Friday, July 24, 2009

How students learned in summer term (2009)

(大四)畢業專題研究 -- 4 students
No exams
One end-of-term oral team presentation
One paper (teamwork)
Average: 81
H~L: 86~78
Failure ratio: 0%


(大一)總體經濟學原理 -- 22 students
3 better exams out of 4 exams
Average: 64.4
H~L: 79~51
Failure ratio: 13.6%


(大一)管理數學 -- 17 students
3 better exams out of 4 exams
Average: 61.4
H~L: 78~42
Failure ratio: 29%

(reported on 07242009)

Wednesday, July 15, 2009

Solution to Exam 3 for Math for Mgmt (summer 2009)

★★★★ Detailed Solution to Examination 3 (Int’l Business, WUCL) ★★★★
Summer 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
9:20 am ~ 10:30 am, July 15, 2009
Open books/notes exam. 100 points in 70 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。
Questions 1 to 10 are multiple choice questions. That is, choose the most appropriate one from four alternatives. 每題6分

1. Let f be a function mapping from A to B. To make f a real-valued function, we need
(A) the domain of f to be a subset of R;
(B) the range set of f to be a subset of R;
(C) the image set of f to be a subset of R;
(D) both A and B to be subsets of R.
Ans: C. [Recall Exam 2.]

2. Define f(x) := 2x3 + 3x2 - 3x + 8 for all x of R. The graph of f contains the point
(A) (0, 0);
(B) (1, 13);
(C) (2, 18);
(D) (3, 80).
Ans: D. [Obviously, f(0) = 8, f(1) = 10, f(2) = 30, and f(3) = 80]

3. Define f(x, y) := Min{x, y} for all (x, y) of R2+ (i.e., the first quadrant). The graph of f contains
(A) ((0, 0), 1) or (0, 0, 1);
(B) (0, (0, 0)) or (0, 0, 0);
(C) ((1, 3), 3) or (1, 3, 3);
(D) ((2, 0), 0) or (2, 0, 0).
Ans: D. [Trivial yet make sure you know why (B) is false.]

4. Consider the following constrained maximization problem. Choose (x, y) from the first quadrant to maximize 2x + y - 3 subject to (1) x + y ≦ 3, (2) 1 ≦ x ≦ 3, and (3) y ≧ 1. The slope of a typical level curve of the objective function is
(A) -2;
(B) -1;
(C) 1;
(D) 2.
Ans: A. [For any k > 0, the slope of 2x + y = k is -2.]

5. [continued from question 4] The constraint set (made by putting together those three weak inequalities) contains points
(A) (0, 0) and (1, 2);
(B) (2, 1) and (1, 2);
(C) (1, 2) and (2, 2);
(D) (1, 2) and (0, 3).
Ans: B. [The constraint set is the triangle with three vertex points, (1, 1), (2, 1), and (1, 2).]

6. [continued from question 4] The solution to this problem
(A) does not exist;
(B) is (2, 1);
(C) is (1, 2);
(D) is (3, 0).
Ans: B. [By visual inspection and recall that the slope of level curves is -2]

7. [continued from question 4] The maximized value of f is
(A) 2;
(B) 3;
(C) 5;
(D) None of the above is correct.
Ans: A. [2(2) + 1 - 3 = 2]

8. Consider the function f(x) := Min{x, 3} defined for all non-negative real numbers x. We know that
(A) f is differentiable;
(B) f has no local maximum;
(C) f has no local minimum;
(D) f can be maximized and minimized.
Ans: D. [Recall lectures]

9. [continued from question 8] The level curve of f at (level) 3 is
(A) a point;
(B) a ray;
(C) a line segment;
(D) an interval.
Ans: B. [Solutions to Min{x, 3} = 3 are those x satisfying x ≧ 3, which is a ray on the real line.]

10. [continued from question 8] The level curve of f at (level) 4 is
(A) a point;
(B) a line segment;
(C) an open interval;
(D) None of the above is correct.
Ans: D. [Solution to Min{x, 3} = 4 does not exist.]

