Exercise 04-solution

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PRML第三章习题答案

PRML第三章习题答案

PRML第三章习题答案Chapter 3. Linear Models for Regression⽬录更新⽇志(截⾄20210710)习题简述线性回归3.1:\text{tanh}可由\sigma线性变换得到3.2:最⼩⼆乘解为正交投影:加权最⼩⼆乘对应数据依赖的噪声或重复数据:带噪声的输⼊相当于权重正则,类别神经⽹络的数据增强:带权重正则的最⼩⼆乘等同于带约束优化:多元线性回归的极⼤似然估计3.7:权重的最⼤后验估计:线性回归的序列学习:利⽤⾼斯线性模型证明3.8:计算预测分布:证明后验⽅差随数据量增⼤⽽减⼩3.12:权重分布的共轭先验:证明基于 Gaussian-gamma 先验的权重分布的预测分布是 Student's t 分布:正交基函数诱导的等价核的性质经验贝叶斯-3.19:evidence 的对数似然:推导\alpha的优化过程:利⽤⾏列式对数的导数优化\alpha:推导\beta的优化过程:计算 evidence 的边际分布:⽤贝叶斯公式重新推导 3.23习题详解Exercise 3.3Hint.\begin{aligned} E_D(\mathbf{w}) &=\frac{1}{2}\sum^N_{n=1}r_n\|\mathbf{t}_n-W^T\phi(\mathbf{x}_n)\|^2_2\\ &=-\sum^N_{n=1}\ln\mathcal{N} (\mathbf{t}_n|W^T\phi(\mathbf{x}_n),r_n^{-1}I)+\text{const.} \end{aligned}第⼀个等号可以把r_n理解为样本权重,第⼆个等号可以把r_n理解为样本噪声的精度(precision)。

Comment.Exercise 3.4Solution.由于样本独⽴,噪声与输⼊独⽴,只需考虑⼀个样本的情形。

\begin{aligned} \underset{\epsilon}{\mathbb{E}}\left[(w^T(x+\epsilon)-t)^2\right] &= \underset{\epsilon}{\mathbb{E}}\left[((w^Tx-t)+w^T\epsilon)^2\right]\\ &=\underset{\epsilon}{\mathbb{E}}\left[(w^Tx-t)^2\right] + \underset{\epsilon}{\mathbb{E}}\left[(w^T\epsilon)(\epsilon^Tw)\right] + \underset{\epsilon}{\mathbb{E}}\left[ (w^Tx-t)w^T\epsilon\right]\\ &=(w^Tx-t)^2 + w^T\underset{\epsilon}{\mathbb{E}}\left[\epsilon\epsilon^T\right]w + (w^Tx-t)w^T\underset{\epsilon}{\mathbb{E}}\left[ \epsilon\right]\\ &=(w^Tx-t)^2 + \sigma^2 w^T w \end{aligned}Comment.该结论对多元输出的情形亦成⽴,只需⽤迹技巧展开 F-范数。

