★★★★ Detailed Solution to Midterm Examination (Int'l Business, WUCL) ★★★★
Spring 2009 Instructor: 衛忠欣 (Jong-Shin Wei)
總體經濟學原理 (Principles of Macroeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw jsw12011958@gmail.com
3:10 pm ~ 4:40 pm, April 20, 2009
Open books/notes exam. 105 points in 90 minutes; absolutely no talking nor borrowing items during exams. 可使用自己的資料、字典或翻譯機。行動電話若響起，該生扣十分、以強調基本禮貌。務必工整依序作答。平時上課頻尿的極少數同學，考試時，切勿改變習慣。理由一：有害健康；理由二：迫使教師合理懷疑平時是否謊報。只是題目很多，目的在於測試是否有平日閱讀原文書之習慣。Watch your time and have fun!
Part One: 30 Multiple choice questions. [By multiple choice in an English-speaking academic environment, we mean that you must choose the most appropriate one from 4 alternatives. 依慣例，答錯不倒扣！] 75 points
1. Before taking externality into consideration, we know that demand for aluminum is P + Q = 10; supply of aluminum is 2P - Q = 8. At equilibrium, P* =
(A) 4;
(B) 6;
(C) 5;
(D) None of the above is correct.
Ans: B. [By 10 - P = 2P - 8 we have P* = 6 and Q* = 4.]
2. [continued from question 1] Q* =
(A) 4;
(B) 5;
(C) 6;
(D) None of the above is correct.
Ans: A.
3. [continued from question 1] The market allocates resources in a way that maximizes the total value to the consumers who buy and use aluminum minus the total costs to the producers who make and sell aluminum. Here, the maximized value is
(A) 12 (dollars);
(B) 10;
(C) 8;
(D) 6.
Ans: A. [Recall that CS + PS is the area of the triangle with vertex points (0, 4), (0, 10), and (4, 6), which is 4(10 - 4)/2 = 12.]
4. [continued from question 3] Here, the insight is
(A) Governments can sometimes improve market outcomes;
(B) Markets are usually a good way to organize economic activity;
(C) Sometimes we have government failure;
(D) There is no such thing as a free lunch.
Ans: B. [See p.203, text]
5. [continued from question 1] We now take negative externality into consideration. Suppose that the new supply (curve) of aluminum becomes 2P - Q = 10 while the demand for aluminum remains the same. This suggests that producing each unit of aluminum adds external cost to the society in the amount of
(A) 4 (dollars);
(B) 3;
(C) 2;
(D) 1.
Ans: D. [From P = 0.5Q + 4 to P = 0.5Q + 5]
6. [continued from question 5] The new equilibrium price is
(A) 19/3;
(B) 20/3;
(C) 6;
(D) 5.
Ans: B. [From P + Q = 10 and 2P - Q = 10 we obtain P** = 20/3 and Q** = 10/3.]
7. [continued from question 5] The new equilibrium quantity is
(A) 5;
(B) 4;
(C) 10/3;
(D) 11/3.
Ans: C.
8. [continued from question 5] Now CS + PS equals
(A) 12;
(B) 11;
(C) 10;
(D) None of the above is correct.
Ans: D. [It is (10/3)(10 - 5)/2 = 25/3.]
9. [continued from question 5] The social planner can achieve the optimal outcome (i.e., less aluminum at higher price) by
(A) subsidizing aluminum producers;
(B) increasing the number of aluminum producers;
(C) taxing aluminum producers;
(D) letting the invisible hand take full charge.
Ans: C. [See p.207, text]
10. Examples of internalizing the externality do not include
(A) 教師優先向授課中途尿遁的同學提問；
(B) 教師優先向授課中途伏案沉思的同學提問；
(C) 教師故意找勇於發言(even not appropriate sometimes)的同學提問；
(D) 班代呼籲同學在 red vs. green 加分題 (see the extra credits question)，一致採取某一行動。
Ans: D.
*11. Professors are hired by universities to provide teaching service for students who pay the tuition and fees in advance. Under such a contract, university administration also legitimately reviews professors’ performance based on teaching evaluations made by students. The resulting externalities do not include
(A) Professors tend to inflate grades, hence lower the reputation of the university;
(B) Students tend to demand easy grades (and easy courses) from professors;
(C) Professors with better evaluation scores may get a pay raise;
(D) Professors tend to put more effort on their own research and outside connection.
Ans: C. [Recall the definition of externalities]
*12. 如果宣導兩性(平權)教育的校外公益團體，在活動中免費發送保險套。其「外部性」包含
(A) 節省同學 (those who are sexually active) 的開支；
(B) 導致若干同學產生性衝動、嘗試性行為；
(C) 活動相關人員因此受懲處；
(D) 未婚懷孕案件數目下降。
Ans: B. [誰說經濟學很抽象？]
13. 如果學校禁止「身上有煙味、有狐臭、香水味道過重、剛吃完大蒜」的人員，使用電梯，此一規定
(A) 愚蠢；
(B) 反映對「外部性」之處理；
(C) 符合成本效益原則；
(D) 弘揚教義。
Ans: A. [Obvious]
14. The social planner recognizes the positive externalities in education. Hence, the planner will draw the demand curve by shifting up the original demand curve while keeping the supply curve unchanged. This justifies
(A) private schools being superior to public schools;
(B) public schools being superior to private schools;
(C) heavy subsidization made by governments;
(D) heavy taxation made by governments.
Ans: C. [See p.207, text]
15. If governments suddenly reduce subsidies in education, the initial impact will not include
(A) (average) price of education falls;
(B) level of education (in terms of the number of students receiving education) falls;
(C) positive externalities of education are diminishing;
(D) the economy achieves social optimum.
Ans: D. [See pp.207-8, text]
16. Ever wonder why most people do not litter? There are laws against it, yet these laws are not vigorously enforced. The old saying, “Do unto others as you would have them do unto you,” actually
(A) does not make sense to economists;
(B) is a good example of internalizing externalities as a private solution;
(C) is the opposite of internalizing externalities;
(D) shows the failure of government operation.
Ans: B. [See p.209, text]
*17. Bob owns a dog who barks at night and drives his neighbor Cindy crazy. Suppose that Bob gets $500 benefit from having that dog; Cindy bears $800 cost from the barking. Which one of the following is incorrect?
(A) Since cost (800) exceeds benefit (500), Bob should get rid of that dog, leading to social optimum;
(B) If Bob has the legal right to keep a barking dog while Cindy does not have the right to have a quiet night, then Cindy can pay Bob to get rid of that dog, leading to social optimum;
(C) If Cindy has legal right to have a quiet night while Bob does not have the right to keep a barking dog, then Bob must get rid of his dog, leading to social optimum;
(D) If Bob does not have the legal right to keep a barking dog and Cindy does not have the right to have a quiet night, then Cindy can still pay Bob to get rid of that dog, leading to social optimum.
Ans: A. [See pp.210-211, text. The key is Coase theorem.]
18. Question 17 illustrates a major contribution by R. Coase, namely,
(A) Cost-benefit analysis always works;
(B) Bargaining always works even at the presence of transaction costs;
(C) At zero transaction cost, private parties can bargain and lead to social optimum regardless of the initial distribution of property rights;
(D) Different initial distributions of property rights have no influence over final outcomes.
