Chapter 3: Discussion Questions and Problems
1. Differentiate the following terms/concepts:
a. Lottery and insurance
A lottery is a prospect with a low probability of a high payoff. Many people buy lottery tickets, even with negative expected values. The same people buy insurance to protect themlves from risk. Normally, insurance is a hedge against a low-probability large loss. The choices are inconsistent with traditional expected utility framework but can be explained by prospect theory.
b. Segregation and integration
Integration occurs when positions are lumped together, while gregation occurs when situations are viewed one at a time.once的用法
c. Risk aversion and loss aversion
A person who is risk aver prefers the expected value of a prospect to the prospect itlf, whereas for a person who is loss aver, loss loom larger than gains.
d. Weighting function and event probability no more
Event probability is simply the subjective view on how likely an event is. The weighting function is associated with the probability of an outcome, but is not strictly the same as the probability as in expected utility theory.
2. According to prospect theory, which is preferred?
a. Prospect A or B?
Decision (i). Choo between:
A(0.80, $50, $0)and B(0.40, $100, $0)
Prospect A is preferred due to risk aversion for gains. While both have the same expected change in wealth, A has less risk.广州职称英语成绩查询
b. Prospect C or D?
Decision (ii). Choo between:
C(0.00002, $500,000, $0) and D(0.00001, $1,000,000, $0)
Prospect D, with more risk, is preferred due to the risk eking that occurs when there are very low probabilities of positive payoffs.
c. Are the choices consistent with expected utility theory? Why or why not?
Violation of EU theory becau preferences are inconsistent. The same sort of Allais paradox proof from chapter 1 can be ud. It is also necessary to make the assumption of preference homogeneity, which means that if D is preferred to C, it will also be true that D* is preferred to C* where the are:
C*:(0.00002, $50, $0) and D*: (0.00001, $100, $0)
3. Consider a person with the following value function under prospect theory:
v(w) = w.5八年级下册英语 when w > 0
= -2(-w) .5 when w < 0
a. Is this individual loss-aver? Explain.efix
This person is loss aver. Loss are felt twice as much as gains of equal magnitude.
visin
b. Assume that this individual weights values by probabilities, instead of using a prospect theory weighting function. Which of the following prospects would be preferred?
P1(.8, 1000, -800)
P2(.7, 1200, -600)
tovP3(.5, 2000, -1000)
We calculate the value of each prospect:
V(P1) = .8(31.62)+.2(-2)(28.27)= 13.982
V(P2) = .7(34.64)+.3(-2)(24.49)= 9.55
V(P3) = .5(44.72)+.5(-2)(31.62)= 9.265
Therefore prospect P1 is preferred.
4. Now consider a person with the following value function under prospect theory:儿童节快乐的英文
higher erik gronwall v(z) = z.8 when z ≥ 0
= -3(-z).8 when z < 0
This individual has the following weighting function:
同桌教育where we t =.65.
a. Which of the following prospects would he choo?
PA(.001, -5000)
PB(-5)
Compare the value of each prospect:
V(PA) = .983(0) + (-3)(910.28)(.011) = -30.15 (note u of weights)
V(PB) = 3 * 1 * -3.62 = -10.87
Therefore you would prefer B.
b. Repeat the calculation but using probabilities instead of weights. What