USP 641 Completeness of solution溶液澄清度

USP 641 Completeness of solution溶液澄清度

276〈631〉 Color and Achromicity / Physical Tests USP 36Matching Fluids nologies from being used, but this chapter provides guid-ance on how to qualify these analytical technologies for use Parts of Parts of as well as guidance on how to interpret instrument results Match-Cobaltous Ferric Parts of for use as a limit test.ing Chloride Chloride Cupric Parts of Apparatus commonly used to determine TOC in water for Fluid CS CS Sulfate CS Water pharmaceutical use have in common the objective of oxidiz-A0.10.40.1 4.4ing the organic molecules in the water to produce carbon B0.30.90.3 3.5dioxide followed by the measurement of the amount of car-C0.10.60.1 4.2bon dioxide produced. Then the amount of CO2 producedis determined and used to calculate the organic carbon con-D0.30.60.4 3.7centration in the water.E0.4 1.20.3 3.1All technologies must discriminate between the inorganic F0.3 1.20.0 3.5carbon, which may be present in the water from sources G0.5 1.20.2 3.1such as dissolved CO2 and bicarbonate, and the CO2 gener-H0.2 1.50.0 3.3ated from the oxidation of organic molecules in the sample.I0.4 2.20.1 2.3The discrimination may be accomplished either by deter-mining the inorganic carbon and subtracting it from the J0.4 3.50.1 1.0total carbon (total carbon is the sum of organic carbon and K0.5 4.50.00.0inorganic carbon), or by purging inorganic carbon from the L0.8 3.80.10.3sample before oxidation. While purging may entrain organic M0.1 2.00.1 2.8molecules, such purgeable organic carbon is present in neg-N0.0 4.90.10.0ligible quantities in water for pharmaceutical use.O0.1 4.80.10.0Apparatus Requirements—This test method is per-P0.20.40.1 4.3formed either as an on-line test or as an off-line laboratorytest using a calibrated instrument. The suitability of the ap-Q0.20.30.1 4.4paratus must be periodically demonstrated as described be-R0.30.40.2 4.1low. In addition, it must have a manufacturer’s specified S0.20.10.0 4.7limit of detection of 0.05mg of carbon per L (0.05ppm ofT0.50.50.4 3.6carbon) or lower.When testing water for quality control purposes, ensurethat the instrument and its data are under appropriate con-trol and that the sampling approaches and locations of bothon-line and off-line measurements are representative of thequality of the water used. The nature of the water produc-tion, distribution, and use should be considered when se-lecting either on-line or off-line measurement.〈641〉 COMPLETENESS OFUSP Reference Standards 〈11〉—USP 1,4-Benzoquinone SOLUTIONRS. USP Sucrose RS.Reagent Water—Use water having a TOC level of notmore than 0.10mg per L. [N OTE—A conductivity require-ment may be necessary to ensure method reliability.] Place the quantity of the substance specified in the indi-Container Preparation—Organic contamination of con-vidual monograph in a meticulously cleansed, glass-stop-tainers results in higher TOC values. Therefore, use labware pered, 10-mL glass cylinder approximately 13mm ×and containers that have been scrupulously cleaned of or-125mm in size. Using the solvent that is specified in the ganic residues. Any method that is effective in removing monograph or on the label of the product, fill the cylinder organic matter can be used (see Cleaning Glass Apparatus almost to the constriction at the neck. Shake gently to effect〈1051〉). Use Reagent Water for the final rinse.solution: the solution is not less clear than an equal volumeStandard Solution—Unless otherwise directed in the in-of the same solvent contained in a similar vessel and ex-dividual monograph, dissolve in the Reagent Water an accu-amined similarly.rately weighed quantity of USP Sucrose RS, to obtain a solu-tion having a concentration of 1.19mg of sucrose per L(0.50mg of carbon per L).System Suitability Solution—Dissolve in Reagent Wateran accurately weighed quantity of USP 1,4-Benzoquinone RSto obtain a solution having a concentration of 0.75mg per 〈643〉 TOTAL ORGANIC CARBONL (0.50mg of carbon per liter).Reagent Water Control—Use a suitable quantity of Rea-gent Water obtained at the same time as that used in thepreparation of the Standard Solution and the System Suitabil-Total organic carbon (TOC) is an indirect measure of or-ity Solution.ganic molecules present in pharmaceutical waters measuredWater Sample—Obtain an on-line or off-line sample that as carbon. Organic molecules are introduced into the watersuitably reflects the quality of water used.from the source water, from purification and distributionOther Control Solutions—Prepare appropriate reagent system materials, and from biofilm growing in the system.blank solutions or other specified solutions needed for estab-TOC can also be used as a process control attribute to mon-lishing the apparatus baseline or for calibration adjustments itor the performance of unit operations comprising the puri-following the manufacturer’s instructions, and run the ap-fication and distribution system. A TOC measurement is notpropriate blanks to zero the instrument, if necessary.a replacement test for endotoxin or microbiological control.While there can be a qualitative relationship between a food System Suitability—Test the Reagent Water Control in the source (TOC) and microbiological activity, there is no direct apparatus, and record the response, r W. Repeat the test us-numerical correlation.ing the Standard Solution, and record the response, r S. Cal-A number of acceptable methods exist for analyzing TOC.culate the corrected Standard Solution response, which is This chapter does not endorse, limit, or prevent any tech-also the limit response, by subtracting the Reagent Water。