Ans: C. [See pp.210-211, text]
19. Economists argue that clean air and clean water
(A) obey the law of demand and have positive income effect;
(B) obey the law of demand and have negative income effect;
(C) violate the law of demand but have positive income effect;
(D) violate the law of demand and have negative income effect.
Ans: A. [See p.219, text]
20. Goods that are excludable but not rival in consumption include
(A) fish in the ocean;
(B) singing at KTV;
(C) using cable TV service;
(D) driving on congested toll roads.
Ans: C. [See p.224, text]
21. What public goods and common resources have in common is
(A) non-excludability;
(B) rivalry in consumption;
(C) low price;
(D) violating the law of demand.
Ans: A. [See p.224, text]
22. What common resources and private goods have in common is
(A) excludability;
(B) rivalry in consumption;
(C) low price;
(D) violating the law of demand.
Ans: B. [See p.224, text]
23. The free rider problem occurs with
(A) public goods but not with common resources;
(B) common resources but not with public goods;
(C) both public goods and common resources;
(D) goods that are non-rival in consumption.
Ans: C. [Non-excludability is the key]
24. 在全面點名的現況下，如果眾多同學任意翹課，事後(因為沒有擔當而)請假，教師不得已開始嚴格核假，此乃
(A) 莫非定律；
(B) 骨牌效應；
(C) 月暈效應；
(D) the tragedy of the commons.
Ans: D. [See p.231, text]
25. “What is common to many is taken least care of, for all men have greater regard for what is their own than for what they process in common with others,” was said by
(A) Socrates;
(B) Aristotle;
(C) Plato;
(D) V. Pareto.
Ans: B. [See p.230, text. Just want to find out who did not read the text page by page.]
26. A nice example of avoiding or resolving the tragedy of the commons is
(A) 國人習於構築籬笆或矮牆，圍成私人庭院；
(B) 系辦公室中午不開放；
(C) 系資源教室中午不開放；
(D) 社區球場夜間不開放。
Ans: A. [See p.231, text]
27. Last year Henry bought a made-in-Taiwan air-conditioner. It was included in the computation of last year’s GDP, along with
(A) Henry’s income tax collected by the government;
(B) Henry’s spending on building a new plant for a business at which he is an entrepreneur;
(C) Henry’s payment for speeding tickets;
(D) Henry’s mortgage loan payment.
Ans: B. [GDP := C + I + G.]
28. Find the correct statement about 消費券。
(A) The English term is consumption ticket;
(B) The English term is spending bonus;
(C) It increased the aggregate consumption (demand);
(D) It increased the money supply.
Ans: C. [Consumption voucher is the correct term.]
29. The circular flow diagram does not explain
(A) how prices are determined;
(B) what are in GDP;
(C) why economists often say that it takes two to tango;
(D) how savings and investment are related.
Ans: A. [It is called a fixed-price model.]
30. Pigovian tax may be inferior to setting up the pollution permit if
(A) producers have self-interest in mind;
(B) producers do not care about externalities;
(C) reducing pollution is costly;
(D) governments do not know the demand for pollution.
Ans: D.
Part Two: Analytical questions. [注意字體工整、邏輯順暢與不要出現錯別字或注音(與火星文)！如果字跡難以辨認，視同未答。畫蛇添足、答非所問、不知所云、自曝其短，將不利得分。教師也有權公告具有特色之作答。] 30 points
31. There are three industrial firms in Smog Valley, A, B, and C. The initial pollution level for A is 70 units; for B is 80 units; for C is 50 units. Under the current technology, the cost of reducing pollution by one unit is $30 for A; $25 for B; $10 for C. At present, the government gives each firm 50 tradable pollution permits.
Firm C proposes to sell 20 units of permits to firm A; sell 30 units of permits to B. For each permit sold, firm C has for $20. Explain why A and B agree to trade with C. Will this trading be socially optimal? Carefully justify your answers.
Ans: For A, -400 > -600; for B, -600 > -750; for C, 500 > 0. That is, two trades proposed by C will make each of these three firms better off. Since the total pollution level is still kept at 150, we can call it socially optimal.
32. 如果國家公園 (e.g., Grand Canyon) 一方面大幅提高門票價格，也同時提供當地居民優惠入場。理由為何？
Ans: skipped.
33. 文藻要求所有課程皆要點名，其立意是要求同學養成認真到課之好習慣。
(i) 此規定有那些「外部性」？
(ii) 針對你(妳)在 (i) 的一個答案，提出 “internalizing the externality” 之具體作法。
Ans: skipped.
Extra credits question (bonus range: 0 ~ 6 points)
red vs. green -- 選紅球呢？還是選綠球？規則如下：
如果在你(妳)以外的相對多數選的是紅球，你(妳)正好也選紅球，你(妳)會被加 5分。
如果在你(妳)以外的相對多數選的是綠球，你(妳)正好也選綠球，你(妳)會被加 2分。
如果在你(妳)以外的相對多數選的是紅球，而你(妳)卻選綠球，你(妳)會被加6 分。
如果在你(妳)以外的相對多數選的是綠球，而你(妳)卻選紅球，你(妳)會被加0 分。
Now make your pick.
Result: 40 GREENs and 14 REDs. In a way, we can say that we have the so-called prisoners’ dilemma here.
(撰寫試題無著作權；歡迎全貌下載流傳。)
Wednesday, April 22, 2009
Solution to Midterm Exam (Math for Mgmt) Spring 2009
★★★ Detailed Solution to Midterm Examination (Int’l Business, WUCL) ★★★
Spring 2009 Instructor: 衛忠欣 (Jong-Shin Wei)
管理數學 (Mathematics for Management) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw jsw12011958@gmail.com
3:10 pm ~ 4:40 pm, April 22, 2009
Open books/notes exam. 110 points in 90 minutes; absolutely no talking nor borrowing items during exams. 可使用自己的資料、字典或翻譯機。行動電話若響起，該生扣十分、以強調基本禮貌。務必工整依序作答。平時上課頻尿的極少數同學，考試時，切勿改變習慣。理由一：有害健康；理由二：迫使教師合理懷疑平時是否謊報。只是題目很多，目的在於測試是否有平日閱讀英文資料之習慣。Watch your time and have fun!
Part One: 30 Multiple choice questions. [By multiple choice in an English-speaking academic environment, we mean that you must choose the most appropriate one from 4 alternatives. 依慣例，答錯不倒扣！] 90 points (別懷疑，看看誰是實力派！)
1. Once upon a time in Utopia a small kingdom was ruled by The Mighty King Richard (李察王). The actual weight of King Richard was way over 80 kg but he insisted that his weight was only 60 kg. One day, John, who was his prime minister, joked about it, “My Lord, I have no problem with your weight record. Yet, if your weight is 60 kg, some child might have zero in weight.” Since the King was also good in mathematics, he immediately found a flaw in John’s statement. Which of the following made the King detect the flaw?
(A)E = mc2;
(B)畢氏定理；
(C)兩條平行線永不相交；
(D)A:B = C:D.
Ans: D. [Recall lectures. Now we can see who actually paid attention to lectures.]
