a statistical-cost approach to unwrapping the phase of insar time series

A Simplicial Approach for DiscreteFixed Point Theorems(Extended Abstract)Xi Chen1and Xiaotie Deng2⋆1Department of Computer Science,Tsinghua Universityxichen00@2Department of Computer Science,City University of Hong Kongdeng@.hkAbstract.We present a new discretefixed point theorem based on anovel definition of direction-preserving maps over simplicial structures.We show that the result is more general and simpler than the two re-cent discretefixed point theorems by deriving both of them from ours.The simplicial approach applied in the development of the new theoremreveals a clear structural comparison with the classical approach for thecontinuous case.1IntroductionThere has recently been a sequence of works related tofixed point theorems in a discrete disguise,started with the seminal work of Iimura[12]which introduced a crucial concept of direction-preserving maps.Iimura,Murota and Tamura[13] corrected the proof of Iimura for the definition domains of the maps.With a different technique,Chen and Deng introduced another discretefixed point the-orem in order to achieve the optimal algorithmic bound forfinding a discrete fixed point for allfinite dimensions[1].In[14],Laan,Talman and Yang designed an iterative algorithm for the discrete zero point problem.Based on Sperner’s lemma which is fundamental for deriving Brouwer’sfixed point theorem,Friedl, Ivanyosy,Santha and Verhoeven defined the black-box Sperner problems.They √also obtained aon the simplicial structure in the study of the discrete version will help us gain a full and clear understanding of the mathematical structures and properties related to discretefixed point theorems.Furthermore,even for continuousfixed point theorems,discrete structural propositions are needed to derive them.Our study would provide a unified view of thefixed point theorem,both discrete and continuous,instead of treating them with ad hoc techniques.Our simplicial ap-proach unveils the mystery behind the recent results on discretefixed points and settles them under the same mathematical foundation as the classical continuous fixed point theorems.The discrete nature of thefixed point theorem has been noticed previously, mainly due to the proof techniques of Sperner’s lemma[15].The recent effort in direct formulation of the discrete version of thefixed point theorem would be especially useful in the complexity analysis of related problems.The recent work in characterizing the complexity of Nash Equilibria,by Daskalakis,Goldberg, Papadimitriou[8],Chen and Deng[2],Daskalakis and Papadimitriou[9],Chen and Deng[3],has been based on another innovative formulation of the2D(or 3D)discretefixed point problem,where afixed point is a collection of four[6] (or eight[8])corners of a unit square(or cube).It’s difficult to generalize such a formulation to high dimensional spaces,since a hypercube has an exponential number of corners,which is computationally infeasible.Instead,a simplicial de-finition has been necessary in extending those results to a non-approximability work obtained recently[9].Wefirst introduce notations and definitions with a review of previous works of Murota,Iimura and Tamura[13],as well as Chen and Deng[1].The simplicial model is then introduced in section3and the fundamental discretefixed point theorem is proved in section4.In section5,we present the discrete Brouwer’s fixed point theorem for simplicial direction-preserving maps,with the theorem of Murota,Iimura and Tamura[13]derived as a simple corollary.In Section6, we give an explicit explanation for the definition of bad cubes in[1]and show that,the theorem of Chen and Deng is a special case of the fundamentalfixed point theorem.Finally,we conclude in section7.2Preliminaries2.1Notations and DefinitionsInformally speaking,map F(or function f)is hypercubic direction-preserving on afinite set X⊂Z d if for every two neighboring points in X,their directions given by F(or f)are not opposite.The neighborhood relation considered here is defined by the infinity norm.Definition1(Hypercubic Direction-Preserving Maps)Let X be afinite subset of Z d.Map F from X to R d is said to be hypercubic direction-preserving on X if for every two points r1,r2∈X with||r1−r2||∞≤1,we have(F i(r1)−r1i)(F i(r2)−r2i)≥0,for all i:1≤i≤d.2Definition2(Hypercubic Direction-Preserving Functions)Let X be a finite subset of Z d.Function f from set X to{0,±e1,±e2...±e d−1,±e d}is said to be hypercubic direction-preserving if for every two points r1,r2∈X such that ||r1−r2||∞≤1,we have||f(r1)−f(r2)||∞≤1.Point r∈X is called afixed point of F(or f)if F(r)=r(or f(r)=0). 2.2The Fixed Point Theorem of Murota,Iimura and TamuraMurota,Iimura and Tamura proved in[13]that every hypercubic direction-pre-serving map from an integrally convex set X toX to denote the convex hull offinite set X⊂Z d.Definition3(Integrally Convex Sets)Finite set X⊂Z d is integrally con-vex if for all x∈X∩N(x)where N(x)={r∈Z d|||r−x||∞<1}.Theorem1([13])Let X be an integrally convex set in Z d,then every hyper-cubic direction-preserving map F from X to3Simplicial Direction-Preserving Maps and FunctionsIn this section,we introduce simplicial direction-preserving maps and functions based on simplicial structures.Let X be afinite set in R d.Here we only con-sider nondegenerate cases whereX such that for every S∈S,V S⊂X,where V S is the vertex set of simplex S.Given a simplicial decomposition S of X,we use F S to denote the set of (d−1)-simplices on the boundary ofX:F S={(d−1)-simplex S∈S|S⊂F and F is a facet ofX}.Definition8(Simplicial Direction-Preserving Maps)A simplicial direc-tion-preserving map is a triple M=(F,X,S).Here X is afinite set in R d and S is a simplicial decomposition of X.Map F from X to R d satisfies for every two points r1,r2∈X,if there exists a simplex S∈S such that r1,r2∈V S,then (F i(r1)−r1i)(F i(r2)−r2i)≥0,for all i:1≤i≤d.Definition9(Simplicial Direction-Preserving Functions)A triple G= (f,X,S)is said to be a simplicial direction-preserving function if X is afinite set in R d,S is a simplicial decomposition of X,and function f from set X to {0,±e1,...±e d}satisfies for every two points r1,r2∈X,if there exists S∈S such that r1,r2∈V S,then||f(r1)−f(r2)||∞≤1.In other words,for every two neighboring points in X,their directions given by map F(or function f)can’t be opposite.The only difference with the hy-percubic model is that the neighborhood relation is now defined by simplices in the simplicial decomposition S instead of unit d-cubes in Z d.4The Fundamental Discrete Fixed Point TheoremIn this section,we present the fundamental discretefixed point theorem which is both simple and powerful.Any simplicial direction-preserving function which satisfies the boundary condition of the theorem must have afixed point.Definition10(Bad Simplices)Let G=(f,X,S)be a simplicial direction-preserving function,where X⊂Z d.A t-simplex S∈S where0≤t≤d is said to be bad(relative to function G)if f(V S)={e1,e2,...e t+1},where V S is the vertex set of S.We use N G to denote the number of bad(d−1)-simplices in F S.4Lemma1For any simplicial direction-preserving function G=(f,X,S),if there exists nofixed point in X,then N G is even.Proof.Firstly,one can show that for every(d−1)-simplex S∈S,if S∈F S, then there exists exactly one d-simplex in S containing S.Otherwise,there are exactly two such ing this property,the parity of N G is same as the one of the following summation:d-simplex S d∈Sbad(d−1)-simplices in S d.As G is direction-preserving and has nofixed point,the number of bad(d−1)-simplices in S d is either0or2.Therefore,the summation above must be even.We now get the fundamental theorem as a simple corollary of Lemma1. Theorem3(The Fundamental Discrete Fixed Point Theorem)Let G=(f,X,S)be a simplicial direction-preserving function.If N G,i.e.the number of bad(d−1)-simplices on the boundary is odd,then G must have afixed point r∈X such that f(r)=0.5The Discrete Brouwer’s Fixed Point TheoremIn this section,the fundamental discretefixed point theorem will be employed to prove afixed point theorem concerning simplicial direction-preserving maps. It can be recognized as a discrete version of Brouwer’sfixed point theorem.It states that for any simplicial direction-preserving map from somefinite set to its convex hull,there must exist afixed point in the definition domain.We will also derive the theorem of Murota,Iimura and Tamura as a simple corollary.Actually,the one derived here is much stronger than theirs.5.1PreliminariesWe use e k to denote the k th unit vector of Z d where e k k=1and e k i=0for all i:1≤i=k≤d.Definition11For every(d−1)-simplex S∈F S,we let e S be the unit vector which is outgoing and perpendicular to S.For all r∈X if e S·(r−r S)>0for some r S∈S. Construction1(Extension of Simplicial Decomposition)Let X⊂R d be afinite set and S be a simplicial decomposition of X.For every point r/∈Given a simplicial direction-preserving map M=(F,X,S),we can convert it into a direction-preserving function G=(f,X,S)as follows.Construction2Given a simplicial direction-preserving map M=(F,X,S), we can build a simplicial direction-preserving function G=(f,X,S)as follows. For every r∈X,if F(r)=r,then f(r)=0.Otherwise,let i:1≤i≤d be the smallest integer such that F i(r)−r i=0,then f(r)=sign(F i(r)−r i)e i.5.2The Key LemmaLemma2Let M=(F,X,S)be a simplicial direction-preserving map where F is from X toX′where F′(r)=F((n+1)r) n+1.Let G′be the function constructed from map M′=(F′,X′,S′),then it is easy to check that N G=N G′.Therefore,we only need to prove the lemma for maps M=(F,X,S)with X⊂(−1,1)d.From now on,we always assume that X⊂(−1,1)d.If f has afixed point in set B X,then the lemma is proven.Otherwise,we extend(by applying Construction1for d times)G=(f,X,S)to be a new function G∗=(f∗,X∗,S∗)such that X⊂X∗,Lemma3guarantees the existence of G′.Lemma3For every triple G=(f,X,S)which satisfies all the conditions inDefinition12,there exists a triple G′=(f′,X′,S′)which is an extension of G along the k th coordinate.Proof.We only need to prove that there exists a simplicial decomposition S′ofX′satisfies S⊂S′.Actually,it can be constructed as follows.We list all the points in X′−X using the lexicographic order,add them into X one by one,and extend the original decomposition S step by step using the method described inDefinition1.Definition13G∗is said to be an extension of G if there exists a sequence G d+1...G2,G1such that G d+1=G,G∗=G1and G i is an extension of G i+1along the i th coordinate.The existence of G∗is guaranteed by Lemma3.Let G k=(f k,X k,S k).The following lemma is easy to check.Lemma4If r∈X k,r′∈[−1,1]d and r i=r′i for all1≤i<k,then r′∈X k.The following two corollaries