security C, D, and E are traded for 31 PA, 11 PA, and 10 PA respectively. Security C pays 70 GA, 40 FA, and 15 BA. Security D pays 30 GA, 15 FA, and 2.5 BA. Security E pays 40 GA, 10 FA, and 0 BA 2) Consider another world similar to the one considered in Question 1 except there is a new set of atomic prices involving dealers. 2.1) Dealer I is willing to trade 0.15PA for 1GA (or vice versa), and dealer II is willing to trade 1GA for 0.6FA (or vice versa) and dealer III is willing to trade 1FA for 0.5BA. a) What is the arbitrage-free price of a BA in terms of PA? b) What is the arbitrage-free discount factor? 2.2) In addition, dealer IV is willing to trade 1 PA for 4 BA (or vice versa). Are there arbitrage opportunities? If so, design a profitable arbitrage strategy