2. There are twenty basketball teams. Each team must play exactly one game with the rest 19 teams. How many games will be played in total?
(A) 200;
(B) 190;
(C) 400;
(D) None of the above is correct.
Ans: B. [Recall lectures. Note that (20)(20 - 1)/2 = 190.]
3. Let f be a function mapping from R to R, defined by f(x) := x(superscript 3). Find the incorrect statement.
(A) The graph is convex-shaped;
(B) It has no local minimum;
(C) It has no local maximum;
(D) df(x)/dx = 0 at x = 0 only;
Ans: A. [For non-negative x, it is convex-shaped; for non-positive x, it is concave-shaped.]
4. Let f be a function mapping from R to R, defined by f(x) := x(superscript 3).
(A) d(superscrpt 2)f(x)/dx(superscript 2) < 0 for all x;
(B) d(superscrpt 2)f(x)/dx(superscript 2) ≧ 0 for all x;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 only when x = 0;
(D) d(superscrpt 2)f(x)/dx(superscript 2) is not defined at x = 0.
Ans: C. [Obviously, d2f(x)/dx2 > 0 for all x > 0; d(superscrpt 2)f(x)/dx(superscript 2) < 0 for all x < 0; d(superscrpt 2)f(x)/dx(superscript 2) = 0 when x = 0.]
5. Let f be a function mapping from R to R, defined by f(x) := ∣x∣. The graph of f
(A) looks like the English letter V;
(B) is a straight line;
(C) looks like the putting the letter V upside down;
(D) is not in one piece.
Ans: A.
6. Let f be a function mapping from R to R, defined by f(x) := ∣x∣. We know that d2f(x)/dx2
(A) > 0 for all x > 0;
(B) < 0 for all x < 0;
(C) = 0 when x = 0;
(D) = 0 for all non-zero x.
Ans: D. [The function is not differentiable at x = 0.]
7. Let f be a function mapping from R to R, defined by f(x) := ∣x∣.
(A) f has a local minimum but no global minimum;
(B) f has a global minimum but no local minimum;
(C) f has neither local minimum nor global minimum;
(D) None of the above is correct.
Ans: B. [Clearly, f(0) < f(x) for all x ≠ 0.]
8. Recall that a relation can be a function. Which of the following is the graph of some function?
(A) {(a, 1), (b, 2), (a, 2), (c, 3)};
(B) {(1, (0, 0)), (2, (0, 1)), (3, (0, 2), …};
(C) {(x, y) of R (superscript 2): x (superscript 2) + y (superscript 2) = 1};
(D) {(x, y) of R (superscript 2): y = x or y = -x}.
Ans: B. [Recall lectures]
9. English teacher asks each student to pick his/her favorite English first name. This is a well-known way of illustrating the notion of functions. Here
(A) the set of all students is the domain of this function;
(B) the set of all English first names is the domain of this function;
(C) the graph of this function has more elements than the domain has;
(D) this function is a real-valued function.
Ans: A. [Recall lectures]
10. Which of the following cannot serve as an application of equation x + y = 1?
(A) price-taking consumer’s budget line;
(B) production possibility frontier;
(C) demand curve;
(D) money supply curve.
Ans: D.
*11. Let f be a function mapping from R to R, defined by f(x) := 1 if x is rational (有理數); -1 if x is irrational (無理數).
(A) The function f is continuous but not differentiable;
(B) For any real number x, f(x) is either a global maximum or a global minimum (but not both);
(C) For any real number x, f(x) is either a local maximum or a local minimum (but not both);
(D) Neither global maximum nor global minimum exist for this function.
Ans: B.
12. Let f be a function defined as follows. f(x) := A if x belongs to [80, 100]; f(x) := B if x belongs to [70, 79]; f(x) := C if x belongs to [60, 69]; f(x) := F if x belongs to [0, 59]. Here,
(A) the domain of f is R;
(B) the range of f is R;
(C) f is not a real-valued function;
(D) f has a (global) maximum.
Ans: C.
13. On the x-y space, if we draw the graph of some function in a “continuous” way (一筆畫出來), then this function
(A) must be differentiable;
(B) must be continuous;
(C) must have at least one local maximum;
(D) must have the global maximum.
Ans: B. [Trivial]
14. The demand schedule is given as follows, P = 1, Q = 9; P = 2, Q = 8; P = 3, Q = 7; P = 4, Q = 6; P = 5, Q = 5; P = 6, Q = 4. We know nothing else. The price elasticity of demand
(A) is -1 at P = 5;
(B) is 1 at P = 5;
(C) is increasing as P goes up;
(D) is not defined here.
Ans: D. [Recall lectures]
15. Let f be a function mapping from an open interval in R to R such that d2f(x)/dx2 < 0 holds for all x. We know that
(A) df(x)/dx < 0 holds for all x;
(B) df(x)/dx > 0 holds for all x;
(C) df(x)/dx ≠ 0 holds for all x;
(D) df(x)/dx is a decreasing function of x.
Ans: D.
*16. Let f be a function mapping from an open interval in R to R such that
d(superscrpt 2)f(x)/dx(superscript 2) ≦ 0 holds for all x (in the domain). We know that
(A) if f has a local maximum at x*, then f(x*) is the global maximum;
(B) f must have at least one local maximum;
(C) f can be maximized;
(D) f cannot have any local minimum.
Ans: A. [Note that (B) and (C) are false in light of the case where df(x)/dx > 0. We eliminate (D) by considering the case where f is a constant function.]
*17. Let f be a function mapping from an open interval in R to R such that (1)
df(x)/dx = 0 at some x* in the domain, and (2) d(superscrpt 2)f(x)/dx(superscript 2)≦ 0 holds for all x. We know that
(A) f cannot have a local minimum at x*;
(B) f(x*) cannot be the global minimum;
(C) there exists no x** satisfying x** ≠ x* and df(x)/dx = 0 holds for x**;
(D) f has a local maximum at x* and that f(x*) is the global maximum.
Ans: D.
18. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := (x) (superscript 0.5) for all x. Then
(A) df(x)/dx > 0 for all x in the domain;
(B) df(x)/dx is defined everywhere but at x = 0;
(C) d2f(x)/dx2 < 0 for all x in the domain;
(D) f is not concave-shaped.
Ans: B. [是在幫忙複習微積分嗎？ Well, it is on the house.]
19. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := 2x + 3 for all x. Then
(A) df(x)/dx > 0 for all x in the domain;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 for all x in the domain;
(D) f cannot be maximized.
Ans: D.
20. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := Min{x, 100} for all x. Then
(A) df(x)/dx > 0 for all x > 0;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 for all x > 0 and x ≠ 100;
(D) f cannot be maximized.
Ans: C.
21. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := Max{x, 100} for all x. Then
(A) df(x)/dx = 1 for all x > 0;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) is not defined for all x > 0;
(D) f cannot be maximized.
Ans: D.
22. Let the graph of some function f be {(x, y): x can be either man or woman; y = 1 if x is a man; y = 0 if x is a woman}. We know that
(A) the domain of f is {0, 1};
(B) f can be both maximized and minimized;
(C) f has a local maximum;
(D) f is continuous.