can be derived from Lemma4.Corollary1X. Corollary2If v=e k−1or−e k−1is an outgoing vector at r∈X k,thenr+ǫv+di=kc i e i/∈X.If G is the function constructed from M using the method in Definition2,then any extension G∗of G is also simplicial direction-preserving.7Proof.We will use induction on k to prove that triple G k=(f k,X k,S k)is a simplicial direction-preserving function.The case for k=d+1is trivial.For case k≤d,if G k is not direction-preserving,then there must exist S∈S k−S k+1 and r1,r2∈V S such that f k(r1)and f k(r2)are opposite.As G k+1is direction-preserving,one of these two points belongs to X k+1,and the other is added into X k when G k+1is extended along the k th coordinate.Without loss of generality,we assume r1∈X k+1and r2k=1.As a result, f k(r2)=−e k and f k(r1)=+e k,as f k(r1)is opposite to f k(r2).The value of f k(r1)implies r1∈X and f(r1)=+e k.The way we construct G from map M guarantees F i(r1)=r1i for any1≤i<k and F k(r1)>ing Corollary2, we see that+e k is not an outgoing vector at r1∈X k+1,as F(r1)∈X k+1. Hence lemma5asserts that no pair(r2,S)where r2∈X k−X k+1and S∈S k−S k+1can satisfy that r2k=+1and r1,r2∈V S,which contradicts with our assumption in thefirst paragraph.Property1is a simple corollary of Lemma7.Lemma7For every triple G=(f,X,S)wherefinite set X⊂(−1,1)d,S is a simplicial decomposition of X and f is a direction function on X,if G∗= (f∗,X∗,S∗)is an extension of G,then N G∗is odd.Proof.We will use induction on d.The base case for d=1is trivial.For case d≥2,wefirst prove that every bad(d−1)-simplex S∈S∗on the boundary of [−1,1]d satisfies r d=−1for any r∈V S.Let S∈F S∗be such a simplex,then there exists r∈V S satisfies f∗(r)=+e d according to the definition of badness. Thus r is added into X when it is extended along the d th coordinate.We have r d=−1and−1<r i<1for any1≤i<d.This shows that S is covered by the hyperplane H which passes0[d→−1]and is perpendicular to+e d.Assume N is the number of bad(d−1)-simplices in H,then we only need to prove N is odd.Let X′=P(X)and X′′=P(H∩X∗)where projection P(r)=(r1,r2,...r d−1)∈R d−1,then S′and S′′are simplicial decompositions of X′and X′′respectively whereS′= P(S)S∈S∗and V S⊂X[d→−1] ,S′′= P(S)S∈S∗and S⊂H .Let f′be an arbitrary direction function on X′,then we extend it to be direc-tion function f′′on X′′as follows.For any r∈X′,f′′(r)=f′(r).Otherwise, f′′(r)=f∗((r1,r2,...r d−1,−1)).It’s easy to check that G′′=(f′′,X′′,S′′)is an extension of triple G′=(f′,X′,S′)in the(d−1)-dimensional space.Using arguments which are similar to those in the proof of Lemma1,the parity of N is same as the number of bad(d−2)-simplices on the boundary of8G′′.We know that the latter is odd according to the induction hypothesis,and Property1is proven.Property2.Let M=(F,X,S)be a simplicial direction-preserving map where F maps X toX, there must exist afixed point in X.Now we prove thefixed point theorem of Murota,Iimura and Tamura[13] as a direct corollary of Theorem4.Lemma8(Property of Integrally Convex Sets[13])For every integrally convex set X,there exists a simplicial decomposition S ofX,letting S x∈S be the smallest simplex containing x,then all of its vertices belong to N(x)={r∈Z d|||r−x||∞<1}.Let F be a hypercubic direction-preserving map from integrally convex set X⊂Z d todirection-preserving map from X toC a,b=X=∪P∈P P,and for every polytope P∈P, all of its vertices are drawn from X;2).For every two polytopes P1,P2∈P,if P1∩P2=∅,then P1∩P2is a face of both P1and P2.Definition16Let P be a convex t-polytope in R d and V P be its vertex set.The center point c P of polytope P is defined as c P= r∈V P(r/|V P|).Obviously,we have c P∈P and c P/∈V P.For example,let C⊂Z d be a t-cube centered at r∈Z d and perpendicular to T,then the center point c ofX into X and construct a simplicial decomposition S′for the new set X′. Details of the construction are described by the algorithm in Figure1. Every lattice set C a,b⊂R d has a natural convex subdivision P where P= {Fig.1.The Construction of S′and X′6.2Extension of Hypercubic Direction-Preserving FunctionsLet f be a hypercubic direction-preserving function on C a,b,we now extend it onto set D a,b as follows.For every r∈D a,b−C a,b,assume it is the center point of t-cube C⊂C a,b.If0∈f(C),then f(r)=0.Otherwise,let1≤t≤d be the largest integer such that f(C)∩{±e t}=∅,then f(r)=e t if e t∈f(C)and f(r)=−e t if−e t∈f(C).One can prove the following two properties.Property1Let f be a hypercubic direction-preserving function on C a,b⊂Z d, then G=(f,D a,b,S)is a simplicial direction-preserving function.Property2If the extended function G=(f,D a,b,S)has afixed point in D a,b, then the original function must have afixed point in C a,b.6.3The Nature of Bad CubesWe are ready to give an explicit explanation for the definition of bad cubes. Lemma9Let f be a hypercubic direction-preserving function on C a,b⊂Z d and G=(f,D a,b,S)be the extend function.For every t-cube C t in C a,b where 0≤t≤d−1,it is bad relative to f iffthe cardinality of the following set is odd:S C t= t-simplex S∈S is bad relative to G S⊂C t,then the way we build simplicial decomposition S implies that t-simplex S t⊂C t where S t−1is used to denote(t−1)-simplices in S.Firstly,we prove that,if t-cube C t⊂Z d is not bad,then|S C t|is even.If 0∈f(C t),then f(c)=0.As each t-simplex inC t,e k/∈f(V S),and thus,S C t=∅.Otherwise,we have f(C t)= {e1,...,e t+1},and thus f(c)=e t+1.Because C t is not bad,the number of bad11(t−1)-cubes on the boundary of C t is ing the induction hypothesis on t−1,a(t−1)-cube is bad iffthe number of bad(t−1)-simplices in it is odd. As a result,the number of bad(t−1)-simplices on the boundary of C t is even. Using the equation in thefirst paragraph,we know|S C t|is even too.On the other hand,we prove if C t is bad,then|S C t|is odd.Since f(C t)= {e1,...,e t+1},we have f(c)=e t+1.As the number of bad(t−1)-cubes on the boundary of C t is odd,the number of bad(t−1)-simplices on the boundary of C t is also odd,according to the induction hypothesis on case t−ing the equation in thefirst paragraph again,we know|S C t|is odd.We now get Lemma10as a direct corollary of Lemma9.Lemma10The parity of N B(the number of bad(d−1)-cubes on the boundary of C a,b)is same as the one of N G(the number of bad(d−1)-simplices on the boundary of D a,b).With Property1,2and Lemma10above,Chen and Deng’s theorem can be immediately derived from the fundamental discretefixed point theorem.7Concluding RemarksIn this paper,we generalize the concept of direction-preserving maps and char-acterize a new class of discrete maps over simplicial structures.The fundamental discretefixed point theorem is then proposed,which is based on the counting of bad(d−1)-simplices on the boundary.The power of this theorem is demon-strated in two ways.First,it is applied to prove the discrete Brouwer’sfixed point theorem which is much more general than the one of Murota,Iimura and Tamura.Second,we resolve the puzzle of bad cubes,and show that the bound-ary condition of Chen and Deng’s theorem is exactly equivalent to the one of the fundamental theorem.Our work would immediately imply the corresponding discrete concept of degree.It would be an especially interesting problem to study the case when the fixed point is defined in the recent model of a set of points.An immediate follow-up research direction is to understand other concepts and theorems related to degree.A clear understanding would definitely advance the state of art of the numerical computation of related problems,such as the case of discretefixed points versus approximatefixed points[1].References1.X.Chen and X.Deng.On Algorithms for Discrete and Approximate BrouwerFixed Points.In STOC2005,pages323–330.2.X.Chen and X.Deng.3-Nash is PPAD-complete.ECCC,TR05-134,2005.3.X.Chen and X.Deng.Settling the Complexity of Two-Player Nash-Equilibrium.FOCS,2006.124.X.Chen,X.Deng,and S-H puting Nash Equilibria:Approximationand Smoothed Complexity.FOCS,2006.5.X.Chen and ttice Embedding of Direction-Preserving CorrespondenceOver Integrally Convex Set.AAIM2006,2006,pp.53–63.6.X.Chen and X.Deng.On the Complexity of2D Discrete Fixed Point Problem.ICALP2006,pp.489–5007.P.Crescenzi and R.Silvestri.Sperner’s lemma and robust put.Complexity,7(2):163–173,1998.8. C.Daskalakis,P.W.Goldberg,and C.H.Papadimitriou.The Complexity of Com-puting a Nash Equilibrium.STOC,2005.9. C.Daskalakis and C.H.Papadimitriou.Three-player games are hard.ECCC,TR05-139.10.K.Friedl,G.Ivanyos,M.Santha,and F.Verhoeven.On the black-box complexityof Sperner’s Lemma.In FCT2005.11.M.D.Hirsch,C.H.Papadimitriou,and S.Vavasis.Exponential lower bounds forfinding Brouwerfixed plexity,5:379–416,1989.12.T.Iimura.A discretefixed point theorem and its applications.Journal of Mathe-matical Economics,39(7):725–742,2003.13.T.Iimura,K.Murota,and A.Tamura.Discrete Fixed Point Theorem Reconsid-ered.Journal of Mathematical Economics,to appear.an,D.Talman,and Z.Yang.Solving discrete zero point problems.TinbergenInstitute Discussion Papers,2004.15. E.Sperner.Neuer Beweis fur die Invarianz der Dimensionszahl und des Gebietes.16.G.M.Ziegler.Lectures on Polytopes.Springer-Verlag,New York,1982.13。

