Solutions needed.
6. {a} Consider a twoperiod bargaining problem. Two players, 1 and 2. are trying to divide Rs. 10. Each player has an outside option. Player 1's outside option is Rs. 6 and player 2's outside option is Rs. 3. Outside option refers to the value that a player can get if the game bargaining game ends without an agreement. Note that this is different from the usual bargaining model where the players end with {1' if the bargaining game ends without an agreement. Player 1 makes the rst offer. Player 2 has three options: [i] she can accept the offer in which case the game ends according to the offer made by player 1; {ii} she can reject the offer and take the game to the second round of bargaining; (iii) she can reject the offer and end the game in which case both players get their outside options. If the game reaches the second round, then player 2 makes an offer. If player 1 accepts, then the game ends according to the offer made by player 2. If player 1 rejects, the game ends with both players getting their outside options. Denote :5,- E (l), 1] as player 3-15 discount factor- Find the subgame perfect equilibrium outcome of this game. [ID] {b} Suppose a person {the seller} is trying to sell a good to another person (the buyer}. It is known to both of them that the good is worth 1000 to the seller and 1200 to the buyer. The two engage in an innite-horizon alternating bargaining process with the seller making the rst offer. Let 5 be the common discount factor of the two players. i. What is the surplus value over which the two players are bargaining? Use the results of the innite-horizon bargaining model derived in class to calculate the selier's share of that surplus. Hence, write down the price, w a function of d, that the Seller demands in the rst round of bargaining? Will the buyer accept? (T) ii. Let t be the time period that elapses betwem each round of bargaining. Assume liming. 6 = 1; in as the time difference between two olfers approach zero, the discount rate approaches 1. Using the answer to part [i] of (b) of this question, find the selling price as t > i}. (3) Question 7. Let 0, -T = 0,2 (c) ) = ti (d) ) =1tiQuestion 5. Solve the following system using Laplace transforms: = 20 -y+1 dt = 3x - 2y - 1 r(0) = 0, y(0) =0\"Orgakola,\" an allnatural drink synthesized from the extract pm unusual kola nuts, is produced and consumed only in the country of Puglonia. The market for orgakola initially has the following characteristics: 1. The market has two phases, winter and summer, and each mufor 6 months of the year. There is no government policy toward the market. There are no externalities from this product. The industry is competitive, and the same upward-sloping market supply curve applies in each of the two halves of the year. Firms in the industry produce and immediately sell the product in each halfyear, as shown by the supply curve for each half year. (The attached graphs show this market supply curve and the two halves of the year.) The market demand curve is downward-sloping in each halfyear, and market demand varies between the two halves of the year. Also, when people buy orgakola, they consume it on the same day that they buy it. The market price during the winter is $12 per liter, and the market price during the summer is $18 per liter. There is no general growth in the marketeach year has the same fundamental characteristics as the year before. [Inyom'answerstoquestionsAandB ofthisPaoftheexmyoumayusethegraphsonthe attached page, adding any lines, curves, or labels that you need. You may also draw your own half-year-phase graphsthese should be essentially the same as those shown on the attached page-l [In your answers to the questions in this Part, you can assume, if you need to, that the (short- term) interest rate is so low that you can ignore it] A. Show graphically and explain how the market works, showing the situations in each of the winter phase and the summer phase. What is the total surplus created by the market over a one-year period