Ans: B. [The maximum of f is 1; the minimum of f is 0. See slide no.9 of Lecture 1.]
23. The derivation of delta TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) is mainly for
(A) estimating the price elasticity of demand;
(B) maximizing total revenue;
(C) using the rate of change in price to find the rate of change in total revenue;
(D) using the change of price to find the change of total revenue.
Ans: C. [Recall handout]
24. Let the demand curve be P(square)Q = 9 defined for all P > 0.
(A) The price elasticity of demand is -1 when P = 5;
(B) The price elasticity of demand is -1 when P = 3;
(C) The price elasticity of demand is -1 when P = 1;
(D) None of the above is correct.
Ans: D. [Straightforward]
25. Let the demand curve be downward-sloping, continuous (in shape) but not linear. Suppose that the demand function is not in the form of f(P) := P (superscript -0.5) for all P > 0.
(A) Total revenue can be maximized;
(B) Total revenue will rise when we increase the price;
(C) Total revenue will rise when we decrease the price;
(D) None of the above is correct.
Ans: D. [See Proposition 3]
26. Let the demand curve be given by Q = P(superscript -1) for all P > 0.
(A) Total revenue can be minimized;
(B) Total revenue will rise when we increase the price;
(C) Total revenue will rise when we decrease the price;
(D) None of the above is correct.
Ans: A. [Obvious]
27. If the demand curve is linear and downward-sloping. Currently n* = -0.5 and total revenue is 1,200. If we double the price, the total revenue will be
(A) 1,000;
(B) 2,400;
(C) 1,200;
(D) None of the above is correct.
Ans: C. [By TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) we know that delta TR/TR = 0.]
28. If the demand curve is linear and downward-sloping. Currently n* = -2 and total revenue is 1,000. If we cut the price by one-half, the total revenue will be
(A) 525;
(B) 625;
(C) 1,000;
(D) None of the above is correct.
Ans: C. [Note TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) = (-2)(-0.5)(square) + (1 - 2)(superscript -0.5) = 0.]
29. If the demand curve is linear and downward-sloping. At any point with n* < -1,
(A) any increase in price will increase total revenue;
(B) any increase in price will decrease total revenue;
(C) any reduction in price will increase total revenue;
(D) total revenue remains constant regardless of the price change.
Ans: B. [See Proposition 1 and related discussion]
30. 以上29題選擇題的正確答案中，出現最頻繁的是
(A) A;
(B) B;
(C) C;
(D) D.
Ans: D. [There are 5 As, 8 Bs, 6 Cs, and 10 Ds. Have you ever seen a weird question like this one? – I can picture that many of you are looking up the word weird at the moment. I doubt but I am shamelessly proud of my design here. Now think strategically why I made this question.]
Part Two: Analytical questions. [注意字體工整、邏輯順暢與不要出現錯別字或注音(與火星文)！如果字跡難以辨認，視同未答。畫蛇添足、答非所問、不知所云、自曝其短，將不利得分。教師也有權公告具有特色之作答。] 20 points
31. Let f be a continuous function mapping from R to R. It has a local maximum at x = 1. It has another local maximum at x = 3. It has the global maximum at x = 1 only. It has no local minimum. Furthermore, it is differentiable everywhere but at x = 2. Now you are asked to carefully sketch the graph of f to satisfy all these conditions listed above.
Ans: (to be given on the chalkboard at our next meeting)
32. By now you should have read, with great care, my handout on price elasticity, which is also on e-learning. 請扼要陳述此份講義的特色與貢獻。
Ans: (trivial and skipped here)
Extra credits question (bonus range: 0 ~ 6 points)
red vs. green -- 選紅球呢？還是選綠球？規則如下：
如果在你(妳)以外的相對多數選的是紅球，你(妳)正好也選紅球，你(妳)會被加 5分。
如果在你(妳)以外的相對多數選的是綠球，你(妳)正好也選綠球，你(妳)會被加 2分。
如果在你(妳)以外的相對多數選的是紅球，而你(妳)卻選綠球，你(妳)會被加6 分。
如果在你(妳)以外的相對多數選的是綠球，而你(妳)卻選紅球，你(妳)會被加0 分。
Now make your pick.
(歡迎全貌下載流傳。)
Spring 2009 Instructor: 衛忠欣 (Jong-Shin Wei)
管理數學 (Mathematics for Management) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw jsw12011958@gmail.com
3:10 pm ~ 4:40 pm, April 22, 2009
Open books/notes exam. 110 points in 90 minutes; absolutely no talking nor borrowing items during exams. 可使用自己的資料、字典或翻譯機。行動電話若響起，該生扣十分、以強調基本禮貌。務必工整依序作答。平時上課頻尿的極少數同學，考試時，切勿改變習慣。理由一：有害健康；理由二：迫使教師合理懷疑平時是否謊報。只是題目很多，目的在於測試是否有平日閱讀英文資料之習慣。Watch your time and have fun!
Part One: 30 Multiple choice questions. [By multiple choice in an English-speaking academic environment, we mean that you must choose the most appropriate one from 4 alternatives. 依慣例，答錯不倒扣！] 90 points (別懷疑，看看誰是實力派！)
1. Once upon a time in Utopia a small kingdom was ruled by The Mighty King Richard (李察王). The actual weight of King Richard was way over 80 kg but he insisted that his weight was only 60 kg. One day, John, who was his prime minister, joked about it, “My Lord, I have no problem with your weight record. Yet, if your weight is 60 kg, some child might have zero in weight.” Since the King was also good in mathematics, he immediately found a flaw in John’s statement. Which of the following made the King detect the flaw?
(A)E = mc2;
(B)畢氏定理；
(C)兩條平行線永不相交；
(D)A:B = C:D.
Ans: D. [Recall lectures. Now we can see who actually paid attention to lectures.]
2. There are twenty basketball teams. Each team must play exactly one game with the rest 19 teams. How many games will be played in total?
(A) 200;
(B) 190;
(C) 400;
(D) None of the above is correct.
Ans: B. [Recall lectures. Note that (20)(20 - 1)/2 = 190.]
3. Let f be a function mapping from R to R, defined by f(x) := x(superscript 3). Find the incorrect statement.
(A) The graph is convex-shaped;
(B) It has no local minimum;
(C) It has no local maximum;
(D) df(x)/dx = 0 at x = 0 only;
Ans: A. [For non-negative x, it is convex-shaped; for non-positive x, it is concave-shaped.]
4. Let f be a function mapping from R to R, defined by f(x) := x(superscript 3).
(A) d(superscrpt 2)f(x)/dx(superscript 2) < 0 for all x;
(B) d(superscrpt 2)f(x)/dx(superscript 2) ≧ 0 for all x;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 only when x = 0;
(D) d(superscrpt 2)f(x)/dx(superscript 2) is not defined at x = 0.
Ans: C. [Obviously, d2f(x)/dx2 > 0 for all x > 0; d(superscrpt 2)f(x)/dx(superscript 2) < 0 for all x < 0; d(superscrpt 2)f(x)/dx(superscript 2) = 0 when x = 0.]
5. Let f be a function mapping from R to R, defined by f(x) := ∣x∣. The graph of f
(A) looks like the English letter V;
(B) is a straight line;
(C) looks like the putting the letter V upside down;
(D) is not in one piece.
