Reference no: EM131388050

Consider the model of Tversky and Kahneman (1991) developed in class. Suppose that each person’s wealth consists of three parts: mug (denoted as M), candy (denoted as C), and money (denoted as m). People take their initial endowments as their reference points. Therefore, if you are initially endowed with rM mugs, rC candies and rm dollars, then your reference point is r = (rM, rC, rm). Given this reference point, if your final payoff contains xM mugs, xC candies and xm dollars, then your utility is given by Ur=(rM,rC ,rm)(xM, xC, xm) = 3 · v(xM − rM) + 2 · v(xC − rC) + xm − rm where v(x) = x for x ≥ 0 and v(x) = 2x for x < 0. For all the questions below, assume that you are initially endowed with 2 mugs, 1 candy and $20 as the reference point. (1). What is your utility of owning a bundle with 1 mug, 2 candies and $20 as the final payoff? (2). Assume that you decide to sell one of the two mugs that you initially have. What is your selling price of the mug? (Hint: The selling price is the minimum price at which you are willing to given up one mug. In other words, you are indifferent between your endowment and owning only one mug but earning some extra money. So Ur=(2,1,20)(2, 1, 20) = Ur=(2,1,20)(1, 1, 20 + p)) (3). Assume that instead of selling the mugs, you want to buy a third mug. What is your buying price of the mug? (Hint: The buying price is the maximum price at which you are willing to pay for the additional mug. In other words, you are indifferent between your endowment and owning a third mug while sacrificing some money. So Ur=(2,1,20)(2, 1, 20) = Ur=(2,1,20)(3, 1, 20 − p)). (4). Assume that instead of trading the mugs, you decide to sell your endowment of the candy. Calculate your selling price of the candy. (Hint: Similar to the hint in part (2), you need to first find the indifference problem and then set up the corresponding equality.) (5). Assume that instead of trading the mugs, you decide to purchase a second candy. Calculate your buying price of the candy. (Hint: Similar to the hint in part (3), you need to first find the indifference problem and then set up the corresponding equality.)