数据分析英语试题及答案一、选择题（每题2分，共10分）1. Which of the following is not a common data type in data analysis?A. NumericalB. CategoricalC. TextualD. Binary2. What is the process of transforming raw data into an understandable format called?A. Data cleaningB. Data transformationC. Data miningD. Data visualization3. In data analysis, what does the term "variance" refer to?A. The average of the data pointsB. The spread of the data points around the meanC. The sum of the data pointsD. The highest value in the data set4. Which statistical measure is used to determine the central tendency of a data set?A. ModeB. MedianC. MeanD. All of the above5. What is the purpose of using a correlation coefficient in data analysis?A. To measure the strength and direction of a linear relationship between two variablesB. To calculate the mean of the data pointsC. To identify outliers in the data setD. To predict future data points二、填空题（每题2分，共10分）6. The process of identifying and correcting (or removing) errors and inconsistencies in data is known as ________.7. A type of data that can be ordered or ranked is called________ data.8. The ________ is a statistical measure that shows the average of a data set.9. A ________ is a graphical representation of data that uses bars to show comparisons among categories.10. When two variables move in opposite directions, the correlation between them is ________.三、简答题（每题5分，共20分）11. Explain the difference between descriptive andinferential statistics.12. What is the significance of a p-value in hypothesis testing?13. Describe the concept of data normalization and its importance in data analysis.14. How can data visualization help in understanding complex data sets?四、计算题（每题10分，共20分）15. Given a data set with the following values: 10, 12, 15, 18, 20, calculate the mean and standard deviation.16. If a data analyst wants to compare the performance of two different marketing campaigns, what type of statistical test might they use and why?五、案例分析题（每题15分，共30分）17. A company wants to analyze the sales data of its products over the last year. What steps should the data analyst take to prepare the data for analysis?18. Discuss the ethical considerations a data analyst should keep in mind when handling sensitive customer data.答案：一、选择题1. D2. B3. B4. D5. A二、填空题6. Data cleaning7. Ordinal8. Mean9. Bar chart10. Negative三、简答题11. Descriptive statistics summarize and describe thefeatures of a data set, while inferential statistics make predictions or inferences about a population based on a sample.12. A p-value indicates the probability of observing the data, or something more extreme, if the null hypothesis is true. A small p-value suggests that the observed data is unlikely under the null hypothesis, leading to its rejection.13. Data normalization is the process of scaling data to a common scale. It is important because it allows formeaningful comparisons between variables and can improve the performance of certain algorithms.14. Data visualization can help in understanding complex data sets by providing a visual representation of the data, making it easier to identify patterns, trends, and outliers.四、计算题15. Mean = (10 + 12 + 15 + 18 + 20) / 5 = 14, Standard Deviation = √[(Σ(xi - mean)^2) / N] = √[(10 + 4 + 1 + 16 + 36) / 5] = √52 / 5 ≈ 3.816. A t-test or ANOVA might be used to compare the means ofthe two campaigns, as these tests can determine if there is a statistically significant difference between the groups.五、案例分析题17. The data analyst should first clean the data by removing any errors or inconsistencies. Then, they should transformthe data into a suitable format for analysis, such ascreating a time series for monthly sales. They might also normalize the data if necessary and perform exploratory data analysis to identify any patterns or trends.18. A data analyst should ensure the confidentiality andprivacy of customer data, comply with relevant data protection laws, and obtain consent where required. They should also be transparent about how the data will be used and take steps to prevent any potential misuse of the data.。

薪酬管理外文文献翻译The existence of an agency problem in a corporation due to the separation of ownership and control has been widely studied in literatures. This paper examines the effects of management compensation schemes on corporate investment decisions. This paper is significant because it helps to understand the relationship between them. This understandings allow the design of an optimal management compensation scheme to induce the manager to act towards the goals and best interests of the company. Grossman and Hart (1983) investigate the principal agency problem. Since the actions of the agent are unobservable and the first best course of actions can not be achieved, Grossman and Hart show that optimal management compensation scheme should be adopted to induce the manager to choose the second best course of actions. Besides management compensation schemes, other means to alleviate the agency problems are also explored. Fama and Jensen (1983) suggest two ways for reducing the agency problem: competitive market mechanisms and direct contractual provisions. Manne (1965) argues that a market mechanism such as the threat of a takeover provided by the market can be used for corporate control. "Ex-post settling up" by the managerial labour market can also discipline managers and induce them to pursue the interests of shareholders. Fama (1980) shows that if managerial labour markets function properly, and if the deviation of the firm's actual performancefrom stockholders' optimum is settled up in managers' compensation, then the agency cost will be fully borne by the agent (manager).The theoretical arguments of Jensen and Meckling (1976) and Haugen and Senbet (1981), and empirical evidence of Amihud andLev (1981), Walking and Long (1984), Agrawal and Mandelker (1985), andBenston (1985), among others, suggest that managers' holding of common stock and stock options have an important effect on managerial incentives. For example, Benston finds that changes in the value of managers' stock holdings are larger than their annual employment income. Agrawal and Mandelker find that executive security holdings have a role in reducing agency problems. This implies that the share holdings and stock options of the managers are likely to affect the corporate investment decisions. A typical management scheme consists of flat salary, bonus payment and stock options. However, the studies, so far, only provide links between the stock options and corporate investment decisions. There are few evidences that the compensation schemes may have impacts on thecorporate investment decisions. This paper aims to provide a theoretical framework to study the effects of management compensation schemes on the corporate investment decisions. Assuming that the compensation schemes consist of flat salary, bonus payment, and stock options, I first examine the effects of alternative compensation schemes on corporate investment decisions under all-equity financing. Secondly, I examine the issue in a setting where a firm relies on debt financing. Briefly speaking, the findings are consistent with Amihud and Lev's results.Managers who have high shareholdings and rewarded by intensive profit sharing ratio tend to underinvest.However, the underinvestment problem can be mitigated by increasing the financial leverage. The remainder of this paper is organised as follows. Section II presents the model. Section HI discusses the managerial incentives under all-equity financing. Section IV examines the managerial incentives under debt financing. Section V discusses the empirical implications and presents the conclusions of the study.I consider a three-date two-period model. At time t0, a firm is established and goes public. There are now two kinds of owners in the firm, namely, the controlling shareholder and the atomistic shareholders. The proceeds from initial public offering are invested in some risky assets which generate an intermediate earnings, I, at t,. At the beginning, the firm also decides its financial structure. A manager is also hired to operate the firm at this time. The manager is entitled to hold a fraction of the firm's common stocks and stock options, a (where0<a<l), at the beginning of the first period. At time t,, the firm receives intermediate earnings, denoted by I, from the initial asset. At the same time, a new project investment is available to the firm. For simplicity, the model assumes that the firm needs all the intermediate earnings, I, to invest in the new project. If the project is accepted at t,, it produces a stochastic earnings Y in t2, such that Y={I+X, I-X}, with Prob[Y=I+X] = p and Prob[Y=I-X] = 1-p, respectively. The probability, p, is a uniform density function with an interval rangedfrom 0 to 1. Initially, the model also assumes that the net earnings, X, is less than initial investment, I. This assumption is reasonable since most of the investment can not earn a more than 100% rate of return. Later, this assumption is relaxed to investigate the effect of the extraordinarily profitable investment on the results. For simplicity, It is also assumed that there is no time value for the money and no dividend will be paid before t2. If the project is rejected at t,, the intermediate earnings, I, will be kept in the firm and its value at t2 will be equal to I. Effects of Management Compensation Schemes on Corporate Investment Decision Overinvestment versus UnderinvestmentA risk neutral investor should invest in a new project if it generates a positiexpected payoff. If the payoff is normally or symmetrically distributed, tinvestor should invest whenever the probability of making a positive earninggreater than 0.5. The minimum level of probability for making an investment the neutral investor is known as the cut-off probability. The project will generzero expected payoff at a cut-off probability. If the investor invests only in tprojects with the cut-off probability greater than 0.5, then the investor tendsinvest in the less risky projects and this is known as the underinvestment. Ifinvestor invests the projects with a cut-off probability less than 0.5, then tinvestor tends to invest in more risky projects and this is known as thoverinvestment. In the paper, it is assumed that the atomistic shareholders risk neutral, the manager and controlling shareholder are risk averse.It has been argued that risk-reduction activities are considered as managerial perquisites in the context of the agency cost model. Managers tend to engage in these risk-reduction activities to decrease their largely undiversifiable "employment risk" (Amihud and Lev 1981). The finding in this paper is consistent with Amihud and Lev's empirical result. Managers tend to underinvest when they have higher shareholdings and larger profit sharing percentage. This result is independent of the level of debt financing. Although the paper can not predict themanager's action when he has a large profit sharing percentage and the profit cashflow has high variance (X > I), it shows that the manager with high shareholding will underinvest in the project. This is inconsistent with the best interests of the atomistic shareholders. However, the underinvestment problem can be mitigated by increasing the financial leverage.The results and findings in this paper provides several testable hypotheses forfuture research. If the managers underinvest in the projects, the company willunderperform in long run. Thus the earnings can be used as a proxy forunderinvestment, and a negative relationship between earningsandmanagement shareholdings, stock options or profit sharing ratiois expected.As theunderinvestment problem can be alleviated by increasing the financialleverage, a positiverelationship between earnings and financial leverage isexpected.在一个公司由于所有权和控制权的分离的代理问题存在的文献中得到了广泛的研究。

机器学习题库一、 极大似然1、 ML estimation of exponential model (10)A Gaussian distribution is often used to model data on the real line, but is sometimesinappropriate when the data are often close to zero but constrained to be nonnegative. In such cases one can fit an exponential distribution, whose probability density function is given by()1xb p x e b-=Given N observations x i drawn from such a distribution:(a) Write down the likelihood as a function of the scale parameter b.(b) Write down the derivative of the log likelihood.(c) Give a simple expression for the ML estimate for b.2、换成Poisson 分布：()|,0,1,2,...!x e p x y x θθθ-==()()()()()1111log |log log !log log !N Ni i i i N N i i i i l p x x x x N x θθθθθθ======--⎡⎤=--⎢⎥⎣⎦∑∑∑∑3、二、 贝叶斯假设在考试的多项选择中，考生知道正确答案的概率为p ，猜测答案的概率为1-p ，并且假设考生知道正确答案答对题的概率为1，猜中正确答案的概率为1，其中m 为多选项的数目。