Ans: A.
6. Let f be a function mapping from R to R, defined by f(x) := ∣x∣. We know that d2f(x)/dx2
(A) > 0 for all x > 0;
(B) < 0 for all x < 0;
(C) = 0 when x = 0;
(D) = 0 for all non-zero x.
Ans: D. [The function is not differentiable at x = 0.]
7. Let f be a function mapping from R to R, defined by f(x) := ∣x∣.
(A) f has a local minimum but no global minimum;
(B) f has a global minimum but no local minimum;
(C) f has neither local minimum nor global minimum;
(D) None of the above is correct.
Ans: B. [Clearly, f(0) < f(x) for all x ≠ 0.]
8. Recall that a relation can be a function. Which of the following is the graph of some function?
(A) {(a, 1), (b, 2), (a, 2), (c, 3)};
(B) {(1, (0, 0)), (2, (0, 1)), (3, (0, 2), …};
(C) {(x, y) of R (superscript 2): x (superscript 2) + y (superscript 2) = 1};
(D) {(x, y) of R (superscript 2): y = x or y = -x}.
Ans: B. [Recall lectures]
9. English teacher asks each student to pick his/her favorite English first name. This is a well-known way of illustrating the notion of functions. Here
(A) the set of all students is the domain of this function;
(B) the set of all English first names is the domain of this function;
(C) the graph of this function has more elements than the domain has;
(D) this function is a real-valued function.
Ans: A. [Recall lectures]
10. Which of the following cannot serve as an application of equation x + y = 1?
(A) price-taking consumer’s budget line;
(B) production possibility frontier;
(C) demand curve;
(D) money supply curve.
Ans: D.
*11. Let f be a function mapping from R to R, defined by f(x) := 1 if x is rational (有理數); -1 if x is irrational (無理數).
(A) The function f is continuous but not differentiable;
(B) For any real number x, f(x) is either a global maximum or a global minimum (but not both);
(C) For any real number x, f(x) is either a local maximum or a local minimum (but not both);
(D) Neither global maximum nor global minimum exist for this function.
Ans: B.
12. Let f be a function defined as follows. f(x) := A if x belongs to [80, 100]; f(x) := B if x belongs to [70, 79]; f(x) := C if x belongs to [60, 69]; f(x) := F if x belongs to [0, 59]. Here,
(A) the domain of f is R;
(B) the range of f is R;
(C) f is not a real-valued function;
(D) f has a (global) maximum.
Ans: C.
13. On the x-y space, if we draw the graph of some function in a “continuous” way (一筆畫出來), then this function
(A) must be differentiable;
(B) must be continuous;
(C) must have at least one local maximum;
(D) must have the global maximum.
Ans: B. [Trivial]
14. The demand schedule is given as follows, P = 1, Q = 9; P = 2, Q = 8; P = 3, Q = 7; P = 4, Q = 6; P = 5, Q = 5; P = 6, Q = 4. We know nothing else. The price elasticity of demand
(A) is -1 at P = 5;
(B) is 1 at P = 5;
(C) is increasing as P goes up;
(D) is not defined here.
Ans: D. [Recall lectures]
15. Let f be a function mapping from an open interval in R to R such that d2f(x)/dx2 < 0 holds for all x. We know that
(A) df(x)/dx < 0 holds for all x;
(B) df(x)/dx > 0 holds for all x;
(C) df(x)/dx ≠ 0 holds for all x;
(D) df(x)/dx is a decreasing function of x.
Ans: D.
*16. Let f be a function mapping from an open interval in R to R such that
d(superscrpt 2)f(x)/dx(superscript 2) ≦ 0 holds for all x (in the domain). We know that
(A) if f has a local maximum at x*, then f(x*) is the global maximum;
(B) f must have at least one local maximum;
(C) f can be maximized;
(D) f cannot have any local minimum.
Ans: A. [Note that (B) and (C) are false in light of the case where df(x)/dx > 0. We eliminate (D) by considering the case where f is a constant function.]
*17. Let f be a function mapping from an open interval in R to R such that (1)
df(x)/dx = 0 at some x* in the domain, and (2) d(superscrpt 2)f(x)/dx(superscript 2)≦ 0 holds for all x. We know that
(A) f cannot have a local minimum at x*;
(B) f(x*) cannot be the global minimum;
(C) there exists no x** satisfying x** ≠ x* and df(x)/dx = 0 holds for x**;
(D) f has a local maximum at x* and that f(x*) is the global maximum.
Ans: D.
18. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := (x) (superscript 0.5) for all x. Then
(A) df(x)/dx > 0 for all x in the domain;
(B) df(x)/dx is defined everywhere but at x = 0;
(C) d2f(x)/dx2 < 0 for all x in the domain;
(D) f is not concave-shaped.
Ans: B. [是在幫忙複習微積分嗎？ Well, it is on the house.]
19. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := 2x + 3 for all x. Then
(A) df(x)/dx > 0 for all x in the domain;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 for all x in the domain;
(D) f cannot be maximized.
Ans: D.
20. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := Min{x, 100} for all x. Then
(A) df(x)/dx > 0 for all x > 0;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) = 0 for all x > 0 and x ≠ 100;
(D) f cannot be maximized.
Ans: C.
21. Let f be a function mapping from the set of non-negative real numbers to R, defined by f(x) := Max{x, 100} for all x. Then
(A) df(x)/dx = 1 for all x > 0;
(B) f cannot be minimized;
(C) d(superscrpt 2)f(x)/dx(superscript 2) is not defined for all x > 0;
(D) f cannot be maximized.
Ans: D.
22. Let the graph of some function f be {(x, y): x can be either man or woman; y = 1 if x is a man; y = 0 if x is a woman}. We know that
(A) the domain of f is {0, 1};
(B) f can be both maximized and minimized;
(C) f has a local maximum;
(D) f is continuous.
Ans: B. [The maximum of f is 1; the minimum of f is 0. See slide no.9 of Lecture 1.]
23. The derivation of delta TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) is mainly for
(A) estimating the price elasticity of demand;
(B) maximizing total revenue;
(C) using the rate of change in price to find the rate of change in total revenue;
(D) using the change of price to find the change of total revenue.
Ans: C. [Recall handout]
24. Let the demand curve be P(square)Q = 9 defined for all P > 0.
(A) The price elasticity of demand is -1 when P = 5;
(B) The price elasticity of demand is -1 when P = 3;
(C) The price elasticity of demand is -1 when P = 1;
(D) None of the above is correct.
Ans: D. [Straightforward]
25. Let the demand curve be downward-sloping, continuous (in shape) but not linear. Suppose that the demand function is not in the form of f(P) := P (superscript -0.5) for all P > 0.
(A) Total revenue can be maximized;
(B) Total revenue will rise when we increase the price;
(C) Total revenue will rise when we decrease the price;
(D) None of the above is correct.
Ans: D. [See Proposition 3]
26. Let the demand curve be given by Q = P(superscript -1) for all P > 0.
(A) Total revenue can be minimized;
(B) Total revenue will rise when we increase the price;
(C) Total revenue will rise when we decrease the price;
(D) None of the above is correct.
