problem set 1

Political Economy of Institutions and

Development:14.773

Problem Set1

Due date:February,29,2008.

Question1

1.Consider the example of a three-person three-policy society with pref-

erences

1a b c

2b c a

3c b a

Voting is dynamic:…rst,there is a vote between a and b.Then,the winner goes against c,and the winner of this contest is the social choice.Find the subgame perfect Nash equilibrium voting strategy pro…les in this two-stage game in“weakly undominated”(recall that each player’s strategy has to specify how they will vote in the…rst round,and how they will vote in the second round as a function of the outcome the…rst round).[Hint:for“weakly undominated”strategies,…rst eliminate weakly dominated strategies in the last round,and then eliminate whatever is weakly dominated in the previous round,etc.].

2.Suppose a generalization whereby there are…nite number of policies, Q=f q1;q2;:::;q N g and M agents(which you can take to be an odd number for simplicity).Voting takes N 1stages.In the…rst stage, there is a vote between q1and q2.In the second stage,there is a vote between the winner of the…rst stage and q3,until we have a…nal vote against q N.The winner of the…nal vote is the policy choice of the society.Prove that if preferences of all agents are single peaked(with

a unique bliss point for each),then the unique subgame perfect Nash

equilibrium in“weakly undominated”implements the bliss point of the median voter.

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3.[For Bonus Points]Why is“weakly undominated”in quotation marks?

[Hint:can you construct other equilibria in parts1and2,when you simply focus on weakly undominated strategies(that is,without doing the sequential elimination described in the Hint of part1)?].

Question2

Consider party competition in a society consisting of a continuum1of agents.The policy space is the[0;1]interval and assume that preferences of all agents are single peaked and political bliss points are uniformly distrib-uted over this interval.

1.To start with,suppose that there are two parties,A and B.They

both would like to maximize the probability of coming to power.The game involves both parties simultaneously announcing q A2[0;1]and q B2[0;1],and then voters voting for one of the two parties.The platform of the party with most votes gets implemented.Determine the equilibrium of this game.How would the result be di¤erent if the parties maximized their vote share rather than the probability of coming to power?

2.Now assume that there are three parties,simultaneously announcing

their policies q A2[0;1],q B2[0;1],and q C2[0;1],and the platform of the party with most votes is implemented.Assume that parties maximize the probability of coming to power.Characterize all pure strategy equilibria.

3.Now assume that the three parties maximize their vote shares.Prove

that there exists no pure strategy equilibrium.Characterize the mixed strategy equilibrium(Hint:assume the same symmetric probability distribution for two parties,and make sure that given these distribu-tions,the third party is indi¤erent over all policies in the support of the distribution).

Question3

Consider the following one-period economy populated by a mass1of agents.A fraction of these agents are capitalists,each owning capital k. The remainder have only human capital,with human capital distribution F(h).Output is produced in competitive markets,with aggregate produc-tion function

Y=K1 H ;

2

where uppercase letters denote total supplies.Assume that factor markets are competitive and denote the market clearing rental price of capital by r and that of human capital by w.

1.Suppose that agents vote over a linear income tax, .Because of tax

distortions,total tax revenue is

T ax=( v( )) rk+(1 )w Z hdF(h)

where v( )is strictly increasing and convex,with v(0)=v0(0)=0 and v0(1)=1(why are these conditions useful?).Tax revenues are redistributed lump sum.Find the ideal tax rate for each agent.Find conditions under which preferences are single peaked,and determine the equilibrium tax rate.How does the equilibrium tax rate change when k increases?How does it change when increases?Explain.

2.Suppose now that agents vote over capital and labor income taxes,

k and h,with corresponding costs v( k)and v( h),so that tax revenues are

T ax=( k v( k)) rk+( h v( h))(1 )w Z hdF(h)

Determine ideal tax rates for each agent.Suppose that <1=2.

Does a voting equilibrium exist?Explain.How does it change when increases?Explain why this would be di¤erent from the case with only one tax instrument?

3.In this model with two taxes,now suppose that agents…rst vote over

the capital income tax,and then taking the capital income tax as given,they vote on the labor income tax.Does a voting equilibrium exist?Explain.If an equilibrium exists,how does the equilibrium tax rate change when k increases?How does it change when increases?

Question4

A society is a two party democracy with population normalized to1,with political parties R and D competing to maximize their vote share.Parties compete by proposing a tax rate with proceeds distributed lump sum to each member of society.Taxing income introduces distortions,so the tax revenue,distributed lump-sum,is( v( )) y,where y is average income

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in society and v(0)=v0(0)=0and v0(1)=1,and the government budget constraint is

T ( v( )) y

The society is strati…ed into n groups.The size of each group varies, but members of the same group have the same income,denoted by y j,but di¤ering political ideology.Let the political leaning towards party R of individual i in group j be i j and the size of group j be j,with P n j=1 j=1 and naturally P n j=1 j y j= y.Assume that i j has a symmetric distribution 1j F(x)with j>0:

Assume that individuals of the society all share a common utility func-tion

U i j(c i; i j)=c i+[ i j+ ]I R

where I R is an indicator for party R coming to power,and is a random popularity measure for party R,with distribution G( ).