以下每題 10 分

11. Choose x to maximize f(x) = (x)0.5 for all x ≧ 0 subject to Max{x, 3} ≦ 4. Solve it
with help from a diagram. What is the role of calculus here?
Ans: First notice that Max{x, 3} ≦ 4 is the same as x belonging to [0, 4]. Since f is strictly increasing, we see that the solution is x = 4. No calculus is needed here.

12. You are given a rope with length k > 0. You can use it to either make a square or
make a circle. If you wish to maximize the formed area, what will you do? A square or a circle? Justify your choice.
Ans: By [k/(2pi)]2 - (k/4)2 = k2/(4pi) - k2/(16) > 0 due to pi < 4, we know that a circle has larger area than a square does. 這是很多中學生也會的應用題。

13. Recall the movie “The Emperor’s Club” shown on July 14. Carefully choose a
scenario from that film and make it a decision tree having two players. Be precise and organized.
Ans: skipped.

14. 課程已過3/4,此題係測試大家對學習「管理數學」的正確認知。Have fun!

※ good job 這門課太酷了! ............根本不知道自己在幹嘛 = =

※ 感覺老師好像在賣弄學問,管理數學卻一直教經濟學,管理數學真正的內容到底是什麼???如果上學期是你教微積分,那也會把這堂課變成經濟學嗎?老師只重視經濟學而已嗎?

※ 老師你上課教好多經濟,管數好少,雖然上課題材很新鮮很有趣,希望能教一點感覺回家會有收穫的,還有就是能教仔細一點嗎,我還是老話一句希望少用ppt,數學類的這樣真的會很想睡覺

※ 字太醜 看不懂評語

The above (※) are written comments from the end-of-semester teaching evaluations for this course offered in Spring 2009 (i.e., the class of 2012). 在大學評鑑時,訪視委員與同學對談時,如果這些正好是這四位寶貝同學(天兵?)所表達的,訪視委員應如何接話?
Ans: Here are some samples.
(i) Ask students to recall what the course syllabus is; compare students’ recollection with the syllabus on e-learning. Also check if teacher issued typewritten solutions to all exams. [委員皆有電腦可上網]
(ii) Ask some simplest questions such as “Give me an example of constrained maximization”, “What is the use of second-order condition”, and “Tell me why prisoners’ dilemma game is well known outside the economics field.”
(iii) Ask students how, in their opinions, teachers should teach this course if a large number of students did fail calculus in the previous semester.
(iv) Ask students why the college strongly (and proudly) encourages teachers to use PPT in teaching; ask students whether they feel sleepy now.

[訪視委員是來評鑑打分數的,不是來輔導、調停、扮演包青天的。在我自己與友人的評鑑經驗裡,以上的(i)至(iii)皆偶有聽說,(iv)就不容易啦(應該不是文藻學生嗜睡或體弱,只是點名制度把所有人框在教室吧)。俗話說,一樣米養百種人,何況那一班59人(有16位遭期中預警、期末考平均成績退步近10分,學期成績不及格之比例高達42%),背景迥異,也希望大家都能認真解析這一族群的想法。畢竟,我們不知道60~80%的同學的想法為何,委員也不會知道拔河活動與體育課,帶來的外部性。還好我懂一些訊息經濟學。]

(歡迎全貌下載流傳)

Thursday, July 09, 2009

Solution to Exam 2 for Macro Principles (summer 2009)

★★★ Detailed Solution to Examination 2 (Int'l Business, WUCL) ★★★
Summer 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
1:10 pm ~ 2:20 pm, July 8, 2009
Open books/notes exam. 100 points in 70 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。
Part One: 10 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!] 60 points
1. A car is sold at the price of USD20,000 while, at the same time, strawberries are sold at the price of USD3 (for one box). When we talk about how those production activities contribute to our economy, we
(A) should not compare cars with strawberries;
(B) must consider cars’ depreciation;
(C) only compare the difference in quantities;
(D) use prices to measure their contributions.
Ans: D. [See p.510, text]