商务英语自考试题及答案一、选择题（每题2分，共20分）1. The term "B2B" stands for ________.A. Business to BusinessB. Business to ConsumerC. Consumer to ConsumerD. Consumer to Business答案：A2. In international trade, "FOB" refers to ________.A. Free on BoardB. Free of BoardC. Freight on BoardD. Freight of Board答案：A3. The abbreviation "CEO" stands for ________.A. Chief Executive OfficerB. Chief Executive OfficerC. Chief Executive OfficerD. Chief Executive Officer答案：A4. Which of the following is not a form of payment in international trade?A. Letter of CreditB. Cash in AdvanceC. ConsignmentD. Barter答案：D5. The term "TQM" stands for ________.A. Total Quality ManagementB. Total Quantity ManagementC. Total Quality MonitoringD. Total Quantity Monitoring答案：A6. "CIF" in international trade means ________.A. Cost, Insurance, and FreightB. Cost, Insurance, FreightC. Cost, Insurance, and FreightD. Cost, Insurance, Freight答案：A7. Which of the following is not a type of business letter?A. Sales LetterB. MemoC. Proposal LetterD. Invoice答案：B8. "MOQ" stands for ________.A. Minimum Order QuantityB. Maximum Order QuantityC. Maximum Order QualityD. Minimum Order Quality答案：A9. The term "ROI" stands for ________.A. Return on InvestmentB. Risk of InvestmentC. Rate of InvestmentD. Result of Investment答案：A10. In a business context, "RFQ" stands for ________.A. Request for QuotationB. Request for QuestionC. Request for QualificationD. Request for Quantity答案：A二、填空题（每题2分，共20分）1. When a company offers a product or service to another business, it is known as ________.答案：B2B2. The term used for the point at which the buyer and seller agree on the price of goods and the delivery terms is________.答案：contract3. The process of improving the quality and efficiency of a service or product is known as ________.答案：quality management4. The document that guarantees payment for goods shipped is called a ________.答案：letter of credit5. The minimum number of units a manufacturer will produce ata set price is known as the ________.答案：MOQ6. The acronym for a document that lists the details of a transaction and is used to bill the buyer is ________.答案：invoice7. The process of exchanging goods or services for other goods or services without using money is called ________.答案：barter8. The term used to describe the act of selling goods to customers directly is ________.答案：retail9. The process of managing the entire life cycle of a product from inception to disposal is known as ________.答案：product lifecycle management10. The term used to describe the process of identifying potential customers and persuading them to buy a product or service is ________.答案：marketing三、简答题（每题10分，共30分）1. Explain the concept of "outsourcing" in business.答案：Outsourcing refers to the practice of hiring another company to perform tasks that were traditionally performedin-house. It is a strategic initiative aimed at reducing costs, improving efficiency, and allowing a company to focus on its core competencies.2. What are the key components of a business proposal?答案：A business proposal typically includes an executive summary, problem statement, solution overview, implementation plan, cost analysis, benefits, and a call to action.3. Describe the role of a sales manager in a company.答案：A sales manager is responsible for leading a sales team, setting sales goals, developing sales strategies, training sales personnel, and monitoring sales performance to ensurethe company meets its revenue targets.四、论述题（共30分）Discuss the importance of effective communication in international business.答案：Effective communication is crucial in international business as it helps to build relationships, resolve misunderstandings, and facilitate negotiations. It also aidsin the clear conveyance of information, which is vital forsuccessful transactions and collaborations across different cultures and languages.。

Chapter17Macroeconomic and industry Analysis1. A top down analysis of a firm starts with ____________.D. the global economy2. An example of a highly cyclical industry is ________.A. the automobile industry3. Demand-side economics is concerned with _______.A. government spending and tax levelsB. monetary policyC. fiscal policyE. A, B, and C4. The most widely used monetary tool is ___________.C. open market operations5. The "real", or inflation-adjusted, exchange rate, isC. the purchasing power ratio.6. The "normal" range of price-earnings ratios for the S&P 500 Index isD. between 12 and 257. Monetary policy is determined byC. the board of Governors of the Federal Reserve System.8. A trough is ________.B. a transition from a contraction in the business cycle to the start of an expansion9. A peak is ________.A. a transition from an expansion in the business cycle to the start of a contraction10. If the economy is growing, firms with high operating leverage will experience __________.A. higher increases in profits than firms with low operating leverage.11. If the economy is shrinking, firms with high operating leverage will experience __________.A. higher decreases in profits than firms with low operating leverage.12. If the economy is growing, firms with low operating leverage will experience __________.C. smaller increases in profits than firms with high operating leverage.13. If the economy is shrinking, firms with low operating leverage will experience__________.C. smaller decreases in profits than firms with high operating leverage.14. Industrial production refers to _________.C. the total manufacturing output in the economy.15. GDP refers to _________.D. the total production of goods and services in the economy16. A rapidly growing GDP indicates a(n) ______ economy with ______ opportunity for a firm to increase sales.D. expanding; ample17. A declining GDP indicates a(n) ______ economy with ______ opportunity for a firm to increase sales.A. stagnant; little18. The average duration of unemployment and changes in the consumer price index for services are _________.C. lagging economic indicators19. A firm in an industry that is very sensitive to the business cycle will likely have a stock beta ___________.A. greater than 1.020. If the economy were going into a recession, an attractive industry to invest in would be the ________ industry.B. medical services21. The stock price index and contracts and new orders for nondefense capital goods areA. leading economic indicators.22. A firm in the early stages of the industry life cycle will likely have ________.B. high risk.C. rapid growthE. B and C23. Assume the U.S. government was to decide to increase the budget deficit. This action will most likely cause __________ to increaseA. interest ratesB. government borrowingD. both A and B24. Assume the U.S. government was to decide to decrease the budget deficit. This action will most likely cause __________ to decreaseA. interest ratesB. government borrowingD. both A and B25. Assume that the Federal Reserve decreases the money supply. This action will cause________ to decrease.C. investment in the economy26. If the currency of your country is depreciating, the result should be to ______ exports and to _______ imports.B. stimulate, discourage27. If the currency of your country is appreciating, the result should be to ______ exports and to _______ imports.C. discourage, stimulate28. Increases in the money supply will cause demand for investment and consumption goods to _______ in the short run and cause prices to ________ in the long run.A. increase, increase29. The North American Industry Classification System (NAICS)A. are for firms that operate in the NAFTA region.B. group firms by industry.D. A and B.30. If interest rates increase, business investment expenditures are likely to ______ and consumer durable expenditures are likely to _________.D. decrease, decrease31. Fiscal policy generally has a _______ direct impact than monetary policy on the economy, and the formulation and implementation of fiscal policy is ______ than that of monetary policy.B. more, slower32. Fiscal policy is difficult to implement quickly becauseA. it requires political negotiations.B. much of government spending is nondiscretionary and cannot be changed.D. A and B.33. InflationA. is the rate at which the general level of prices is increasing.B. rates are high when the economy is considered to be "overheated".D. A and B.Two firms, A and B, both produce widgets. The price of widgets is $1 each. Firm A has total fixed costs of $500,000 and variable costs of 50 cents per widget. Firm B has total fixed costs of $240,000 and variable costs of 75 cents per widget. The corporate tax rate is 40%. If the economy is strong, each firm will sell 1,200,000 widgets. If the economy enters a recession, each firm will sell 1,100,000 widgets.34. If the economy enters a recession, the after-tax profit of Firm A will be ________.C. $30,00035. If the economy enters a recession, the after-tax profit of Firm B will be _______.E. none of the above36. If the economy is strong, the after-tax profit of Firm A will be _______.D. $60,00037. If the economy is strong, the after-tax profit of Firm B will be __________.C. $36,00038. Calculate firm A's degree of operating leverage.A. 11.039. Calculate firm B's degree of operating leverage.C. 29.8640. Classifying firms into groups, such as _________ provides an alternative to the industry life cycle.A. slow-growersB. stalwartsD. A and B41. Supply-side economists wishing to stimulate the economy are most likely to recommendD. a decrease in the tax rate.42. Which of the following are not examples of defensive industries?B. durable goods producers.43. Which of the following are examples of defensive industries?A. food producers.C. pharmaceutical firms.D. public utilitiesE. A, C and D44. ________ is a proposition that a strong proponent of supply side economics would most likely stress.B. Higher marginal tax rates promote economic inefficiency and thereby retard aggregate output as they encourage investors to undertake low productivity projects with substantial tax shelter benefits45. The industry life cycle is described by which of the following stage(s)?A. start-up.B. consolidation.D. A and B.46. In the start-up stage of the industry life cycleA. it is difficult to predict which firms will succeed and which firms will fail.B. industry growth is very rapid.D. A and B.47. In the consolidation stage of the