1.First ignore the ideological leanings of each group and the relative

popularity measure(i.e., i j= =0).Find the equilibrium in the party competition game and the tax rate announced by the two parties.

Does a pure strategy equilibrium always exist?

2.Now characterize the equilibrium with the ideological leanings.Does

a pure strategy equilibrium always exist?

3.Now assume the parties can o¤er group-speci…c transfers(instead of

the lump sum redistribution)denoted by!j 0,so the government budget constraint thus becomes

n

X j=1 j!j ( v( )) y

Show,using an example,that there may exist no pure strategy equi-librium for the game when is known in advance to be0.Determine conditions for an equilibrium to exist when is random with distri-bution G,and characterize such an equilibrium.Explain why a pure strategy equilibrium is more likely to exist when is random?Will the two parties necessarily o¤er the same policy platform?

4.Now fully characterize the equilibrium in this probablilistic voting model assuming that i j is uniform over h 1j; 1j i for all j and is uniform over 1; 1 .4

Question5

Consider a society consisting of r rich agents, m> r middle-class agents and p> m+ r poor agents.All individuals are in…nitely lived in discrete time and maximize the net present discounted value of their lifetime income with discount factor 2(0;1).There are three political states: oligarchy(O),in which the rich agents are in power,limited franchise(L) in which the rich and the middle class vote,and full democracy in which all individuals are enfranchised(D).The society starts with oligarchy.

The political game is as follows:in each period,the median voter,of the prevailing political regime,decides a policy 2T R,and also what the political regime should be tomorrow(from the set f O;L;D g).Each agent’s income depends directly on the regime(for example,because dif-ferent economic relationships are possible within di¤erent regimes),and on the policy .In particular,let y i(S; )be the income of individual of class i2f r;m;p g in political state S2f O;L;D g when the policy is .Assume that the following are uniquely de…ned:

r arg max 2T y r(O; )

m arg max 2T y m(L; )

p arg max 2T y p(D; ):

Individuals do not take any other action than the political actions described above.

1.De…ne a Markov Perfect Equilibrium(MPE)of this dynamic game.

2.Show that when y r(O; r)>max f y r(L; m);y r(D; p)g,the unique

MPE involves the society remaining in oligarchy forever with policy r.Explain the intuition for this result.

3.Suppose that y r(O; r)

Show that in this case the unique MPE involves the society immedi-ately switching to limited franchise and remaining there forever with policy m.Interpret this result.

4.Suppose that y r(D; p)

y m(L; m)and that y p(D; p)>max f y p(O; r);y p(L; m)g.Show that there exists such that when < ,the unique MPE in-volves the society becoming a limited franchise in the…rst period, then democracy in the following period,and remaining in democracy

5

with policy p thereafter.When > ,then the unique MPE in-volves a society remaining in oligarchy forever with policy r.Explain why limited franchise cannot persist at the equilibrium regime in this case.Why is a higher discount factor making democracy less likely?

6

Practice Problem Set-1

Practice Problem Set – 1 ( The following problems are from Corporate Finance by Ross, Westerfield, and Jaffe – Tenth edition, McGraw-Hill / Irwin – ISBN 978-0-07-803477-0 ) 1.Audrey Sanborn has just arranged to purchase a $ 550,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 6.1 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8. There were no other transaction costs or finance charges. How much will Audrey’s balloon payment be in eight years ? 2.Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $ 65,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 10 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today ? 3. A 15-year annuity pays $ 1,500 per month, and payments are made at the end of each month. If the interest rate is 12 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity ? 4.You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $ 45,000 per year per child, payable at the beginning of each school year. The annual interest rate is 7.5 percent. How much money must you deposit in an account each year to fund your children’s education ? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college. 5. An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: the purchaser ( say, the parent ) makes the following six payments to the insurance company: Birthday First Second Third Fourth Fifth Sixth Deposit ($) 500 600 700 800 900 1,000 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $ 275,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying ?

读音规则

德语读音规则 1.元音在下列情况下读长音： a)元音字母之后有长音符合h时。（注意：h不发音）如：Kuh, geht. b)双元音aa, ee, oo, ie。如：Paar, Tee, Boot, Dieb. c)元音后只有一个辅音。如：Tag, gut. d)元音在一个词的末尾。如：du, da. e)双音节的词，两个元音中间只有一个辅音时，元音为长音。如： Gotik, Kuba, Name. 2.元音在下列情况下读短语： a)在双辅音前面。如：Bett, Gott. b)在两个或两个以上辅音前。如：Takt, gibt. 3.浊辅音清化 a)在一个单词中，清浊辅音之间有语音的同化现象，这种同化现 象是指德语中浊辅音的清音化。浊辅音b, d, g 读成相应的清辅 音p, t, k 。 ①当浊辅音位于词尾时，浊辅音要清化，发清辅音。 Dieb Hieb Tod Mund Tag Teig ②在词干中浊辅音位于清辅音之前，浊辅音发清辅音 Obst Abt 但是，当词形变化而后面加上元音时，读浊音。如：Diebe, Tage, Hunde

b)辅音s 的发音 ①当s 位于元音之前并和这一元音构成一个音节时，s 发浊音。 So satt sein Sinn Sonne Sohn Suppe Dose ②当s 位于词尾时，或其后无元音，或s重复时，发清音。 bis Bus Post Tast Tasse Busse ③? 是s的特色形式，永远发清辅音 Ma ? So ?e Stra ?e 4.关于ch 的读音规则 a)当ch在元音a o u au 后面时，它发，德语称作Ach-Laut machen Loch Buch auch rauchen flach Tochter acht b)当ch在a o u au 以外的元音或辅音后面时，它发，德语称 作ich-Laut。 euch ich echt leicht frech Milch durch Pech