2. Last year Andy paid NTD20,000 per month for renting an apartment while Becky lived in the apartment that she owned. Suppose that both apartments are very much alike (in quality and in market value). When we compute last year's GDP, as far as these two people are concerned, it should include
(A) NTD240,000;
(B) NTD480,000;
(C) NTD120,000;
(D) None of the above is correct.
Ans: B. [See p.510, text]

3. GDP includes
(A) market values of illegal drugs sold on street;
(B) market values of tomatoes grown in your backyard;
(C) the NTD1,000 you lost in one bet with your friend;
(D) the imputed rent.
Ans: D. [See p.510, text]

4. Nancy paid Henry to wash her car last year. This year, they got married but Henry still washes her car (for fun or for love). The effect of this marriage on GDP is
(A) making GDP fall;
(B) making GDP rise;
(C) making GDP unchanged;
(D) None of the above is correct.
Ans: A. [See p.510, text]

5. Last year Ursuline Greeting Card Company spent USD600,000 on purchasing paper. Half of them were used in producing greeting cards; half of them were left at the factory and added to her inventory. Suppose that sales revenue of those greeting cards is USD 800,000. When we compute last year’s GDP,
(A) both 800,000 and 600,000 should be included;
(B) both 800,000 and 300,000 should be included;
(C) only 800,000 should be included;
(D) only 200,000 should be included.
Ans: B. [See p.511, text]

*6. If you bought a used car (say, Honda made in 2007 and in Taiwan) last year and that expenditure was not included in last year’s GDP, then
(A) you must buy it from a dealer;
(B) you must buy it from a friend;
(C) it does not matter whom you bought it from;
(D) None of the above is correct.
Ans: C.

7. Quarterly data for GDP
(A) can not take out the seasonal cycle;
(B) is GDP divided by four;
(C) is GDP multiplied by four;
(D) must be modified by seasonal adjustment.
Ans: D. [See p.511, text]

8. Last year, your parents paid NTD120,000 for your tuition and fees. While computing last year’s GDP,
(A) it should be included in C;
(B) it should be included in I;
(C) it should be included in G;
(D) None of the above is correct.
Ans: A. [See p.513, text]

9. Last year, Cindy paid NTD10,000,000 for a new house at Taipei. While computing last year’s GDP,
(A) it should be included in C;
(B) it should be included in I;
(C) it should be included in G;
(D) None of the above is correct.
Ans: B. [See p.513, text]

10. In general and take USA as an example. How would we rank components of GDP in their magnitude (or size)?
(A) G > I > C > NX;
(B) G > C > I > NX;
(C) C > I > G > NX;
(D) C > G > I > NX.
Ans: D. [See p.515, text]

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。] 40 points

11. Two goods are produced and sold in an economy. In 2001, P1 = 10, Q1 = 100,
P2 = 50, and Q2 = 80. In 2002, P1 = 20, Q1 = 120, P2 = 60, and Q2 = 50.
(i) Let 2001 be the base year. Calculate the real GDP for 2002.
(ii) From 2001 to 2002, what do we know about the change in the general price level (by making use of those data)? Hint: GDP deflator.
Ans:
(i) The real GDP for 2002 is: (10)(120) + (50)(50) = 1200 + 2500 = 3700.
(ii) The GDP for 2002 is: (20)(120) + (60)(50) = 2400 + 3000 = 5400.
Hence, the GDP deflator for 2002 is (5400/3700)(100), is about 146.
We shall say that from 2001 to 2002, the general price went up by 46%.
[source: Lecture 3, Spring 2009]

12. 眾所周知:節儉是美德、資源要珍惜。尤其在當下,很多人認為,大家應多買二手傢俱、汽車、房屋。可是,罕見政府積極鼓勵此類交易,何故?
Ans: (given on July 9, 2009 and skipped here)

(撰寫試題無著作權;歡迎全貌下載流傳。)

Solution to Exam 1 for Macro Principles (summer 2009)