阐述运动原因和效果的英文作文

阐述运动原因和效果的英文作文

阐述运动原因和效果的英文作文英文回答:Reasons for Exercise:There are several reasons why I choose to exercise regularly. Firstly, exercise is a great way to stay healthy and fit. It helps to improve cardiovascular health, strengthen muscles, and increase flexibility. Regular exercise also boosts the immune system and reduces the risk of developing chronic diseases such as heart disease, diabetes, and obesity.Secondly, exercise is a great stress reliever. Whenever I feel stressed or overwhelmed, going for a run or hitting the gym helps to clear my mind and release tension. It's like a natural mood booster that leaves me feeling refreshed and rejuvenated.Lastly, exercise is a social activity for me. Whetherit's joining a sports team, attending group fitness classes, or going for a hike with friends, exercising together creates a sense of camaraderie and makes the experiencemore enjoyable. It's a great way to meet new people and make lasting connections.Effects of Exercise:Regular exercise has had a positive impact on my lifein many ways. Firstly, it has significantly improved my physical health. I have noticed an increase in my energy levels and stamina. I no longer feel tired and sluggish throughout the day. My overall strength and endurance have also improved, allowing me to perform better in daily activities and sports.Exercise has also had a positive effect on my mental health. It has helped to reduce feelings of anxiety and depression. Whenever I engage in physical activity, I feela sense of accomplishment and satisfaction. It helps to boost my self-confidence and improve my overall mood. Exercise has become my go-to solution for managing stressand maintaining a positive mindset.Furthermore, exercise has helped me build strong relationships and create lasting memories. Whether it's participating in a charity run with friends or joining a sports team, exercising together has brought us closer and created a strong bond. It has provided us withopportunities to challenge ourselves, support each other, and celebrate our achievements together.Overall, exercise has become an essential part of my life. It not only keeps me physically fit but also helps me maintain a positive mindset and build meaningful relationships. It's a lifestyle choice that I will continue to prioritize for the rest of my life.中文回答:运动的原因:我选择经常锻炼的原因有几个。

大学英语(三)Unit 6 Passage A Exercise

大学英语(三)Unit 6  Passage A  Exercise

proud
She refused to accept help in changing a tire.
2. Find out more supporting details in the passage for the following statements, especially the underlinedlowing questions.
1) When did the author arrive in Cairo? At midnight.
2) Who was the author traveling with? ___________________
Answer:Men would smile and respectfully and kindly chat with her.
Answer:She invites goodwill from the people she meets.
3 . Fill each of the blanks with an appropriate word.
approach core counterpart economy efficient
exception invite relief punctually vague
1. The mayor is scheduled to meet his American (您未填写此题) during his 7-day visit to San Francisco.
1. We stop at a worn car.(Para. 4)
It has seen a better day.
Answer:There are quite a few scrapes on its body.

StudentSolutionManual

StudentSolutionManual

follows as:
r(t, T ) = − 1 ln P .
(3)
τ 100
Finally, to obtain the semi-annually compounded yield for the 1-year T-bill, use:
r2(0, 1) = 2 ×
1 (P /100)1/2

1
Yield Duration Modified Macaulay
a. 6.95%
3
3
2.8993
b. 6.28% 2.9542 2.9974 2.9061
c. 6.66% 0.9850 0.9850 0.9689
d. 0.00% 0.5
0.5
0.5
e. 6.82% 0.5111 0.5111 0.4943
Exercise 7.
Price Duration $ Duration
a. $89.56 4.55
$407.88
b. $67.63 -7.00 ($473.39)
c. $79.46 3.50
$277.74
d. $100.00 0.5
$50.00
e. $100.00 -$102.70 -0.2763 ($28.38)
a. $10 mn
b. Compute the dollar duration of the cash flows in each bond, and then the dollar duration of the portfolio:
Security 6yr IF @ 20% - fl quart
4yr fl 45bps semi 5yr zero Portfolio

高中英语七选五解题技巧课件(共36张)

高中英语七选五解题技巧课件(共36张)

03
Provide a sentence or paragraph with missing
information and ask students to fill in the missing part.
Characteristics of question types
1 Matching questions
总结词
提高学生解题技巧
详细描述
通过练习2017年全国卷I的题目,学生可以熟悉高考英语七选五的题型和难度, 提高解题技巧和答题速度。
Exercise 2: 2018 National Volume II
总结词
巩固所学知识
详细描述
通过练习2018年全国卷II的题目,学生可以巩固七选五阅读理解中的词汇、语法和阅读技巧,加深对文章的理 解和分析能力。
correct answer from the given choices.
True/False questions
02
Provide a statement and ask students to determine
whether it is true or false.
Fill in the blank questions
Identify the problem - Make sure you understand the problem and what information is needed to solve it.
Technique 2
Gather information - Search for relevant information that could help with the problem-solving process.