发音规律

规律概述 英语当中音与音变化是非常的有规律的。这些规律也不是大家想象的那么复杂，大家在掌握了这些规律之后，会对听力和口语当中音与音的变化有个清晰地把握，听力和口语会有长足的进步。我在下文中会详细地提到这些规律。但是这些毕竟是文字上的东西，真正的规律的体会是需要大量的听力经验作保证的。大量的听力经验如何取得？哈哈……听写是提高听力的唯一途径。 语音语调问题的来源 中国学生的语音普遍很好，对单音节词的把握也比较到位，归根结底有两个原因：1.无论是单个音标的发音还是单音节词都是比较简单的发音过程，简单的东西大家容易掌握。 2.可能跟我们的母语有关系，汉语拼音由声母和韵母两个部分构成，我们可以大致的把声母比作英文中的辅音，而韵母就相当于元音。这样的话我们在母语中拼读的一个一个的汉字就相当于英文中的单音节词，这样的发音比较符合我们的习惯。中国学生的问题在于中文中并没有双音节词或者多音节词，换句话说就是中文当中的所有汉字的发音都是由一个辅音和一个元音构成的单音节词。而英文不是这样的，它不仅仅只有单音节词，还有双音节，三音节，四音节以及四音节以上的词，正是有了这些多音节的组合，于是英文中产生了一个中国学生最头疼的问题——重音。如果把多音节词简单的看作是若干个单音节的叠加那就大错特错了。这也是导致中国学生中式英语发音的根源所在，很多中国学生在说英语的时候不注意重音，没有重音甚至读错重音。这样的英文就会显得很诡异，英文是强调连贯性和节奏的语言。这就是中英文的差异。举个例子：现在热播的NBA球星麦蒂为阿迪达斯拍摄的无兄弟不篮球的广告中，麦蒂最后用中文数123的时候大家有没有仔细听？麦蒂是土生土长的美国人，所以他在说中文的时候会带有美语的节奏，大家仔细听会发现麦蒂说的123重读程度是不一样的，而且他会把最重的音落在最后一个音节上，也就是3上，而我们中国人不会那样说，在大多数情况下我们会把重音平分到三个音节上，读起来会有一种直线的感觉，大家可以自己试试看。用中文的节奏说123是正宗的中文，用麦蒂的节奏说one two three是纯正的美语。但是麦蒂用自己的节奏说123就会显得很诡异，试想一下我们用中文的节奏说one two three 是不是同样也很诡异呀 再举个比较猥琐的例子吧，也是最近热播的广告，“我们也用妇炎洁”大家一定对这句话记忆犹新吧。虽然此广告被评为国内十大恶心广告之一，但是还是有值得我们学习的地方，那就是语音语调。哈哈^_^ 规律总结 一、连读

读音规则

巧记读音规则中学课本中所出现的读音规则、一些单词的特殊读音等归纳如下：一、元音字母读音规则1．元音字母a在重读开音节中读/ei/例如make，name等；a在重读闭音节中读/?/，例如map，that等。其他主要情况有如下几种：（1）在非重读相对开音节中，a的发音： （2）a的后面是ss，st，sk，sp，th，f，n时，则读/a:/。例：class，pass，task，grasp，chance，plant，cast，after，path，但entrance中的a发/+/音。（3）any，many，ate中的a发/e/音。a在闭音节中，前面是辅音/w/时读作/￠/，例：want，warm，warn．（4）ar常读/a:/，例：yard，carpet，garment，farm；但在辅音/w/之后常读作/￠:/，例：war，warm，warn． （6）字母组合are常读/ε?/音，例如：bare，hare，care，glare，dare。字母组合al+辅音字母时，al常读/￠:l/，但在shall中al读/$/；在half，calm中发/a:/音。2．元音字母e在重读开音节中，读/ i:/，例：we，be，these，e在重读闭音节中读/e/，例：help，member，then，beg；但在arithmetic中，e发/+/音，元音字母e的字母组合读音： （4）eer常读/i?/，例：deer，cheer，pioneer，engineer，volunteer（志愿者）。（5）字母组合ex的读音规则：a．以字母组合ex开头的词，若ex后接一个元音字母且重音不落在第一个音节上，则ex的发音为/igz/。例如：exact，exam，example，exist。