★★ Detailed Solution to Examination 1 (Int'l Business, WUCL) ★★
Summer 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
2:50 pm ~ 4:00 pm, July 3, 2009
Open books/notes exam. 100 points in 70 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。
Part One: 10 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!] 50 points
1. Before taking externality into consideration, we know that demand for aluminum is P + Q = 10; supply of aluminum is 3P - 2Q = 0. At equilibrium, P* =
(A) 4;
(B) 6;
(C) 5;
(D) None of the above is correct.
Ans: A. [By quantity demanded equals quantity supplied, we have Q* = 6 and P* = 4.]
2. [continued from question 1] Q* =
(A) 4;
(B) 5;
(C) 6;
(D) None of the above is correct.
Ans: C.
3. [continued from question 1] The market allocates resources in a way that it 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) 20;
(C) 30;
(D) 25.
Ans: C. [Recall that CS + PS is the area of the triangle with vertex points (0, 10), (0, 0), and (6, 4), which is 30.]
4. [continued from question 3] Here, the insight is:
(A) Markets are usually a good way to organize economic activity;
(B) Governments can sometimes improve market outcomes;
(C) Sometimes we have government failure;
(D) There is no such thing as a free lunch.
Ans: A. [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 3P - 2Q = 3 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 = (2/3)Q to P = (2/3)Q + 1]
6. [continued from question 5] The new equilibrium price is
(A) 23/3;
(B) 20/3;
(C) 23/5;
(D) 4.
Ans: C. [From P + Q = 10 and 3P - 2Q = 3 we obtain Q** = 27/5 and P** = 23/5.]
7. The best way to measure the annual economic performance of a country is to find her
(A) income;
(B) population;
(C) stock index;
(D) education.
Ans: A. [Recall lecture]
8. “How can you put a price on clean air and clean water?!” is a strong statement often made by
(A) environmentalists;
(B) politicians;
(C) soldiers;
(D) economists.
Ans: A. [See p.219, text]
9. If Highway 88 (mentioned in class) becomes highly congested, the first reaction that the government might have is to
(A) build another highway;
(B) widen it;
(C) shut it down twice a day;
(D) charge drivers a toll.
Ans: D. [See p.233, text]
10. Which of the following can best reduce the level of pollution?
(A) issuing more pollution permits;
(B) raising the corrective tax;
(C) lowering the corrective tax;
(D) allowing firms to trade pollution permits.
Ans: B. [p.217, text]

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。] 50 points
11. Initial pollution levels of three firms are: 70, 80, and 50 units for factories A, B, and C respectively. The cost of reducing pollution by one unit is $20, $25, and $10
respectively. [Assume that the cost structure is linear.] The government wants to reduce the total pollution to 120 units and gives each 40 (units of) tradable pollution permits. What happens if each firm gets 40 pollution permits which are not tradable?
Ans: Firm A must reduce pollution by 30 units, causing her $600. Firm B must reduce pollution by 40 units, causing her $1,000. Firm C must reduce pollution by 10 units, causing her $100.

12. [continued from question 11] Will the price for tradable pollution permits be 20 or 15? How about 25? Justify your answer.
Ans: Firm C sells 40 permits to B at price 20, causing B $800. Note that -800 > -1000. Such a transaction makes C earn 800 - (50)(10) = 300, which is better than -100. We see that the aforementioned trade benefits both B and C (while having no effect on A).

13. 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. [See text]

14. Make your own example of illustrating how Coase theorem can be used to resolve the problem with externalities, similar to pp.210-211, text.
Ans: skipped.

15. Write down five most important things for you to do if you are a teacher assigned to teach a course that you are not familiar with.
Ans: For instance,
(i) 將學生分組,輪流上台報告
(ii) 以報告代替考試
(iii) 要求書商提供全套 PPT 與題庫光碟
(iv) 大量請求業界人士來進行協同教學
(v) 常常呼應同學之要求,於課堂播放電影
(vi) 試題回收、嚴禁外洩。不提供解答 (即使提供解答,也只限於板書模式)

(撰寫試題無著作權;歡迎全貌下載流傳。)