Ans: A. [Obvious]
27. If the demand curve is linear and downward-sloping. Currently n* = -0.5 and total revenue is 1,200. If we double the price, the total revenue will be
(A) 1,000;
(B) 2,400;
(C) 1,200;
(D) None of the above is correct.
Ans: C. [By TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) we know that delta TR/TR = 0.]
28. If the demand curve is linear and downward-sloping. Currently n* = -2 and total revenue is 1,000. If we cut the price by one-half, the total revenue will be
(A) 525;
(B) 625;
(C) 1,000;
(D) None of the above is correct.
Ans: C. [Note TR/TR = n*(delta P/Po)(square) + (1 + n*)(delta P/Po) = (-2)(-0.5)(square) + (1 - 2)(superscript -0.5) = 0.]
29. If the demand curve is linear and downward-sloping. At any point with n* < -1,
(A) any increase in price will increase total revenue;
(B) any increase in price will decrease total revenue;
(C) any reduction in price will increase total revenue;
(D) total revenue remains constant regardless of the price change.
Ans: B. [See Proposition 1 and related discussion]
30. 以上29題選擇題的正確答案中，出現最頻繁的是
(A) A;
(B) B;
(C) C;
(D) D.
Ans: D. [There are 5 As, 8 Bs, 6 Cs, and 10 Ds. Have you ever seen a weird question like this one? – I can picture that many of you are looking up the word weird at the moment. I doubt but I am shamelessly proud of my design here. Now think strategically why I made this question.]
Part Two: Analytical questions. [注意字體工整、邏輯順暢與不要出現錯別字或注音(與火星文)！如果字跡難以辨認，視同未答。畫蛇添足、答非所問、不知所云、自曝其短，將不利得分。教師也有權公告具有特色之作答。] 20 points
31. Let f be a continuous function mapping from R to R. It has a local maximum at x = 1. It has another local maximum at x = 3. It has the global maximum at x = 1 only. It has no local minimum. Furthermore, it is differentiable everywhere but at x = 2. Now you are asked to carefully sketch the graph of f to satisfy all these conditions listed above.
Ans: (to be given on the chalkboard at our next meeting)
32. By now you should have read, with great care, my handout on price elasticity, which is also on e-learning. 請扼要陳述此份講義的特色與貢獻。
Ans: (trivial and skipped here)
Extra credits question (bonus range: 0 ~ 6 points)
red vs. green -- 選紅球呢？還是選綠球？規則如下：
如果在你(妳)以外的相對多數選的是紅球，你(妳)正好也選紅球，你(妳)會被加 5分。
如果在你(妳)以外的相對多數選的是綠球，你(妳)正好也選綠球，你(妳)會被加 2分。
如果在你(妳)以外的相對多數選的是紅球，而你(妳)卻選綠球，你(妳)會被加6 分。
如果在你(妳)以外的相對多數選的是綠球，而你(妳)卻選紅球，你(妳)會被加0 分。
Now make your pick.
(歡迎全貌下載流傳。)
Tuesday, April 21, 2009
homework 2 (Workshop on Informationa and Negotiation)
★★★ Homework #2 ★★★
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
Due: 11:59 pm, Monday, April 20, 2009 (以TA電郵收件記錄為準。拒收遲交作業)
Turn in your homework as a Word file (size limit: two pages) to be sent as an email attachment to the TA (not to me). Her email address was given on the chalkboard on March 17, 2009. She will confirm the delivery. 勿抄題，本課程之作業格式與檔案命名規則，已詳載於 Homework #1。
一位明星高中英文男老師游辛基日前於收信匣中，收到一封經網友轉寄極具毀謗意涵的匿名信件，內容是關於校內另一位高一女同學冷如花的不實指控及毀謗。經層層抽絲剝繭的追查，游辛基得知發佈此封信件的人，竟是同校一名高二的男學生梅仁原。梅同學平日個性較沈默，對於電腦相關知識甚為熱衷。前陣子因感情問題與冷如花發生爭執，事後挾怨報復，利用自己所學的電腦相關技術及網路公共資源的方便，快速散播關於冷如花同學的不實謠言，以達詆毀女同學名譽之效果，並將自己網路BBS (and MSN)上之別名，更改為“如花如花冷bitch”…...游老師於知悉此事情的來龍去脈之後，自覺事態之嚴重並認為此風不可長，學生一時的情緒發洩，殊不知己觸及毀謗名譽的罪行，學生間的耳語不斷，謠傳亦不斷推陳出新，游老師認為應找機會向學生來個機會教育。
次日上英文課，游老師於發完考卷下課休息，第二節上課後發現此次考試成績最優的郝瑾璋同學，竟在下課休息時間蹺課出去玩了。由於郝同學平日上課認真且從不遲到早退，今日之蹺課難免引起同學的揣測，一時之間同學的笑鬧帶動謠言，有的同學說「哎唷 ～ 郝瑾璋成績考這麼高， 當然不用上課了啦」；另又有同學笑鬧說「哎唷 ～ 她是運氣好才會考這麼高啦！！」游老師深知謠言之可怕，見機不可失，便向同學提起前陣子在網路上所流傳關於冷同學的謠傳，並信手捻來，借郝同學之名向同學舉例欲說明：
「同學，無論郝同學是不是因為運氣好才會考這麼好還是有其他因素。沒錯，這次月考選擇題占80%，有人會把運氣扯進來。 … 然而…你們一時的討論可能只是一個開玩笑的舉動，但此舉對於最高分的郝同學來說，可能會造成某一程度的傷害。班上大部份同學應該都有使用電腦上網的習慣，大家都知道網路是無遠弗界的，今日你們的玩笑話被有心人士所利用並穿鑿附會在網路上散播關於郝同學的不實傳言，可能編纂說郝同學今日的蹺課是因為成績表現的好而不屑上課……更甚者就像是前陣子一位你們不認識的男同學，在網路上直接以惡意取別名的方式，辱罵一位女同學是bitch等不堪入耳的言語。(游老師隨手在黑板寫下 ~ 瑾璋瑾璋好bitch ~) 你們說，像這類惡意中傷的言語在網路上一旦經有心人士散播，是不是會造成莫大的傷害呢？這種網路散播的謠言一旦觸及人身攻擊，極可能構成民法上的毀謗罪。所以，同學在使用網路資源的同時，務必要遵守網路的禮節與法律。好吧！今天的課就上到這裡……不敬禮下課，同學回家要溫習今天所教的課程。」
翌晨，郝同學到校上課，同學一見到她就譏諷的對她說「昨天發完考卷後就蹺課吼……跟妳說個小八卦，你不要跟別人講是我講的哦！！」郝同學一頭霧水的點了頭，同學接著說「好像有人說你考得好只是因為運氣好而己啦……老師竟也沒幫妳辯解耶，而且老師還趁妳不在時說妳就像是上次網路流傳的那個……那個什麼bitch的……哎呀！我在打瞌睡大概只聽到這些啦……嗯～妳自己看著辦吧！！」 “bitch …… bitch”……這個字猛然在郝瑾璋頭上一擊，這個字是什麼意思呢？於是翻了字典才知此字義之粗鄙……郝瑾璋心中暗自生起一個疑問「老師為什麼要這樣說我呢？難道是氣我翹課嗎？」回家和媽媽提起此事，當然不會傻到提及自己翹課去看電影一事。媽媽自然是怒不可遏，隨後歇斯底里的打電話到教務處投訴說「女兒在學校成績表現得好，竟被老師說成是運氣好而己！他還說我女兒是bitch ～ 天呀！我生的女兒竟被說成是bitch……，叫游老師出來說清楚講明白啦！否則老娘是不會放過他的。」面對郝媽媽的投訴，教務主任柳華韮老師(是一位年過半百假道學的學究，曾經接受廠商招待喝花酒)只覺得莫名其妙，在電話當中承諾郝媽媽，會立即傳喚游老師來問清楚。待聯絡到游老師，柳主任劈頭就問道「游老師，你怎麼會在課堂當中使用不當的言語辱罵女學生呢？」游老師一時也搞不清楚是什麼情況，於是柳主任又接著說「同學指證你在課堂當中說郝同學是婊子(即bitch)，有沒有這件事，有還是沒有，就一句話！？」面對教務主任的指責，游老師才想起那天在課堂上所講的話與情境，自是百口莫辯……想要解釋時，柳主任卻不想聽，直接放話說「我才不管怎麼處理梅仁原和冷如花的事，現在家長郝媽媽找到學校來了，你自己看著辦吧！認錯賠罪 … 還是聽候校方處置！」
面對此一莫須有的事件，若您是案例中的游老師，您會如何處理呢？重點在於所謂的班級經營與談判藝術裡的 damage control。
Note:
I used this scenario (credit: 若干年前研究生陳美惠小姐協助編撰，錯別字已修正)
as a case study in last year’s teaching. All students were required to leave comments on the “discussion room (網路學園討論區)”. To my regret, none of those students did a good job.