problem_set_2

7.36/7.91/BE.490 家庭作业 2 上交时间：3月11号下午 1:00 注意：请查阅课程网站获取如何提交程序设计方面问题的电子版。另外，在本次作业结尾有一些关于编程方面的有用的提示。 1．古基因组学 I ——BLAST检索核酸序列 你的实验室已经找到一种从恐龙化石中提取出DNA序列的新方法，现在为了研究恐龙的进化史和鸟类的起源问题，你们从翼龙的化石中提取出了DNA序列。 该序列保存在dino1.fa文件中。 a. 在NR数据库中使用BLASTN进行检索，在使用缺省参数设置时所得到的检索结果 的第一条序列是什么？它看上去正确吗？为什么？ b. 将错配的罚分从缺省值（-3）改成-1，再检索一次，结果的第一条序列是什么？结 果中的E-value值是多少？跟a的结果相比检索质量上是否有不同？降低错配罚分 的值是否得到了你期望的结果？ c. 如何使用BLASTX检索？使用BLASTX检索结果的第一条序列是什么？结果中的 E-value值和bit得分是多少？它看上去是正确的吗？该生物属于哪一类？它能解释 翼龙的进化问题吗？ d. 试解释为什么BLASTN和BLASTX的结果差异很大。 2．古基因组学 II——BLAST用于基因内含子的影响 你得到了一条新的翼龙的序列，保存在dino2.fa中，你尝试使用BLASTN和BLASTX在NR数据库及蛋白质数据库中检索，但未得到相关结果（请尝试一次确认一下）。由于该序列来自翼龙基因组的富含基因区，因此你怀疑也许是序列中包含了一段未知基因使得BLAST无法正确匹配，为了验证该可能性，你决定对翼龙序列的模体结合位点进行研究，看是否能够提取出dino2.fa序列中的基因外显子。在进行了多次检索后，你找到了56个翼龙基因组DNA片段的BLASTX结果及对应的已知蛋白质序列，同时推断这些结果中很可能包含外显子和结合位点，由于BLASTX的结果经常无法准确的对应外显子的边界，（例如，因为在靠近结合区氨基酸的改变造成序列的删节、在结合位点/内含子的转录错误导致序列延长）你建立了一个数据库，大约包含BLASTX检索结果的从前往后数的前25个碱基，命名为“3primesplicesites.txt”（为的是找到3’的结合位点模体），另一数据集包括BLASTX检索结果的从后往前数的25个碱基，命名为“5primesplicesites.txt”（为的是找到5’的结合位点模体）。 a. 使用以上2个数据集运行MEME（https://www.wendangku.net/doc/704516663.html,/meme/website/meme.html）， 找到56个序列中的共同模体作为恐龙3’和5’的结合位点，你找到了哪些模体？使 用如下所示的单字符编码列出相同的模体： 注意：当使用MEME进行“多级相似序列”输出时将会出现问题，第四条核苷序列不会在模体的指定位置输出。因此，检查“Simplified pos.-specific probability matrix”或者“Information content”图表以确定模体的任意位置都包含所有的4个核苷。 b. 编写python程序读入两条相似序列，找到在“dino2.fa”序列中推断的内含子，并输 出预测结合的mRNA。程序应从命令行接收2个参数，即文件名，其一为包含2条 相似序列的文件，每条序列占一行（分别是3’和5’结合位点的相似序列），每条序

读音规则

前元音小结： 英语中有四个前元音，即：[ i: ] [ i ] [ e ] [ ? ] 发前元音时必须注意： 1) 舌尖要抵住下齿。 2) 舌前部向硬颚部分抬起。 3) 双唇不要收圆，发[ i: ] [ i ] [ e ] 时双唇平展，发[ ? ]时口形要张大，扁唇。 4) 唇形舌位保持不变，否则就要发成双元音。 后元音小结: 英语中一共由六个后元音, 发后元音时必须注意: 1)舌尖不触下齿, 舌身后缩, 舌后部向软颚部分抬起。 2)摩擦音小结: 英语中有十个摩擦音即: [ f ] [ v ][θ][e] [?] [3][ s ] [ z ] [ h ][ r ]发摩擦音时必须注意： 1) 口腔通道不完全阻塞,留有窄小空隙, 气流从中泄出时摩擦或震动成音。 2) 摩擦音可以延长而发音器官位置不变。 鼻辅音小结: 英语中一共由三个鼻辅音，即: [ m ] [ n ] [ ]，发鼻辅音时必须注意： 1) 软颚下垂，口腔通道完全阻塞，气流从鼻腔泄出。 2) 有声带震动，都是浊辅音。 3) 鼻辅音在词末时，发音要略微延长。 元音字母a, e, i, o, u在重读音节中的一般读音规 a e i o u 重读开音节：[ ei ] [ i: ][ ai ] [ ?u ][ju:] [u:] 重读闭音节：[ ? ][ e ][ i ] [ ?][ ?] [ u ] 注意：除了符合读音规则的词以外，还有一些词是例外的，需要逐个记忆。 重读开音节：一个辅音加e结尾的单词, 元音字母a ,e ,i ,o ,u 经常发长音 如: c a ke th e me b i ke cl o se cons u me 重读闭音节：元音字母a ,e ,i ,o ,u 经常发短音 如: h a ve b e d s i t l o ve b u s 常见字母组合在单词中的读音：是由两个字母搭配而成的一种固定组合1. 两个辅音字母在一起，通常只发其中一个辅音字母的音。

