求解几道关于 decision making 的题目（急）

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<p></p><p>1.Mr. F. Slob (risk neutral) is thinking of joining a gym. He does not know whether he will have the resolve to frequent the gym once he has paid the membership fee. He could (i) do nothing, (ii) join now for a year and pay £400 membership fee, or (iii) opt for a £50 one month trial membership and decide at the end of the month whether to join for the rest of the year for an additional £400. If he turns out to like the gym, which happens with probability p, his benefit from membership is £800. </p><p>(a) 1.Draw a decision tree and find the optimal decision for all p </p><p>(b) Graph the EVPI as a function of p.</p><p>      </p><p>2.Toby is indifferent between $7 for sure and a lottery with a 50% chance of payoff<br/>zero and a 50% chance of payoff $20.<br/>(a) Show that this is consistent with Toby’s utility of money function U(x)=1-ax<br/>where a=0.93807.<br/>(b) Show that Toby prefers $1 for sure to a lottery with a chance p of payoff Z and<br/>1-p of payoff zero, for any positive Z, if p<0.06. </p>

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关键词：Decision Making makin Maki CISI additional membership nothing benefit whether

这两个题都和风险无关，和VNM就无关。

你只要计算几个选择带来的效用高低就好了。

我英文不大好，嘿嘿。

唔~您可不可以说得具体些哈，我还是不太理解

以下是引用我爱金融在2008-10-5 15:49:00的发言：

1.Mr. F. Slob (risk neutral) is thinking of joining a gym. He does not know whether he will have the resolve to frequent the gym once he has paid the membership fee. He could (i) do nothing, (ii) join now for a year and pay £400 membership fee, or (iii) opt for a £50 one month trial membership and decide at the end of the month whether to join for the rest of the year for an additional £400. If he turns out to like the gym, which happens with probability p, his benefit from membership is £800.

(a) 1.Draw a decision tree and find the optimal decision for all p

(b) Graph the EVPI as a function of p.（EVPI是什么？）

2.Toby is indifferent between $7 for sure and a lottery with a 50% chance of payoff
zero and a 50% chance of payoff $20.
(a) Show that this is consistent with Toby’s utility of money function U(x)=1-ax
where a=0.93807.
(b) Show that Toby prefers $1 for sure to a lottery with a chance p of payoff Z and
1-p of payoff zero, for any positive Z, if p<0.06.

关键这两个题目都不好写。

第一个题目，根据题意，建立方程

[p×（800-400）+（1-p）×（-400）]=0

p×(800-450)+(1-p)×（-50）=[p×（800-400）+（1-p）×（-400）]

然后算出两个p，就是变换选择的节点了。

很显然第一个是0.5，第二个是0.875

第二个题目的思路类似，你先试试看吧，如果不行，就翻译成中文，我才敢做。

呵呵，看球去。

老师是海归，作业也是英文的

额~这不是我们这次的微观作业题么~一模一样，难道我们是同学？~