Unit+5+Into+the+Wild+词汇课件高中英语外研版(2019)必修第一册

Unit+5+Into+the+Wild+词汇课件高中英语外研版(2019)必修第一册
• 【常与to搭配的名词有: key(关键), answer, approach, way(路), entrance, visit, success】
• solve v. 解决 同义词有: __s_e_t_tl_e_=_d_e_a_l_w_i_th__=_h_a_n_d_le_=__a_d_d_re_s_s__________
• 4.measure [ˈmeʒə(r)] v. 测量,衡量 ;某物体积/长度为..

n.措施,办法
• take measures to do sth_采__取_措__施__做__某__事____
• take effective measures_采__取__有__效__措_施______
• 【高考真题】They have reduced pollution through effective measures . (2014全国卷II)
2019年全国卷2 阅读D 原文
Exercise
• 1. As usual, she found a practical _s_o_lu_t_io_n_ (solve) to the difficult problem.
• 2. They are arguing with their classmates about the solution __t_o___ the quiz(智力游戏).
B1U5重点单词
Come on
• 1.annual [ˈænjuəl] adj.一年一度的,每年的
• 【教材金句】This annual movement is called migration.
• 【高考真题】Earth Day, which is on 22 April, is an annual event aiming to raise public awareness about environmental protection.(2019北京卷)