[耶鲁大学开放课程：博弈论].Problem.Set.2

耶鲁大学公开课：博弈论 习题集2（第4-5讲内容） Ben Polak, Econ 159a/MGT522a. 由人人影视博弈论制作组Darrencui翻译 1.回顾罚球的案例：裁判判罚给参与人1一次点球的机会，参与人1即将执行判罚。她有三种射门路径：左路、中路、右路。参与人2是门将。他可以选择防守左路、中路或者右路。两名参与人的行为同时发出。收益（以达成目概率的十倍计算）如下： 2 (a). 对于每一个参与人来说，有哪个策略严格劣于另一个（纯）策略吗？ (b). 在对参与人1的策略存在何种信念下，参与人2会觉得策略m是最佳对策？在对参与人2的策略存在何种信念下，参与人1会觉得策略M是最佳对策？[提示：本题不需要绘制三维图像！] (c). 假设参与人2站在参与人1的立场上思考后发现，无论参与人1存在何种信念，她都会选择改信念下的最佳对策。在这种情况下，参与人2是否应该选择策略m呢？ (d). 这个博弈是否存在（纯策略）纳什均衡？ 2.回顾合伙人案例（Watson书中习题）：回顾一下我们在第四讲中提到的商业合伙人的案例。两名律师合伙开了一家律师事务所并且平分收益。每名律师都要各自打算一下自己要为事务所付出多少劳动。事务所的收入按照如下公式计算：，其中、分别表示律师1和律师2付出的劳动量。参数反映了两人的协同效果：一名律师付出越多的辛劳，合伙人就会获得越多的收益。假设并且。两名律师的收益分别是： 其中表示劳动的成本（注意：边际成本递增）。假设这家律师事务所没有其它的开销。在课堂上我们论证了，理性策略（即迭代剔除非最佳对策后剩余的策略）是

(a). 假设两名律师达成一致，决定两个人都付出一样多的劳动，并通过合同的形式规定了劳动量的指标。如果他们想要最大化净收益（即收益减去劳动成本），他们应该在合同中规定各自付出多大的劳动量呢？这与课堂上得出的理性策略的劳动量相比有什么不同？[提示：为了解题方便，可以暂时考虑b=0的特殊情况] (b). 假设第(a)题中的合同只对合伙人2有约束力，即合伙人2需要按照要求中的付出等量的劳动，而合伙人1可以任意在[0,4]的劳动量中自由选择。合伙人1会选择付出多少劳动呢？这与 和有什么不同吗？请给出简明的解释。 (c). 回到最开始的博弈状态，假设现在，即合伙人的辛勤劳动起到了反协同效果。求出这种情况下的最佳对策函数，并绘制相应的函数图像，找出这种情况下对应的理性策略。把它与(a)中的指标作比较。[提示：并不需要重做(a)的全部过程] 3. 纳什均衡与迭代剔除（Gibbons教科书上的习题）：请看下面的这个博弈： (a). 哪些策略不会被迭代剔除严格劣势策略的过程剔除？ (b). 找出此博弈的（纯策略）纳什均衡 (c). 请尽可能详尽地解释说明，通常情况下（并不要局限于此博弈），组成纳什均衡的策略是否无法被迭代剔除严格劣势策略的过程剔除？ 4. 分钱计划（Gibbons教科书中习题）：参与人1和参与人2因为如何分配10美元的问题争执不休。每个参与人都说出了一个自己预期金额，该金额在0到10之间且允许出现小数。两人需要同时做出选择。参与人的收益就是她分得的钱款。这个博弈有两条规则。无论按哪条规则来分钱，如果出现的情况，每人获得自己的预期金额，剩余的钱款被销毁。 (a).第一条规则是，如果，那么每个参与人都一无所获并且钱会被销毁。这种情况下的（纯策略）纳什均衡是什么？ (b).第二条规则是，如果，并且每个人的预期金额是不同的，那么预期金额最小的参与人分得等值的钱款而剩余的钱款归另一个参与人。如果，并且，那么每个人都分得5美元。这种情况下的（纯策略）纳什均衡是什么？ (c).假如我们为前两条规则增加一个限制条件，即预期金额必须是整数。这是否会改变前两条规则下的（纯策略）纳什均衡？