industry life-cycleC. the performance of firms will more closely track the performance of the overall industry.48. In the maturity stage of the industry life cycleA. the product has reached full potential.B. profit margins are narrower.C. producers are forced to compete on price to a greater extent.E. A, B, and C.49. In the decline stage of the industry life cycleA. the product may have reached obsolescence.B. the industry will grow at a rate less than the overall economy.C. the industry may experience negative growth.E. A, B, and C.50. A variety of factors relating to industry structure affect the performance of the firm, includingA. threat of entry.B. rivalry between existing competitors.E. A and B.51. The process of estimating the dividends and earnings that can be expected from the firm based on determinants of value is calledD. fundamental analysis.52. The emerging market exhibiting the highest growth in real GDP in 2007 wasA. China53. The emerging stock market exhibiting the highest U.S. dollar return in 2007 wasA. China54. The life cycle stage in which industry leaders are likely to emerge is theC. consolidation stage.55. Investment manager Peter Lynch refers to firms that are in bankruptcy or soon might be asE. turnarounds.56. A top-down analysis of a firm's prospects starts withD. an assessment of the broad economic environment.57. Over the period 1999-2006, which of the following countries had a change in its real exchange rate that was favorable for U.S. consumers who want to buy its goods?E. Japan58. Over the period 1999-2006, which of the following countries had a change in its real exchange rate that was most unfavorable for U.S. consumers who want to buy its goods?A. Canada59. In recent years, P/E multiples haveB. risen dramatically.60. In recent years, P/E multiples for S&P 500 companies haveD. ranged from 12 to 25.61. The industry with the highest ROE in 2007 wasD. iron/steel.62. The industry with the lowest ROE in 2007 wasE. airlines.63. The industry with the lowest return in 2007 wasA. home construction.64. The industry with the highest return in 2007 wasB. oil equipment.65. Investors can ______ invest in an industry with the highest expected return by purchasing ______.B. not; industry-specific iShares66. Which of the following are key economic statistics that are used to describe the state of the macroeconomy?I) gross domestic productII) the unemployment rateIII) inflationIV) consumer sentimentV) the budget deficitE. I, II, III, IV, and V67. An example of a positive demand shock isE. a decrease in tax rates.68. An example of a negative demand shock isA. a decrease in the money supply.B. a decrease in government spending.E. A and B.69. During which stage of the industry life cycle would a firm experience stable growth in sales?A. Consolidation70. The emerging stock market exhibiting the highest local currency return in 2007 wasB. ChinaE. China71. Sector rotationC. is shifting the portfolio more heavily toward an industry or sector that is expected to perform well in the future.72. According to Michael Porter, there are five determinants of competition. An example of _____ is when new entrants to an industry our pressure on prices and profits.A. Threat of Entry73. According to Michael Porter, there are five determinants of competition. An example of _____ is when competitors seek to expand their share of the market.B. Rivalry between Existing Competitors74. According to Michael Porter, there are five determinants of competition. An example of _____ is when the availability limits the prices that can be charged to customers.C. Pressure from Substitute Products75. According to Michael Porter, there are five determinants of competition. An example of _____ is when a buyer purchases a large fraction of an industry's output and can demand price concessions.D. Bargaining power of Buyers76. Assume the U.S. government was to decide to increase the budget deficit. This action will most likely cause __________ to increaseA. interest ratesB. government borrowingD. both A and B77. If interest rates decrease, business investment expenditures are likely to ______ and consumer durable expenditures are likely to _________.A. increase, increase78. An example of a defensive industry is ________.B. the tobacco industryC. the food industryE. B and CTwo firms, C and D, both produce coat hangers. The price of coat hangers is $1.20 each. Firm C has total fixed costs of $750,000 and variable costs of 30 cents per widget. Firm D has total fixed costs of $400,000 and variable costs of 50 cents per widget. The corporate tax rate is 40%. If the economy is strong, each firm will sell 2,000,000 widgets. If the economy enters a recession, each firm will sell 1,400,000 widgets.79. If the economy enters a recession, the total revenue of Firm C will be ________.A. $1,680,00080. If the economy enters a recession, the total cost of Firm C will be ________.B. $1,170,00081. If the economy enters a recession, the before tax profit of Firm C will be ________.C. $510,00082. If the economy enters a recession, the tax of Firm C will be ________.D. $204,00083. If the economy enters a recession, the after tax profit of Firm C will be ________.E. $306,00084. If the economy is strong, the total revenue of Firm C will be ________.D. $2,400,00085. If the economy is strong, the total cost of Firm C will be ________.C. $1,305,00086. If the economy is strong, the before tax profit of Firm C will be ________.B. $1,050,00087. If the economy is strong, the tax of Firm C will be ________.A. $420,00088. If the economy is strong, the after-tax profit of Firm C will be _______.E. $630,00089. If a firm's sales decrease by 15% and profits decrease by 20% during a recession, the firms operating leverage is ____________?A. 1.33Short Answer Questions90. Discuss the tools of the U.S. government's "demand-side" policy. Include in your discussion of these tools the relative advantages and disadvantages of each in terms of the effect of the use of these tools on the economy.The two tools of the government's "demand-side" policy are fiscal and monetary policy. Fiscal policy is the use of government spending and taxing for the specific purpose of stabilizing the economy. Fiscal policy, once enacted, has the most direct and immediate effect on the economy. However, the formulation and implementation of fiscal policy is extremely slow, as such policy must be approved by both the legislative and executive branches of the federal government. Monetary policy consists of actions taken by the Board of Governors of the Federal Reserve System (FRS) to influence the money supply and/or interest rates. Monetary policy is relatively easy to formulate and to implement, but has less direct impact on the economy than fiscal policy. The most widely used tool of the FRS is the open market operations, in which the Fed buys or sells bonds for the Fed's account. Buying securities increases the money supply; selling securities decreases the money supply. Open market operations occur daily. Other FRS tools include adjusting the discount rate, which is the interest rate the Fed charges banks onshort-term loans, and altering reserve requirements, which are the fraction of deposits that banks must maintain in cash deposits with the Fed. Reductions in the money supply signal an expansionary monetary policy; lowering reserve requirements increase the money supply, and thus, stimulate the economy. The Fed walks a fine line: expansionary monetary policy probably will lower interest rates and stimulate investment and consumption in the short run, but ultimately inflation probably will result.Feedback: The rationale of this question is to ascertain whether the student has an understanding of the basic principles of macroeconomics.91. Discuss the National Bureau of Economic Research (NBER)'s indexes of economic indicators, and how each of the categories of these indicators might be used by the securities' analyst.The NBER has developed a set of cyclical indicators to help forecast, measure, and interpret short-term fluctuations in economic activity. The leading economic indicators are those that tend to increase or decrease in advance of the rest of the economy. These indicators are used to forecast the state of the economy for the coming period (usually one year). Coincident economic indicators move in tandem with the broad economy, and are used to confirm (or disconfirm) an earlier economic prediction. Lagging economic indicators are those that move after the broad economy, and are used to identify the end of a stage of the business cycle (such as a trough) and as an indication that another stage of business cycle (such as the expansion) is about to begin. The S&P 500 stock index is an excellent leading economic indicator, as would be expected by market efficiency proponents. However, if the stock market anticipates general economic trends, the task of the fundamentalist using economic forecasts to identify attractive industries (and thus stocks) for the future becomes even more impossible.Feedback: The purpose of this question is to ascertain the student's understanding of the widely quoted economic indicators and the usefulness (and lack thereof) in securities' analysis.92. Discuss the industry life cycle, how this concept can be used by security analysts, and the limitations of this concept for security analysis.The industry life cycle may be defined by the following stages: start up (rapid and increasing growth), consolidation (sable growth), maturity (slowing growth), and relative decline (minimal or negative growth). Investors interested in identifying new, and presumably ultimately successful, industries will use this technique, trying to get in on the "ground floor". In the start up stage, no historical data is present; thus, one cannot identify potentially successful firms. However, typically, all of the firms are selling at low prices and the investor will "diversify across the industry" by buying many different stocks in the industry. If the industry becomes successful, the surviving firms will appreciate substantially in value; the non-surviving firms will be written off as losses. Typically, in this stage, firms are paying little or no dividends. Investment in this stage is for the risk-tolerant investor. As the industry moves from the start up to the consolidation stage, firms begin paying or increasing dividends; the surviving firms become more successful, begin to enjoy economies of scale, and are moving up the learning curve in terms of cost efficiency. In the maturity stage, the growth has slowed and dividends may have increased; less risk is involved. By the relative decline stage, the firm has no new exciting