IMA案例分析题样题答案

IMA案例分析题样题答案

Solution or Key Points:1.1.Solution•Descriptions of the five responsibilities of the management accountant,as well as examples of practices and techniques of each,include the following:o Planning.The manager gains an understanding of the impact on the organization of planned transactions(i.e.,analyzing strengths and weaknesses)and economic events,both strategic and tactical,and sets obtainable goals for the organization.Thedevelopment of budgets in a bottom-up or top-down approach for both the short and longterm is an example of planning.o Evaluating.The manager judges and analyzes the implication of various past and expected events,and then chooses the optimum course of action.The manager alsotranslates data and communicates the conclusions.Graphical analysis(such as trend,barcharts,or regression)and net present value analysis are examples of evaluating.o Controlling.The manager ensures the integrity of financial information,monitors performance against budgets and goals,and provides information internally for decisionmaking.The successful implementation of internal control procedures is an example ofcontrolling.o Accountability.The manager implements a reporting system closely aligned to organizational goals that contributes to the measurement of the effective use of resourcesand safeguarding of assets.Internal reporting,such as comparisons of actuals to budget,is an example of accountability.o External reporting.The manager prepares reports in accordance with generally accepted accounting principles and then disseminates this information to shareholders(both current and potential),creditors,and regulatory and tax agencies.An annual reportor a credit application are examples of external reporting.Solution or Key Points:2.2.SolutionIn referring to the general roles of managers,a.Two interpersonal roles include acting as a1.Leader who hires,trains,motivates employees by integrating individual andorganization goals by using effective communication2.Liaison who deals with people outside the organizationb.Two informational roles include acting as a1.Monitor who seeks information about other internal departments,the externalenvironment,and other organizations2.Disseminator who communicates outside information internally,and internalinformation to the subordinates,while exercising judgment so there is minimalinformation overloadc.Three decisional roles include acting as a1.Negotiator between subordinates,suppliers,contracts,and union2.Resource allocator who distributes funds,equipment,time,etc.,in accordancewith organizational objectives3.Disturbance handler who solves issues of conflict within and without theorganizationSolution or Key Points:3.3.SolutionFor the original organizational structure proposed by Donald Jenkins,a.Advantages include1.Centralized decision making2.Close supervision of subordinates3.Increased opportunities for promotionDisadvantages includeck of flexibility/creativity5.More difficult vertical communication6.Increased costs for additional management personnelb.The span of control will1.Allow for tighter control over employees2.Afford timelier task completion and problem resolution,as the supervisors arecloser to everyday operationsc.As a result of the organizational structure proposed by Donald Jenkins,the employees arelikely to have a clear understanding of what is expected of them.However,because of thetighter span of control,the employees may avoid making decisions and taking risks. Solution or Key Points:4.4.SolutionAn informal group is a number of individuals attracted to one another by common geography,identity, values,and/or goals.The group identifies,then enforces,a set of behavior standards via sanctions and rewards.The informal group exists supplementary to the formal management system within which it is normally found.Solution or Key Points:5.5.SolutionThe working environment where it would be most appropriate to use the task-oriented and relationship-oriented leadership styles,respectively,are as follows:a.The task-oriented leadership style,to some extent,is necessary to make all work groupsfunction effectively.It is usually used where the job is repetitive,under time pressure,andrequires accuracy.b.The relationship-oriented leadership style is used when the work environment is open orunstructured,or the methodology for accomplishing a task is loosely defined and theexercise of judgment is important.Solution or Key Points:6.6.SolutionAccording to Maslow’s theory of motivation,human needs exist in a hierarchy of importance,namely, physiological,security,social,esteem,and self-actualization.Once the first level of physiologicalneeds is satisfied,the individual is no longer motivated by them and moves to the next level.The process continues until the individual reaches self-actualization.a.Unions are often associated with the ability to satisfy the lower level needs by providingcompetitive salaries,safe working conditions,job security,and social belonging.Itappears that these needs were already being satisfied at Spokane Computer Associates,as salaries were relatively high,there was little turnover,and the plant was considered asafe and pleasant place to work.b.The products at Pullman were successful and sold without much effort on the part of thesalespeople.As a result,the salespeople were doing well financially,and their lowerneeds were satisfied.By offering the top performers recognition,the firm was appealing tothem through a higher level motivator,esteem.The salespeople were motivated toincrease sales by the need for recognition and respect from their peers and others.c.Zach Chaudry is leaving Midwest Electronics to accept a teaching and research positionat the university to satisfy the highest level need,self-actualization.In this new position,Chaudry will have the opportunity to control his own research.Solution or Key Points:7.7.Solutiona.The need categories most often associated with professional employees are esteem and self-actualization,since the lower level needs are usually satisfied by professional employment and are no longer motivators(satisficers).b.The need categories most often associated with assembly-line workers(skilled labor)are thephysiological,safety,and social needs.The physiological and safety needs are usually satisfied by employment and are no longer motivators(satisficers).The social needs such as acceptance and affiliation must continue to be fulfilled.Solution or Key Points:8.8.SolutionAt least three general purposes of organizational communication are to1.Integrate efforts of employees2.Build a community of employees with high morale and mutual trust3.Acquire and disseminate informationSolution or Key Points:9.9.Solutiona.Four personal characteristics,attributable to both senders and receivers,that can causecommunications problems include1.Listening problems resulting from the receiver misunderstanding the intended message2.Poor channel or media selection,e.g.,sender has chosen a communication carrier