字母发音规则

1 元音: [i：] [i] [A] [e] [[：] [[] [a：] [Q] [R：] [R] [U：] [U] [ei] [ai] [aU] [EU] [Ri] [i[] [Z[] [UE] 1) [i:] 字母组合:ee ea e ie three tree green sheep meet beef see seek eat tea meat leave lead teacher team mean speak clean please he she me piece receive ceiling 2) [i] 发音字母i y e sit picture it is list six mix fix fit pig big build miss myth many twenty happy dictionary defect decide delicious 3) [] 发音字母a bag hand and ant happy hat map mad bad black back glad flag shall man 4) [e] 字母组合ea e a head bread pleasure elephant electric remember sell shell lesson better bed desk hotel yes many any 5) [ε:] 字母组合ir ur ear ur or girl shirt skirt thirty thirteen third bird turn burn murder nurse turtle Thursday burger learn earn earth heard term her nerd serve work worm work world 6) [ε] 字母组合er or ou ar o a e u teacher leader remember player speaker farmer powder doctor actor mayor author tractor delicious gracious pleasure familiar collar dollar together tomorrow today shallop lesson Washington control polite around account ago elephant manta banana Canada Japan china men listen famulus Saturday 7) [a:] 字母组合ar a car farm card arm garden fast class last glass plant aunt calm 8) [] 发音字母u o ou oo up supper lunch fun gun hunt cup bus come mother dose brother love above trouble rough flourish blood flood 9) []字母组合al or au our ar aw small wall talk tall hall ball call walk short more lord horse for forty sport door floor store

读音规律

音读字促音发音规则: （1）前一个汉字的读音以「つ」结尾，后一个汉字的读音是「は」行的假名，「つ」变成促音，「は」行的假名相应变成「ぱ」行。如： 立派：立（りつ）＋派（は）＝立派（りっぱ） （2）前一个汉字的读音以「つ」结尾，后一个汉字的读音是「か、さ、た」行的假名，「つ」变成促音。如： 括弧：括（かつ）＋弧（こ）＝括弧（かっこ） 雑誌：雑（ざつ）＋誌（し）＝雑誌（ざっし） 発達：発（はつ）＋達（たつ）＝発達（はったつ） （3）前一个汉字的读音以「く」结尾，后一个汉字的读音是「か」行的假名。楽器：樂（がく）＋器（き）＝楽器（がっき） 注：复合名词除外：太極拳（たいきょくけん）、洗濯機（せんたくき）、建設省（けんせつしょう）? 浊音发音规则: 一、音读汉字发音规则: 1、前一汉字以ん结尾，后一汉字发音的第一假名若是は行开头的变为ぱ行，也有少数变成ば行的。例如： 心（しん）＋配（はい）→心配（しんぱい） 神（しん＋秘（ひ）→神秘（しんぴ） 何（なん）＋分（ふん）→何分（なんぷん） 藍（らん）＋本（ほん）→藍本（らんぽん） 南（なん）＋北（ほく）→南北（なんぼく） 二、训读汉字发音规则 1、か?さ?た?は行，即送气音开头的单词，接在其他词后构成复合词时，发生浊音化。例如： 物（もの）＋語り（かたり）→物語（ものがたり） 鼻（はな）＋血（ち）→鼻血（はなぢ） 足（あし）＋取り（とり）→足取り（あしどり） 昔（むかし）＋話（はなし）→昔話（むかしばなし） 人（ひと）＋人（ひと）→人々（ひとびと） ※例外的情况： 1、但本身含浊音的训读词，不发生连浊。例如： 紙屑（かむくず）大風（おおかぜ） 2、动词与动词或动词与宾语的复合不发生连浊。例如： 読み書き（よみかき）飯炊き（めしたき）

读音规则

巧记读音规则 中学课本中所出现的读音规则、一些单词的特殊读音等归纳如下： 一、元音字母读音规则 1．元音字母a在重读开音节中读/ei/例如make，name等；a在重读闭音节中读/?/，例如map，that等。其他主要情况有如下几种： （1）在非重读相对开音节中，a的发音： （2）a的后面是ss，st，sk，sp，th，f，n时，则读/a:/。例：class，pass，task，grasp，chance，plant，cast，after，path，但entrance中的a发/+/音。 （3）any，many，ate中的a发/e/音。a在闭音节中，前面是辅音/w/时读作/￠/，例：want，warm，warn．（4）ar常读/a:/，例：yard，carpet，garment，farm；但在辅音/w/ 之后常读作/￠:/，例：war，warm，warn． （6）字母组合are常读/ε?/音，例如：bare，hare，care，glare，dare。字母组合al+辅音字母时，al常读/￠:l/，但在shall中al读/$/；在half，calm中发/a:/音。 2．元音字母e在重读开音节中，读/ i:/，例：we，be，these，e在重读闭音节中读/e/，例：help，member，then，beg；但在arithmetic中，e发/+/音，元音字母e的字母组合读音：