capital budgeting projects and may have become an "income stock", by paying out a higher than average level of dividends. At this stage, the stock may be attractive for the risk-averse retiree interested in dividend income. However, the stock must be watched carefully in this stage, as this industry may be dying (buggy whips). However, over the industry life cycle, the clientele for the firms' stocks have changed, from the risk-tolerant to the risk averse.The problem with using this concept for investment purposes is identifying where the industry is in the industry life cycle. In addition, all industries do not move through the cycle in the same fashion. In fact, the goal is to avoid the relative decline stage.Feedback: The purpose of this question is to ascertain whether the student understands the industry life cycle, how the concept can be used by investors, and the limitations of the concept for investors.93. Discuss the ways in which the global economy might have an effect on a firm whose headquarters are in Montana. Be specific - cite some of the relevant factors that should be considered.A firm that operates from Montana cannot ignore the global economy. The firm may make sales to other countries, employ people from other countries, and invest in other countries. It may face price competition from similar firms abroad, be subject to wages that are different from those paid by foreign firms, and management may have less power to do what it wants due to labor unions. Exports of its products and imports will be influenced by the global economy. Interest rates in other countries will determine part of the return on the firm's investments. Exchange rates pose an additional risk if the company wants to repatriate its earnings. Countries' political and economic policies should be considered, with some being more predictable than others. Global markets have some linkages, but there are significant variations in performance among countries.Feedback: This question emphasizes the importance of the global economy, which should not be ignored when doing a macroeconomic analysis.94. List and discuss three of the five determinants of competition suggested in Porter's 1985 study.The determinants are: the threat of entry from new competitors, rivalry between existing competitors, price pressure from substitute products, the bargaining power of buyers, and the bargaining power of suppliers. Each of these is discussed below.Threat of entry from new competitors - If there are high profit margins in the industry, new competitors will be likely to enter. There may be some barriers to entry that existing firms can establish to discourage this. Possible barriers include longstanding relationships with suppliers and buyers, proprietary knowledge or patents, brand loyalty, and experience in the market. Rivalry between existing competitors - This could lead to price competition and lower profit margins. Expansion of one firm cuts into the rivals' market shares. Firms with homogeneous products face price pressure because they are unable to differentiate their products from their competitors' products. High fixed costs might force a company to operate at close to full capacity.Price pressure from substitute products - If firms in related industries produce similar products, the firm may not be able to charge as much for its product. Some examples are carbonated beverages and fruit drinks, paint and wallpaper, and movies and videos. Many other examples may be offered.Bargaining power of buyers - Buyers might have bargaining power if they purchase a substantial proportion of the firm's output. The firm might have to settle for accepting a lower price for its products. The automobile industry is an example given in the textbook. Bargaining power of suppliers - If the firm depends on a supplier to provide much of its inputs, the supplier might demand a higher price. This is especially true if there are no easily available alternative suppliers. Labor unions are cited as an example.Feedback: This question tests the student's understanding of the relationships among industry structure, competitive strategy, and profitability.。

Chapter 6Network Design in an Uncertain EnvironmentTrue/False1. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space, cannot be altered in the short term.Answer: TrueDifficulty: Moderate2. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space, rarely remain in place for several years.Answer: FalseDifficulty: Moderate3. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space, define the boundaries within which the supply chain mustcompete.Answer: TrueDifficulty: Moderate4. Long-term contracts for both warehousing and transportation requirements willbe more effective if the demand and price of warehousing do not change in thefuture or if the price of warehousing goes up.Answer: TrueDifficulty: Easy5. Long-term contracts for both warehousing and transportation requirements willbe more effective if either demand or the price of warehousing drops in the future.Answer: FalseDifficulty: Moderate6. The degree of demand and price uncertainty has a significant influence on theappropriate portfolio of long- and short-term warehousing space that a firmshould carry.Answer: TrueDifficulty: Easy7. If price and demand vary over time in a global network, flexible productioncapacity can be reconfigured to maximize profits in the new environment.Answer: TrueDifficulty: Moderate8. A firm may choose to build a flexible global supply chain even in the presence oflittle demand or supply uncertainty if certainty exists in exchange rates or prices.Answer: FalseDifficulty: Moderate9. The present value of a stream of cash flows is what that stream is worth intoday’s dollars.Answer: TrueDifficulty: Easy10. Discretionary cash flow (DCF) analysis evaluates the present value of anystream of future cash flows and allows management to compare two streams of cash flows in terms of their financial value.Answer: FalseDifficulty: Easy11. The present value of future cash flows is found by using a discount factor.Answer: TrueDifficulty: Moderate12. The rate of return k is also referred to as the present value of capital.Answer: FalseDifficulty: Easy13. A negative NPV for an option indicates that the option will lose money for thesupply chain.Answer: TrueDifficulty: Moderate14. The decision with the lowest NPV will provide a supply chain with the highestfinancial return.Answer: FalseDifficulty: Moderate15. In reality, demand and prices are highly uncertain and are likely to fluctuateduring the life of any supply chain decision.Answer: TrueDifficulty: Moderate16. For a global supply chain, exchange rates and inflation are unlikely to vary overtime in different locations.Answer: FalseDifficulty: Easy17. The multiplicative binomial cannot take on negative values and can be used forfactors like demand, price, and exchange rates that cannot become negative.Answer: TrueDifficulty: Moderate18. A logical objection to both the multiplicative and additive binomial is the fact thatthe underlying factor takes on two values at the end of each period.Answer: FalseDifficulty: Hard19. If uncertainty is ignored, a manager will always sign long-term contracts becausethey are typically cheaper and avoid all flexible capacity because it is moreexpensive.Answer: TrueDifficulty: Moderate20. During network design, managers need a methodology that allows them toestimate the certainty in their forecast of demand and price and then incorporate this certainty into the decision-making process.Answer: FalseDifficulty: Hard21. Decision trees with DCFs can be used to evaluate supply chain design decisionsgiven uncertainty in prices, demand, exchange rates, and inflation.Answer: TrueDifficulty: Moderate22. Uncertainty in demand and economic factors should not be included in thefinancial evaluation of supply chain design decisions.Answer: FalseDifficulty: Hard23. In a complex decision tree, there are thousands of possible paths that may resultfrom the first period to the last.Answer: TrueDifficulty: Easy24. Simulation methods are very good at evaluating a decision where the path itselfis decision dependent.Answer: FalseDifficulty: Hard25. Simulation models require a higher setup cost to start and operate compared todecision tree tools.Answer: TrueDifficulty: Easy26. The main advantage of simulation models is that they can provide low-costevaluations of complex situations.Answer: FalseDifficulty: Moderate27. Strategic planning and financial planning should be combined during supplychain network design.Answer: TrueDifficulty: Moderate28. The evaluation of supply chain networks should not use multiple metrics.Answer: FalseDifficulty: Moderate29. Financial analysis should be used as an input to decision making, not as thedecision-making process.Answer: TrueDifficulty: Moderate30. One of the best ways to speed up the process of financial analysis and arrive at agood decision is to use estimates, except when it appears that finding a veryaccurate input would take an inordinate amount of time.Answer: FalseDifficulty: EasyMultiple Choice1. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space,a. can be altered in the short term.b. cannot be altered in the short term.c. cannot be altered in the long term.d. can only be altered in the short term.e. all of the aboveAnswer: bDifficulty: Easy2. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space,a. are realigned every few weeks.b. only remain in place for several years.c. rarely remain in place for several years.d. only remain in place for a few weeks.e. often remain in place for several years.Answer: eDifficulty: Hard3. Decisions made during the supply chain design phase regarding significantinvestments in the supply chain, such as the number and size of plants to build,the number of trucks to purchase or lease, and whether to build or leasewarehouse space,a. define the boundaries within which the supply chain must compete.b. have little impact on how the supply chain must compete.c. are irrelevant regarding how the supply chain will compete.d. are the only consideration regarding how the supply chain will compete.e. none of the aboveAnswer: aDifficulty: Moderate4. Long-term contracts for both warehousing and transportation requirements willbe more effective ifa. the demand and price of warehousing do not change in the future.b. the price of warehousing goes up in the future.c. demand drops in the future.d. the price of warehousing drops in the future.e. a and b onlyAnswer: eDifficulty: Moderate5. Short-term contracts for both warehousing and transportation requirements willbe more effectivea. if the demand and price of warehousing do not change in the future.b. if the price of warehousing goes up in the future.c. if either demand or the price of warehousing drops in the future.d. only if demand drops in the future.e. only if the price of warehousing drops in the future.Answer: cDifficulty: Moderate6. The degree of demand and price uncertainty hasa. no effect on the appropriate portfolio of long- and short-term warehousingspace that a firm should carry.b. a limited influence on the appropriate portfolio of long- and short-termwarehousing space that a firm should carry.c. a minor influence on the appropriate portfolio of long- and short-termwarehousing space that a firm should carry.d. a significant influence on the appropriate portfolio of long- and short-termwarehousing space that a firm should carry.e. None of the above are true.Answer: dDifficulty: Moderate7. Uncertainty of demand and pricea. drives the value of building flexible production capacity at a plant.b. eliminates the value of building flexible production capacity at a plant.c. facilitates the value of building flexible production capacity at a plant.d. has no effect on the value of building flexible production capacity at aplant.e. None of the above are true.Answer: a8. If price and demand do vary over time in a global network,a. flexible production capacity should not be used in the new environment.b. flexible production capacity will be ineffective in the new environment.c. flexible production capacity can be reconfigured to minimize profits in thenew environment.d. flexible production capacity can be reconfigured to maximize profits in thenew environment.e. flexible production capacity should never be used in an uncertainenvironment.Answer: dDifficulty: Moderate9. A firm may choose to build a flexible global supply chain even in the presence oflittle demand or supply uncertainty ifa. certainty exists in both exchange rates and prices.b. certainty exists in exchange rates or prices.c. uncertainty exists in both exchange rates and prices.d. uncertainty exists in exchange rates or prices.e. uncertainty exists only in exchange rates.Answer: dDifficulty: Moderate10. The present value of a future stream of cash flows is what that streama. was worth in yesterday’s dollars.b. is wo rth in today’s dollars.c. will be worth in future dollars.d. might be worth in future dollars.e. none of the aboveAnswer: bDifficulty: Easy11. The process of evaluating the present value of any stream of future cash flows sothat management can compare two streams of cash flows in terms of theirfinancial value isa. annual cash flow(ACF) analysis.b. discretionary cash flow(DCF) analysis.c. discounted cash flow(DCF) analysis.d. future cash flow(FCF) analysis.e. none of the aboveAnswer: cDifficulty: Moderate12. The present value of future cash flow is found bya. locating the correct factor on a z-table.b. using a discount factor.c. plotting the function on a graph.d. adding the total of all future cash flows.e. none of the aboveAnswer: b13. The discount factor used to obtain the present value of money in the next periodwhere k represents the rate of return isa. k.b. 1+k.c. 1/(1+k).d. k /(1+k).e. none of the aboveAnswer: cDifficulty: Moderate14. The rate of return k is also referred to as thea. discount rate.b. hurdle rate.c. opportunity cost of capital.d. all of the abovee. none of the aboveAnswer: dDifficulty: Easy15. What is the present value of a $27 revenue that will be received in one yearwhere the rate of return is 8% (.08)?a. $2.50b. $15.00c. $25.00d. $30.00e. none of the aboveAnswer: cDifficulty: Easy16. The net present value (NPV) of a stream of cash flows is equal toa. the sum of all cash flows for all periods being considered.b. the sum of all cash flows for all periods being considered divided by thenumber of periods.c. the average of all cash flows for all periods being considered.d. the average of all cash flows for all periods being considered multiplied bythe number of periods.e. the sum of all cash flows for all periods being considered discounted bythe rate of return for each period.Answer: eDifficulty: Hard17. A negative NPV (net present value) for an option indicates that the option willa. gain money for the supply chain.b. lose money for the supply chain.c. maximize profit for the supply chain.d. minimize profit for the supply chain.e. none of the aboveAnswer: bDifficulty: Moderate18. The decision with the highest NPV (net present value) will provide a supply chainwitha. the highest financial return.b. the lowest financial return.c. a reasonable financial return.d. the least desirable financial return.e. none of the aboveAnswer: aDifficulty: Moderate19. The NPV (net present value) of a cash stream that is equal to $100 per period for5 periods with a rate of return of 10% (.10) per period would bea. 379.07.b. 416.98.c. 500.00.d. 610.51.e. 671.56.Answer: bDifficulty: Moderate20. The NPV (net present value) of a cash stream that is equal to $75 per period for5 periods with a rate of return of 10% (.10) per period would bea. 221.37.b. 284.30.c. 312.74.d. 375.00.e. none of the aboveAnswer: cDifficulty: Moderate21. In reality, demand and prices area. highly certain and not likely to fluctuate during the life of any supply chaindecision.b. highly certain and likely to fluctuate during the life of any supply chaindecision.c. highly uncertain and not likely to fluctuate during the life of any supplychain decision.d. highly uncertain and likely to fluctuate during the life of any supply chaindecision.e. none of the aboveAnswer: dDifficulty: Moderate22. For a global supply chain, exchange rates and inflation area. likely to vary over time in different locations.b. not likely to vary over time in different locations.c. not likely to vary over time in any locations.d. likely to be stable over time in all locations.e. none of the aboveAnswer: aDifficulty: Easy23. The binomial representation of uncertainty is based on the assumption that whenmoving from one period to the next, the value of the underlying factor (such asdemand or price)a. has only one possible outcome.b. has only two possible outcomes - up or down.c. has many possible outcomes.d. cannot be accurately determined.e. none of the aboveAnswer: bDifficulty: Moderate24. In the commonly used multiplicative binomial, it is assumed that the underlyingfactora. moves up by a factor u > 1 with probability p.b. moves down by a factor u > 1 with probability p.c. moves down by a factor d < 1 with probability 1 – p.d. either a or be. either a or cAnswer: eDifficulty: Hard25. The multiplicative binomial can be used for factors like demand, price, andexchange rates that cannot become negative because ita. can take on negative values.b. cannot take on negative values.c. can take on positive values.d. cannot take on positive values.e. all of the aboveAnswer: bDifficulty: Hard26. A logical objection to both the multiplicative and additive binomial is the fact thatthe underlying factora. takes on only one of two possible values at the end of each period.b. takes on two values at the end of each period.c. takes on one of many possible values at the end of each period.d. takes on several of many possible values at the end of each period.e. none of the aboveAnswer: aDifficulty: Moderate27. If uncertainty is ignored, a manager willa. always sign long-term contracts because they are typically moreexpensive and avoid all flexible capacity because it is more expensive.b. always sign short-term contracts because they are typically cheaper andavoid all flexible capacity because it is more expensive.c. always sign long-term contracts because they are typically cheaper andavoid all flexible capacity because it is more expensive.d. always sign short-term contracts because they are typically cheaper andavoid all flexible capacity because it is less expensive.e. none of the aboveAnswer: cDifficulty: Hard28. A decision tree isa. a graphic device used to evaluate decisions under certainty.b. a graphic device used to evaluate decisions under uncertainty.c. a tabular device used to evaluate decisions under certainty.d. a tabular device used to evaluate decisions under uncertainty.e. none of the aboveAnswer: bDifficulty: Moderate29. Decision tree analysis is based on Bellman’s principle, which states that for anychoice of strategy in a given state,a. the optimal strategy is the one that is selected if the entire analysis isassumed to begin in the first period.b. the optimal strategy is the one that is selected if the entire analysis isassumed to begin in the last period.c. the optimal strategy in the next period is the one that is selected if theentire analysis is assumed to begin in the last period.d. the optimal strategy in the next period is the one that is selected if theentire analysis is assumed to begin in the next period.e. none of the aboveAnswer: dDifficulty: Hard30. The first step in decision tree analysis methodology is toa. identify factors such as demand, price, and exchange rate, whosefluctuation will be considered over the next T periods.b. identify the periodic discount rate k for each period.c. start at period T, work back to Period 0 identifying the optimal decisionand the expected cash flows at each step. Expected cash flows at eachstep in a given period should be discounted back when included in theprevious period.d. identify the duration of each period (month, quarter, etc.) and the numberof periods T over which the decision is to be evaluated.e. identify representations of uncertainty for each factor; that is, determinewhat distribution to use to model the uncertainty.Answer: dDifficulty: Moderate31. The last step in decision tree analysis methodology is toa. identify factors such as demand, price, and exchange rate, whose fluctuationwill be considered over the next T periods.b. identify the periodic discount rate k for each period.c. start at period T, work back to Period 0, identifying the optimal decision andthe expected cash flows at each step. Expected cash flows at each step in agiven period should be discounted back when included in the previous period.d. identify the duration of each period (month, quarter, etc.) and the number ofperiods T over which the decision is to be evaluated.e. identify representations of uncertainty for each factor; that is, determine whatdistribution to use to model the uncertainty.Answer: cDifficulty: Moderate32. Uncertainty in demand and economic factors should be included in the financialevaluation of supply chain design decisions, becausea. the exclusion of certainty may have a significant impact on this evaluation.b. the exclusion of uncertainty may have a significant impact on thisevaluation.c. the inclusion of certainty may have a significant impact on this evaluation.d. the inclusion