Solution
有此一說，有水準的個案研究，至少有一種「結局」，就如同一部電影，該有它的結局。當然，認真的觀眾在觀賞後，心中也可能有自己想像的（更佳）結局。以下是此一個案之結局或後續。
游老師猛然想起，教務主任一直在等待落井下石的機會。「什麼年代了，哪有人公然以bitch稱呼別人的？更何況是一位成績優秀的女學生！這種用詞，也只有教務主任這種假道學的老學究才會想到吧！」有此一警覺，游老師心中已有對策。
首先，他找來郝同學，確定談話場合不是非常公開的，但是有一位教師在旁，他刻意以誠懇關懷的態度，向郝同學致歉，也不責備她蹺課之事。然後，當著郝同學的面，他打電話給郝太太，同樣地道歉，並蓄意誇讚她女兒在校之傑出表現。
次週上課時，游老師平靜地向全班同學，緩緩重述梅同學之惡行，完全不提郝同學缺課或同學之八卦、斷章取義。接著，語氣一轉，自責教師未能有效注意同學之出席，很狗腿地感謝教務主任之提醒。「所以，自即日起，每節課必點名一次，請同學多體諒！」游老師也順便提到，選擇題免不了有運氣(good luck or bad luck)之成分，為了讓大家心服口服，爾後考試皆以申論、問答題型為主。當天的這番規定，游老師在講桌下，悄悄以錄音機全程側錄下來。
日子一天一天過去，漸漸這班同學孤立郝同學，甚至語出怨言，因為每節都點名，蹺課之途已斷。郝同學整個變成另一人，其他老師對這班也敬而遠之。期末考之後，郝同學意外地名次落到中段。那位八卦、斷章取義的同班同學，心理自然是放下一塊大石頭。柳主任竊笑不已，也沒再過問這班學生。
至於導火線梅仁原同學之惡行，冷如花同學之委屈，似乎沒人理會。他們之間的感情糾葛，是否後續有潑鹽酸、有無未婚懷孕，皆不得而知，數年後，游老師把這段過程，寫成一篇小品文，刊登在某大報紙副刊。數日後，柳主任與郝太太分別意外在郵筒中，見到這篇文章之影本。心臟病、高血壓，就不必多說啦。
Note：推薦三部電影：天之驕子、風流教師霹靂妹、我和我的小鬼們。大家可將此個案與一般企管課程之個案教學做一比較。Have fun!
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
Due: 11:59 pm, Monday, April 20, 2009 (以TA電郵收件記錄為準。拒收遲交作業)
Turn in your homework as a Word file (size limit: two pages) to be sent as an email attachment to the TA (not to me). Her email address was given on the chalkboard on March 17, 2009. She will confirm the delivery. 勿抄題，本課程之作業格式與檔案命名規則，已詳載於 Homework #1。
一位明星高中英文男老師游辛基日前於收信匣中，收到一封經網友轉寄極具毀謗意涵的匿名信件，內容是關於校內另一位高一女同學冷如花的不實指控及毀謗。經層層抽絲剝繭的追查，游辛基得知發佈此封信件的人，竟是同校一名高二的男學生梅仁原。梅同學平日個性較沈默，對於電腦相關知識甚為熱衷。前陣子因感情問題與冷如花發生爭執，事後挾怨報復，利用自己所學的電腦相關技術及網路公共資源的方便，快速散播關於冷如花同學的不實謠言，以達詆毀女同學名譽之效果，並將自己網路BBS (and MSN)上之別名，更改為“如花如花冷bitch”…...游老師於知悉此事情的來龍去脈之後，自覺事態之嚴重並認為此風不可長，學生一時的情緒發洩，殊不知己觸及毀謗名譽的罪行，學生間的耳語不斷，謠傳亦不斷推陳出新，游老師認為應找機會向學生來個機會教育。
次日上英文課，游老師於發完考卷下課休息，第二節上課後發現此次考試成績最優的郝瑾璋同學，竟在下課休息時間蹺課出去玩了。由於郝同學平日上課認真且從不遲到早退，今日之蹺課難免引起同學的揣測，一時之間同學的笑鬧帶動謠言，有的同學說「哎唷 ～ 郝瑾璋成績考這麼高， 當然不用上課了啦」；另又有同學笑鬧說「哎唷 ～ 她是運氣好才會考這麼高啦！！」游老師深知謠言之可怕，見機不可失，便向同學提起前陣子在網路上所流傳關於冷同學的謠傳，並信手捻來，借郝同學之名向同學舉例欲說明：
「同學，無論郝同學是不是因為運氣好才會考這麼好還是有其他因素。沒錯，這次月考選擇題占80%，有人會把運氣扯進來。 … 然而…你們一時的討論可能只是一個開玩笑的舉動，但此舉對於最高分的郝同學來說，可能會造成某一程度的傷害。班上大部份同學應該都有使用電腦上網的習慣，大家都知道網路是無遠弗界的，今日你們的玩笑話被有心人士所利用並穿鑿附會在網路上散播關於郝同學的不實傳言，可能編纂說郝同學今日的蹺課是因為成績表現的好而不屑上課……更甚者就像是前陣子一位你們不認識的男同學，在網路上直接以惡意取別名的方式，辱罵一位女同學是bitch等不堪入耳的言語。(游老師隨手在黑板寫下 ~ 瑾璋瑾璋好bitch ~) 你們說，像這類惡意中傷的言語在網路上一旦經有心人士散播，是不是會造成莫大的傷害呢？這種網路散播的謠言一旦觸及人身攻擊，極可能構成民法上的毀謗罪。所以，同學在使用網路資源的同時，務必要遵守網路的禮節與法律。好吧！今天的課就上到這裡……不敬禮下課，同學回家要溫習今天所教的課程。」
翌晨，郝同學到校上課，同學一見到她就譏諷的對她說「昨天發完考卷後就蹺課吼……跟妳說個小八卦，你不要跟別人講是我講的哦！！」郝同學一頭霧水的點了頭，同學接著說「好像有人說你考得好只是因為運氣好而己啦……老師竟也沒幫妳辯解耶，而且老師還趁妳不在時說妳就像是上次網路流傳的那個……那個什麼bitch的……哎呀！我在打瞌睡大概只聽到這些啦……嗯～妳自己看著辦吧！！」 “bitch …… bitch”……這個字猛然在郝瑾璋頭上一擊，這個字是什麼意思呢？於是翻了字典才知此字義之粗鄙……郝瑾璋心中暗自生起一個疑問「老師為什麼要這樣說我呢？難道是氣我翹課嗎？」回家和媽媽提起此事，當然不會傻到提及自己翹課去看電影一事。媽媽自然是怒不可遏，隨後歇斯底里的打電話到教務處投訴說「女兒在學校成績表現得好，竟被老師說成是運氣好而己！他還說我女兒是bitch ～ 天呀！我生的女兒竟被說成是bitch……，叫游老師出來說清楚講明白啦！否則老娘是不會放過他的。」面對郝媽媽的投訴，教務主任柳華韮老師(是一位年過半百假道學的學究，曾經接受廠商招待喝花酒)只覺得莫名其妙，在電話當中承諾郝媽媽，會立即傳喚游老師來問清楚。待聯絡到游老師，柳主任劈頭就問道「游老師，你怎麼會在課堂當中使用不當的言語辱罵女學生呢？」游老師一時也搞不清楚是什麼情況，於是柳主任又接著說「同學指證你在課堂當中說郝同學是婊子(即bitch)，有沒有這件事，有還是沒有，就一句話！？」面對教務主任的指責，游老師才想起那天在課堂上所講的話與情境，自是百口莫辯……想要解釋時，柳主任卻不想聽，直接放話說「我才不管怎麼處理梅仁原和冷如花的事，現在家長郝媽媽找到學校來了，你自己看著辦吧！認錯賠罪 … 還是聽候校方處置！」