（4）eer常读/i?/，例：deer，cheer，pioneer，engineer，volunteer（志愿者）。（5）字母组合ex的读音规则：

a．以字母组合ex开头的词，若ex后接一个元音字母且重音不落在第一个音节上，则ex的发音为/igz/。例如：exact，exam，example，exist。b．以字母组合ex开头的词，若ex后接一个辅音字母，且重音不落在第一个音节上，则ex读/iks/。例：excuse，expect，exchange，except，experience，experi-ment，explain，expose，express，expression，expensive，extend，extraordinary。 c．以字母组合ex开头的词，无论ex后跟着什么字母，只要重音（包括次重音）落在第一个音节上，则ex的发音即为/eks/。例：exercise，expert（专家，能手），extra（额外的），exhibition。3．元音字母i在重读开音节中读/ai/，例如：nice，drive，quite，line，polite，apologize，wise。i在重读闭音节中读/i/，例如：arithmetic，benefit，habit，English，equip。（1）字母组合ie一般读/i：/，例：piece，field，thief，achieve；有时读/ai/，例：lie，die；但friend/frend/，review/ri'vju：/，quiet/kwai+t/例外。（2）字母i在climb，flight，fight，blind，kind，mind，find，frightful，design，sign，wild等含有igh，ign，ind，ild的词中，i发/ai/。（3）April，impossible中的i发/?/。（4）pencil，business，medicine中的i不发音。（5）在quiet，society，empire，entire，violin，diary，lion，wire，tire，giant，dialogue中元音字母i 的字母组合读音均为/ai/。 （6）字母组合ai在重读时一般发/ei/，但在captain，mountain，portrait，foun-tain中的ai发/i/，在curtain 中的ai不发音。 4．元音字母o在重读开音节中读/?u/。例：whole，home，rope，hope；在重读闭音节中，读/￠/，例：foreign，dollar，borrow，forehead，cost，tomorrow，common，province，model，modern，cough，forest，honour，proverb，probably，promise，beyond，modest，honest，stocking；但在improve中的o读/u：/。 （1）在post，most，clothes，both，host，progress，total，won't，soldier，gold，robot，poster，roll，control，scold，hotel等词中的o发/?u/音。（2）o 在n，m，v，th之前常读/)/，例：month，front，son，ton，none，tongue，wonder，dozen，among，above，comfort。 （3）在tomb中的o发/u：/。（4）字母组合oo在一般情况下读/u：/，例：shoot，loose，pool，moon，choose，balloon，smooth，cool，food，fool，school，tooth。但在k前，有时在t，d前，由它们构成的合成词、派生词中均发/u/，例：cook，good，foot，look，wood，stood，took。book在由room构成的合成词中也发/u/；但应注意例外，例：blood，flood中的oo读/)/。 （5）字母组合or在辅音/w/之后一般读/￠：/，例：word，worm，world，work，worth，worthy，worse，worst，worship。 （6）以字母o开头的词中o的读音：

Hk5120ProblemSet2-14L4_r1

The Hong Kong University of Science & Technology Department of Finance FINA 5120: Corporate Finance L4 Fall 2014 Dr. Ahron Rosenfeld Problem Set #2 Guidelines for the analysis: a.Please submit your answers electronically through LMES on or before 7pm on September 25, 2014. b.The submission file must be printer‐friendly. c.The use of Excel functions is strongly encourage d. d.The grade for this homework weighs 5% of the final grade in the cours e. e.The analysis should contain answers to the following questions: Question 1: The XYZ Corporation is considering the installation of a new conveyer system to replace the existing one. The new system has a purchase price of $15,000, useful life of 5 years, and no terminal salvage value. It would reduce annual labor costs by $5,000 per year, require the level of inventory to be higher by $2,000 but would leave all other annual cash flows (except taxes) unchanged. The existing system was purchased 3 years ago for $10,000 with an estimated life of 8 years for tax purposes and no salvage value. It could be sold now for $3,000 or used for the remaining 5 years and then sold for $2,000. Assume the firm uses straight line depreciation on all equipment. The tax rate on income is 40 percent. The appropriate discount rate is 10 percent. a.Show the change in the firm’s free cash flows for each of the next 5 years for the new system. Specify the timing of each item in your answer. b.Show the change in the firm’s free cash flows for each of the next 5 years for the old system. Specify the timing of each item in your answer. c.Would you recommend replacing the system? Why? Question 2: a.In the Ocean Carriers case, use the DCF method to determine if Ms. Linn should purchase the $39 million capesize? Assume that Ocean Carriers is a U.S. firm subject to 35% taxation. Ocean Carriers uses a 9% annual discount rate. b.What do you think of the company's policy of not operating ships over 15 years old? Agree/disagree, why?

汉语拼音规则[1]

汉语拼音学习规则 1、声调：一声平平左到右，二声就像上山坡，三声下坡又上坡，四声就像下山坡。 2、标调规则：ɑo e i u ü，标调时，按顺序，i u并排标在后， i上标调把点抹，轻声不标就空着。 3、拼写规律：j ｑｘ小淘气，从不和ü在一起，它们和ü来相拼，见面帽子就摘掉。小ü见大y，去掉两点还读ü。ü和n、l相拼，两点省不得。 4、两拼法：前音轻短，后音重，两音相连猛一碰。 5、三拼法：声轻介快韵母响，三间连读很顺当。 或：三拼音，要记牢，中间介音别丢掉。 如：ɑ，不可以和j、q、x组成音节，中间要加“i”， o，不可以和g、k、h组成音节，中间要加“u” 6、书写规则： 四线三格记心间，拼音字母住里边。 声调、圆点写上格，胳膊长了住上格。 尾巴长了住下格，其它部分在中格。 中格一定要饱满，上格、下格空一点儿。 书写规则记心间，拼音才能写规范。 7、总结 （1）ɑｏｅ，i u ü，标调多按此顺序；如果i u紧相连，标在后者头上去。 （2）拼写规则讲得细，任何声母不独立；zh ch sh r z c s，自成音节后加i。 （3）iou uei uen，别犹豫，单用头变y或w； （iou uei uen自成音节要用y w开头，如：you，wei，wen）（4）如果前面有声母，去掉o e合规矩。