that does notget to the receivers,or faulty encoding,e.g.,the use of jargon3.The influence that knowledge level,attitude(lack of interest),and background(demographics)will play in sending and receiving an effective message4.Interpersonal dynamics and emotions,including trust in the senderb.Three organizational characteristics that may be barriers to effective communications includeanizational status and power differences,e.g.,lower levels reluctant to communicate withupper levels or upper level perception that lower levels have little to contributeck of formal channels,i.e.,organization must provide adequate upward,downward,andhorizontal communications in the form of surveys,open-door policies,newsletters,memos,task force,and liaison personnel3.Departmental needs and goals;each one views problems and needs in its own termsSolution or Key Points:10.Solution10.a.Responsibility accounting is a system that recognizes various decision or responsibility centersthroughout an organization,and reflects the plans and actions of each of these centers by assigning responsibility for particular revenues and costs(as well as assets and liabilities where pertinent)to the individual managers primarily responsible for making decisions about these revenues and costs.Costs are classified into controllable and non-controllable categories with the responsibility center only charged with costs under its control.b.The advantages a company attains through the use of responsibility accounting include thefollowing:1.Participation in the planning process enhances the acceptance and achievability of the guidelinesestablished by the company.2.Responsibility plans provide clear guidelines to managers for day-to-day decisions and freemanagement from daily operations.3.More involvement will lead to better decision making.c.The use of responsibility accounting is advantageous to the managers in the following ways:1.Responsibility accounting facilitates delegation of decision-making and,therefore,managers areafforded greater freedom of action without daily supervision.This results in greater job satisfaction and higher motivation to improve performance.2.Managers are aware of the basis of their performance evaluations.Solution or Key Points:11.Solution11.The major disadvantages in the procedures employed by Rouge Corporation in preparing and implementing the divisional budgets include the following:a.The procedure is top-down versus a bottom-up approach.The budget is prepared by topmanagement and imposed on the divisions.The divisions do not participate in the budgetpreparation.This lack of participation inhibits goal congruence.b.Corporate management says differences between divisions are factored into the budgetprocess.However,problems unique to each division are best recognized by divisionmanagers.These managers should be allowed to communicate problems to topmanagement.Additionally,division managers should be allowed to suggest modificationsto the budget during the budget period.c.The budget is not flexible.The budget is set for the entire year and is not modified ascircumstances change.Solution or Key Points:12.12.SolutionMultiple performance evaluation criteria would be appropriate for the evaluation for the Star Paper Division.The criteria suggested by George Harris would take into account more of the results of the key decisions being made by the manager,are not conflicting,and emphasize the balance of profits with the control of current assets.These three measures are controllable by the manager and,in conjunction with ROA,would be more representative of the success of the business.Solution or Key Points:13.Solution13.Corporate management has established an environment in which there is an incompatibility(lack of goal congruence)between the achievement of corporate objectives and personal ethics.Under the current situation,severe penalties have been imposed by top management whenever subordinates do not achieve the high levels of performance established by the predetermined objectives.This has caused lower level management to take unethical courses of action.Corporate management apparently utilizes an authoritarian,nonparticipative management style which does not consider contributions from lower level management.As a result of this type of management style,top management may have established unreasonable expectations and may not recognize the need to change the expectations in light of changing circumstances.These factors may result in subordinates choosing any means to reach the objectives.The penalty and reward system appears to be inappropriate.There is no positive feedback or encouragement for effective performance and the penalties are heavy for failure to meet objectives.No code of ethics exists,and penalties are apparently nonexistent or minor for violation of acceptable business practices that are compatible with personal ethical standards.Solution or Key Points:14.14.SolutionAdam Williams should follow the established policies of the organization bearing on the resolution of such conflict.If these policies do not resolve the ethical conflict,Williams should report the problem to successively higher levels of management up to the board of directors until it is satisfactorily resolved.There is no requirement for Williams to inform his immediate superior of this action because he isinvolved in the conflict.If the conflict is not resolved after exhausting all course of internal review, Williams may have no other recourse than to resign from the organization and submit an informative memorandum to an appropriate member of the organization.15.Solution or Key Points:15.SolutionActivities in which JLS could engage to meet a social responsibility with respect to the three areas identified include the following:a.Human resources1.Contribute to the educational development of people through improved trainingand career advancement programs for current employees2.Provide for the well-being of employees by maintaining safe working conditionsb.Physical resources and environmental contributions1.Contribute to improvement in the environment by reducing company pollution ofair and water2.Contribute to energy conservation by taking the lead in promoting community-wide energy conservationc.Product or service contributions1.Design and manufacture safe or better quality products2.Respond quickly to customer complaints3.Develop clear and concise labels and instructions for product usesSolution or Key Points:16.16.SolutionThe arrangements made by Farbell and Cross&Gill exceeded the activities normally performed by an internal auditor for the external auditor and thus should be considered unethical.The external auditor gave up too much responsibility,and Farbell should not have agreed to such a proposal as it diminishes the value of the audit.Internal auditors can assist in performing substantive tests or tests of compliance,but their competence and objectivity must be considered,and the work must be supervised and tested.。