of uncertainty may have a significant impact on thisevaluation.e. none of the aboveAnswer: dDifficulty: Hard33. Flexibility should be valued by taking into account uncertainty in demand andeconomic factors. In general, flexibility will tend toa. decrease in value with a decrease in certainty.b. increase in value with an increase in uncertainty.c. decrease in value with an increase in uncertainty.d. increase in value with an increase in certainty.e. None of the above are accurate.Answer: bDifficulty: Moderate34. A major factor that makes the decision tree methodology quite powerful isa. the choice of certainty.b. the choice of discount rate.c. the choice of uncertainty level.d. the choice of additive factor.e. all of the aboveAnswer: bDifficulty: Moderate35. The appropriate discount rate used in decision tree methodologya. should be risk-adjusted and risk may vary by period and decision node.b. should be risk-adjusted and risk may not vary by period and decisionnode.c. should not be risk-adjusted and risk may vary by period and decisionnode.d. should not be risk-adjusted and risk may not vary by period and decisionnode.e. None of the above are accurate.Answer: aDifficulty: Moderate36. Alternative approaches to decision tree analysis includea. contingent claims analysis (CCA) for discrete time analysis.b. real options for the continuous time case.c. real options for the discrete time analysis.d. all of the abovee. a and b onlyAnswer: eDifficulty: Moderate37. Contingent claims analysis (CCA) and real optionsa. adjust hurdle rate so that the risk-free discount rate may be applied ineach period.b. adjust opportunity cost of capital so that the risk-free discount rate may beapplied in each period.c. adjust rate of return so that the risk-free discount rate may be applied ineach period.d. adjust transition probabilities so that the risk-free discount rate may beapplied in each period.e. none of the aboveAnswer: dDifficulty: Moderate38. Firms should use simulation for evaluating decisions whena. underlying decision trees are simple and explicit solutions for theunderlying decision tree are difficult to obtain.b. underlying decision trees are very complex and explicit solutions for theunderlying decision tree are difficult to obtain.c. underlying decision trees are simple and explicit solutions for theunderlying decision tree are easy to obtain.d. underlying decision trees are very complex and explicit solutions for theunderlying decision tree are easy to obtain.e. none of the aboveAnswer: bDifficulty: Moderate39. In a complex decision tree there area. only a few possible paths that may result from the first period to the last.b. less than thirty possible paths that may result from the first period to thelast.c. thousands of possible paths that may result from the first period to thelast.d. an infinite number of possible paths that may result from the first period tothe last.e. none of the aboveAnswer: cDifficulty: Moderate40. Simulation methods are very good at evaluating a decision wherea. the path itself is decision dependent.b. the path itself is not decision dependent.c. the discount rate is decision dependent.d. the discount rate is not decision dependent.e. none of the aboveAnswer: bDifficulty: Hard41. Simulation modelsa. require a higher setup cost to start and operate compared to decision treetools.b. require a lower setup cost to start and operate compared to decision treetools.c. require a higher setup cost to start but less to operate compared todecision tree tools.d. require a lower setup cost to start but more to operate compared todecision tree tools.e. none of the aboveAnswer: aDifficulty: Hard42. The main advantage of simulation models is that they cana. provide high-quality evaluations of simple situations.b. provide high-quality evaluations of complex situations.c. provide low-cost evaluations of simple situations.d. provide low-cost evaluations of complex situations.e. provide low-quality evaluations of complex situations.Answer: bDifficulty: Easy43. Strategic planning and financial planninga. should be performed independently during supply chain network design.b. should be performed sequentially during supply chain network design.c. should be performed hierarchically during supply chain network design.d. should be performed concurrently during supply chain network design.e. should be combined during supply chain network design.Answer: eDifficulty: Hard44. The evaluation of supply chain networksa. should use only one metric.b. should use multiple metrics.c. should not use more than one metric.d. should not use multiple metrics.e. should be subjective.Answer: bDifficulty: Moderate45. Financial analysis should be used asa. the decision-making process.b. an alternative decision-making process.c. an input to decision making, not as the decision-making process.d. all of the abovee. none of the aboveAnswer: cDifficulty: Moderate46. One of the best ways to speed up the process of financial analysis and arrive at agood decision is toa. use estimates of inputs when it appears that finding a very accurate inputwould take an inordinate amount of time.b. use estimates backed up by sensitivity analysis when it appears thatfinding a very accurate input would take an inordinate amount of time.c. use estimates of inputs except when it appears that finding a veryaccurate input would take an inordinate amount of time.d. make sure that every detail is very accurate.e. none of the aboveAnswer: bDifficulty: ModerateEssay/Problems1. Explain additive and multiplicative binomial representations of uncertainty.Answer: The binomial representation of uncertainty is based on the assumptionthat when moving from one period to the next, the value of the underlying factor(such as demand or price) has only two possible outcomes - up or down. In thecommonly used multiplicative binomial, it is assumed that the underlying factoreither moves up by a factor u > 1 with probability p, or down by a factor d < 1 with probability 1 – p. In the additive binomial, it is assumed that the underlying factor increases by u in a given period with probability p and decreases by d withprobability 1 – p. The multiplicative binomial cannot take on negative values and can be used for factors like demand, price, and exchange rates that cannotbecome negative. It also has the advantage of the growth or decline in the given factor being proportional to the current value of the factor and not fixedindependent of size. A logical objection to both the multiplicative and additivebinomial is the fact that the underlying factor takes on only one of two possiblevalues at the end of each period. Certainly a price can change to more than justtwo values. But by making the period short enough, this assumption may bejustified.Difficulty: Hard2. Summarize the steps in the decision tree analysis methodology.Answer: The decision tree analysis methodology is summarized as follows:1. Identify the duration of each period (month, quarter, etc.) and the number ofperiods T over which the decision is to be evaluated.2. Identify factors such as demand, price, and exchange rate, whose fluctuationwill be considered over the next T periods.3. Identify representations of uncertainty for each factor; that is, determine whatdistribution to use to model the uncertainty.4. Identify the periodic discount rate k for each period.5. Represent the decision tree with defined states in each period, as well as thetransition probabilities between states in successive periods.6. Starting at period T, work back to Period 0, identifying the optimal decision andthe expected cash flows at each step. Expected cash flows at each step in agiven period should be discounted back when included in the previous period.Difficulty: Moderate3. Discuss the ideas that managers should consider to make better supply chainnetwork design decisions under uncertainty.Answer: Managers should consider the following ideas to help them make betternetwork design decisions under uncertainty:1. Combine strategic planning and financial planning during network design. Inmost organizations, financial planning and strategic planning are performedindependently. Strategic planning tries to prepare for future uncertainties butoften without rigorous quantitative analysis, whereas financial planning performsquantitative analysis but assumes a predictable or well-defined future. Decisionmakers should design supply chain networks considering a portfolio of strategicoptions—the option to wait, build excess capacity, build flexible capacity, signlong-term contracts, purchase from the spot market, and so forth. The variousoptions should be evaluated in the context of future uncertainty.2. Use multiple metrics to evaluate supply chain networks. As one metric canonly give part of the picture, it is beneficial to examine network design decisionsusing multiple metrics such as firm profits, supply chain profits, customer servicelevels, and response times. Often, different metrics will recommend differentdecisions and by using multiple metrics, the differences between the strategicchoices will become clearer. The best decisions can be made when a multitudeof metrics are available, because each metric enhances the overall view of thealternatives being considered.3. Use financial analysis as an input to decision making, not as the decision-making process. Financial analysis is a great tool in the decision-making process, as it often produces an answer and an abundance of quantitative data to back up that answer. However appealing this may be, management should not rely solely on financial analysis to make decisions. Use of this analysis as a large part of the decision-making process is fine, but other inputs into the decision process thatare difficult to quantify should be included in the analysis as well. Financialmethodologies alone do not provide a complete picture of the alternatives. These impacts should be considered in addition to the raw financial analysis. In the final analysis, management must use other inputs beyond financial analysis in thedecision-making process to get the most complete view of the alternativespossible.4. Use estimates along with sensitivity analysis. Many of the inputs into financialanalysis can be difficult, if not impossible, to nail down in a very accurate fashion.This can cause financial analysis to be a long and drawn out process. One of the best ways to speed the process along and arrive at a good decision is to useestimates of inputs when it appears that finding a very accurate input would takean inordinate amount of time. Using estimates is fine when the estimates arebacked up by sensitivity analysis. By performing sensitivity analysis on the input’s。