面對此一莫須有的事件，若您是案例中的游老師，您會如何處理呢？重點在於所謂的班級經營與談判藝術裡的 damage control。
Note:
I used this scenario (credit: 若干年前研究生陳美惠小姐協助編撰，錯別字已修正)
as a case study in last year’s teaching. All students were required to leave comments on the “discussion room (網路學園討論區)”. To my regret, none of those students did a good job.
Solution
有此一說，有水準的個案研究，至少有一種「結局」，就如同一部電影，該有它的結局。當然，認真的觀眾在觀賞後，心中也可能有自己想像的（更佳）結局。以下是此一個案之結局或後續。
游老師猛然想起，教務主任一直在等待落井下石的機會。「什麼年代了，哪有人公然以bitch稱呼別人的？更何況是一位成績優秀的女學生！這種用詞，也只有教務主任這種假道學的老學究才會想到吧！」有此一警覺，游老師心中已有對策。
首先，他找來郝同學，確定談話場合不是非常公開的，但是有一位教師在旁，他刻意以誠懇關懷的態度，向郝同學致歉，也不責備她蹺課之事。然後，當著郝同學的面，他打電話給郝太太，同樣地道歉，並蓄意誇讚她女兒在校之傑出表現。
次週上課時，游老師平靜地向全班同學，緩緩重述梅同學之惡行，完全不提郝同學缺課或同學之八卦、斷章取義。接著，語氣一轉，自責教師未能有效注意同學之出席，很狗腿地感謝教務主任之提醒。「所以，自即日起，每節課必點名一次，請同學多體諒！」游老師也順便提到，選擇題免不了有運氣(good luck or bad luck)之成分，為了讓大家心服口服，爾後考試皆以申論、問答題型為主。當天的這番規定，游老師在講桌下，悄悄以錄音機全程側錄下來。
日子一天一天過去，漸漸這班同學孤立郝同學，甚至語出怨言，因為每節都點名，蹺課之途已斷。郝同學整個變成另一人，其他老師對這班也敬而遠之。期末考之後，郝同學意外地名次落到中段。那位八卦、斷章取義的同班同學，心理自然是放下一塊大石頭。柳主任竊笑不已，也沒再過問這班學生。
至於導火線梅仁原同學之惡行，冷如花同學之委屈，似乎沒人理會。他們之間的感情糾葛，是否後續有潑鹽酸、有無未婚懷孕，皆不得而知，數年後，游老師把這段過程，寫成一篇小品文，刊登在某大報紙副刊。數日後，柳主任與郝太太分別意外在郵筒中，見到這篇文章之影本。心臟病、高血壓，就不必多說啦。
Note：推薦三部電影：天之驕子、風流教師霹靂妹、我和我的小鬼們。大家可將此個案與一般企管課程之個案教學做一比較。Have fun!
homework 1 (Workshop on Informationa and Negotiation)
★ Homework #1 ★
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
Due: 11:59 pm, Monday, March 23, 2009 (以TA電郵收件記錄為準。拒收遲交作業)
Turn in your homework as a Word file (two pages) to be sent as an email attachment to the TA (not to me). Her email address was given on the chalkboard on March 17, 2009. She will confirm the delivery.
1. 提供全身彩色近照一張，約占一頁的A4篇幅。解析度應高，衣著正式，顯示國企系畢業生之專業形象。無需說明。
2. 提供全身彩色近照一張，約占一頁的A4篇幅。解析度應高，此照片應最能表現你(妳)的個人特質與優勢，遮掩缺點與劣勢。附上三十字以內的說明。
本課程作業格式如下
★ Homework #1 ★
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
學生姓名：吳明士
學號：s123456789
Email: abcdef@yahoo.com.tw
1.
……
2.
……
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
Due: 11:59 pm, Monday, March 23, 2009 (以TA電郵收件記錄為準。拒收遲交作業)
Turn in your homework as a Word file (two pages) to be sent as an email attachment to the TA (not to me). Her email address was given on the chalkboard on March 17, 2009. She will confirm the delivery.
1. 提供全身彩色近照一張，約占一頁的A4篇幅。解析度應高，衣著正式，顯示國企系畢業生之專業形象。無需說明。
2. 提供全身彩色近照一張，約占一頁的A4篇幅。解析度應高，此照片應最能表現你(妳)的個人特質與優勢，遮掩缺點與劣勢。附上三十字以內的說明。
本課程作業格式如下
★ Homework #1 ★
Spring 2009
訊息與談判實作 (Workshop on Information and Negotiations)
學生姓名：吳明士
學號：s123456789
Email: abcdef@yahoo.com.tw
1.
……
2.
……
Subscribe to:
Posts (Atom)