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Exercise Four: Monetary Approach to Balance of Payments and the others1. According to the equation (4.24), find out the (short-run) effect of the following cases on the balance of payment ( overall balance )? Assume that nominal GDP is initially $100 billion. (foreign price level is fixed)1) The central bank decreases domestic credit by 1%.2) Domestic output grows by $1 billion.Answer: the equation (4.24) is C D Y P E R EF ˆˆˆˆˆ*-+=- 1) When the central bank decreases domestic credit by 1%, it means %1ˆ-=C D, then the change of the balance of payment depends on the exchange rate regime. In case a, the exchange rate is fixed, then the FER must increases by 1%, which relates to an improvement of overall balance. In case b, the exchange rate is flexible, then the FER remains and the overall balance is kept because the exchange rate will absorb all the shock.2) When domestic output grows by $1 billion, Y increases by 1%. Also there are two possible scenarios. In the environment of fixed exchange rate, the FER must increases by 1% and then the improvement of overall balance. In case of flexible exchange rate there will be the same result as 1).2. Think of the Monetary Approach to Balance of Payments, the difference in money market (disequilibrium) will result in the Balance of Payments. So the balance ofpayments could be expressed as the function of the gap between the actual current money supply, M, and desired (long-run) money, M d . And M d is proportional to nominal GDP. PY vM M M FER d d 1),(=--=∆δ 1) Using BP to represent the balance of payments, which is equal to the nominal trade balance in the assumed absence of capital flows, express it as a function of M and PY. What is the effect of ∆M on ∆BP, and why?Answer: The balance of payments is equal toBP = -δ(M -(1/ν)PY)An increase in the money supply will then lead to a balance of payments deficit. This occurs because there is an excess supply of money, some of which is spent abroad.2) Ass ume P=EP*, then what is the effect of a devaluation ∆E, on the balance of payments in the short run? In the long run?Answer: BP = -δ(M -(1/ν)EP *Y)In the short run, ∆BP/∆E = (δ/ν)P *Y > 0, thus a devaluation results in an increase in BP. In the long run, the balance-of-payments surplus means that the money supply isincreasing. Since ∆BP/∆M = -δ < 0, this increase in the money supply reduces BP until BP = 0.3. Multiple Choice.1) Under floating exchange rates, the exchange rate adjusts such that(a) the central bank has met all excess demand or foreign exchange.(b) there is a balance of payments deficit after a devaluation.(c) the economy is at a full employment output level.(d) the central bank must exhaust its foreign exchange reserves.(e) the balance of payments is zero.Answer: (e)2) Which of the following are expenditure-switching policies?(a) Price deflation.(b) Import tariffs.(c) Direct barriers to trade.(d) All of the above.(e) (b) and (c) only.Answer: (d)3) Internal balance is a situation where(a) trade is balanced.(b) output exceeds potential output(c) national savings is zero.(d) output is at the full-employment level.(e) none of the above.Answer: (d)4) The assignment problem refers to the(a) the problem determining whether a policy is expenditure-switching or expenditurereducing.(b) the problem determining whether more output leaks out of an economy through savingsor the trade deficit.(c) the problem determining which part of government, the central bank (with control overthe exchange rate) or the treasury (with control over fiscal policy), is responsible forinternal balance.(d) the problem assigning the cause of a trade deficit as crowding-out or a devaluation.(e) none of the above.Answer: (c)5) The term “sterilization” in the monetary approach to the balance of payments refers to(a) changes in the price level.(b) changes in the money supply.(c) the effects of money supply changes on the exchange rate.(d) central bank actions that prevent reserve changes from altering the monetary base.(e) none of the above.Answer: (d)6) If a country’s international reserves fall by $200 million, and their net domestic assetsincreasesby $100 million, then there will be a change in the balance of payments of(a) $100 million.(b) $200 million.(c) 0.(d) -$100 million.(e) -$200 million.Answer: (e)7) A central bank wishes to sterilize a reserve outflow. Which of the following achieve thisgoal?(a) Expand net domestic assets at the same rate as the reserve outflow is contracting themoney supply.(b) Reduce net domestic assets at the same rate as the reserve outflow is expanding themoney supply.(c) Use open market operations to sell treasury securities on the private market.(d) Use open market operations to reduce domestic money supply.(e) Enlist the help of the fiscal branch to create expenditure-switching activities.Answer: (a)8) In the monetarist small-country model, an exogenous increase in the world price level(a) leads to a higher domestic price level, an increase in domestic money demand and atemporary balance-of-payments surplus.(b) leads to changes in the domestic economy through changes in relative prices as in theelasticity approach.(c) leads to a lower domestic price level, a decrease in domestic money demand and atemporary balance-of-payments surplus.(d) leads to a higher domestic price level, an decrease in domestic money demand and atemporary balance-of-payments deficit.(e) (a) and (b).Answer: (a)。

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