（与其他声母合拼则省略中间的o，e，如：niu 牛） （5）i 母打头搞独立，i in ing前加大y； （当韵母i in ing自成音节前面须加y如：yi 衣） （6）其他所有复韵母，都把小i变大y。 （而其它i行韵母自成章节则i改为y，如：iɑ改为yɑ）（7）u母单打莫迟疑，前加大w就可以； （韵母u自成音节则须加w，如：wu） （8）u母为首独为户，要把小u变大的。 （u开头的韵母自成音节则将u改为w，如：uɑ改为wɑ）（9）凡带ü母要注意，独立去点前加y； （ü开头的韵母自成音节则加上y并省略两点） （10）ü和n l相拼不去点，去点只指j q x。 8、重要规则： （1）标调：见到ɑ母莫放过，没有ɑ母找o、e，i、u并列标在后，i上标调把点抹。 （2）i、in、ing前无声母，加个y母来弥补。（整体认读音节） （3）ü见j、q、x，两点定要抹，ü拼n和l，两点省不得。 （4）轻声音节不标调，er作儿化e不要。 （5）u前无声u改w（独u除外），ü前无声ü改yu。 （6）ɑo e作头易混淆，音节间加隔音号（'）。 （7）b、p、m、f四声母，只拼o来不拼e（m除外）。 9、复习要点及方法 （1）声母

problem set 2

1.3. Describe how, if at all, each of the following developments affects the breakeven and actual investment lines in our basic diagram for the Solow model: (a) The rate of depreciation falls. (b) The rate of technological progress rises. (c) The production function is Cobb–Douglas, f (k) = kα,and capital’s share,α, rises. (d) Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before. 1.4. Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time jump in the number of workers. (a) At the time of the jump, does output per unit of effective labor rise, fall, or stay the same? Why? (b) After the initial change (if any) in output per unit of effective labor when the new workers appear, is there any further change in output per unit of effective labor? If so, does it rise or fall? Why? (c) Once the economy has again reached a balanced growth path, is output per unit of effective labor higher, lower, or the same as it was before the new workers appeared? Why? 1.5. Suppose that the production function is Cobb–Douglas.

常见发音规则

1、在音标表里ear是[ir]或[er]learn [lэ:n]、heart [ha:t] 2、oo其常见的两种发音〔u〕和〔u:〕 好、脚、k前不发长〔u〕， 房间、正午、食物、凉发长〔u:〕，复合词-room中都读短〔u〕， 选择、扫帚、学校中读长〔u:〕，wood、动词过去式也读短〔u〕，不久、月亮、也（太）必读长〔u:〕。 注：1．good foot football look cook book中要发〔u〕 2．room noon afternoon food cool中发〔u:〕 3．bedroom classroom reading-room sitting-room meeting-room dining-room中发〔u〕 4．choose broom school中发〔u:〕 5．wood took stood understood中发〔u〕 6．soon moon too中发〔u:〕 3、ow发音一般为一般发/?u/（读ou）比如window，borrow，yellow,,tomorrow 等等很少发/au/，比如说cow奶牛 4、or 在词中一般念[?:] 或者[?] 如director [di'rekt?] door [d?:]，or [?:]，for [f?:]等 5、are 发/e?/ 比如care,dare,hare ere发/??/比如here,mere ire 发/a??/ 比如fire,hire,wire ore发/?:/比如more,score,before ure发/j??/比如pure,cure -re发/?/centre,fibre 注①are，ere，ire，ore很少出现在非重读音节中，ure在非重读音节中读/?/音，例如：picture，pleasure。 ②重读元音字母加r，再加非重读元字组时，重读元音字母应按-re音节拼读规则拼读，字母r读/r/音。例如：parent，zero，story，during，inspiring。 ③另外，某些常用词及多音节词经常出现长音短化现象。例如：orange，very，American，paragraph。 6、ai，ay发/e?/比如afraid,rain,wait,day,play air发/e?/ 比如air,hair,chair,pair,repair A l ①在l,k前发/?:/small,ball,talk,wall, all,talk, ②发/?:l/ 比如always, also,s alt, almost ③在f,m前/α:/half,calm au，aw 发/?:/ autumn,daughter,draw ea①发/i:/ 比如teach, easy,ch eap,pl ease②发/e/ 比如heavy,bread,sweater,weather③/e?/比如break,great ear①发/??/hear,d ar,near,clear,year②发/e?/比如bear,pear,wear,swear③/?:/ earth,learn, early ee发/i:/jeep,week,green,three eer 发/??/比如pioneer,deer,beer ei，ey①发/e?/比如eight,neighbor,they②发/i:/比如seize,key eu,ew①在j,l,r,s后发/ju:/比如new,few,newspaper②/u:/flew,brew,jewelry ie,ei发/i:/比如piece,field,receive