Saturday, January 16, 2010

Solution to Final Exam -- 被外行人刪除的課程 Microeconomics (F2009, Wenzao)

★★★★ Solution to Final Exam (Int’l Business Administration, WUCL) ★★★★
Fall 2009 Instructor: 衛忠欣 (Jong-Shin Wei)
個體經濟學 (Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw jsw12011958@gmail.com
3:30 pm ~ 5:15 pm, Wednesday, January 13, 2010
Open books/notes exam. You can consult dictionary of any kind from 3:30 pm to 4:10 pm only. This is intended to creative incentives for you to read materials before the test, not during the test.不可參閱中文書籍與中譯本。教科書影印本,更在嚴禁範圍內。For questions 1 to 30, choose the most appropriate one from four alternatives. Three points for each. Questions 31~33 are analytical questions. Total: 120 points. 題目較靈活、非填鴨式,宜有系統地依序作答。

1. Imagine that you were a vendor of selling coffee at some festival (園遊會) from Monday thru Friday. On each day you had to pay NTD500 in advance for (renting) coffee maker, kitchen facilities, chairs, tables, water and electricity usage (all in one package). On Monday, you paid NTD3,000 for purchasing coffee beans, sugar, milk, and paper cups. All were exhausted at the end of Wednesday. In the early morning on Thursday, you made another (補貨) trip to buy coffee beans, sugar, milk, and paper cups, which cost you NTD5,000. At the end of Friday, luckily all were exhausted. Each day you hired a part-time worker at the cost of NTD1,000 daily. Before the festival, you earned NTD2,000 daily by working at some coffee shop. Assume that you asked 5 days off in order to sell coffee at festival. Those are all we know about your cost structure. From Monday thru Wednesday you sold 100 cups daily; from Thursday to Friday you sold 200 cups daily. The price of coffee was fixed at NTD50 per cup throughout. [This question and some following it were conceived by a stimulating conversation with Mr. Chu, also a student in this class.] Treating those five days as the period of running business, your fixed cost was
(A) 500;
(B) 2,500;
(C) 7,500;
(D) 25,500.
Ans: B. [Note that another (less plausible) way of doing it is to treat salaries paid to part-time helper and your foregone salaries as part of your fixed cost. In that way, the answer becomes 17,500 (= 2,500 + (1,000)(5) + (2,000)(5)).]

2. [continued from question 1] Treating those five days as the period of running business, your variable cost was
(A) 10,000;
(B) 15,000;
(C) 18,000;
(D) 23,000.
Ans: D. [3,000 + 5,000 + (1,000)(5) + (2,000)(5) = 23,000. Again, another (less plausible) way of doing it is to count salaries paid to part-time helper and your foregone salaries as part of your fixed cost. In that way, the answer becomes 8,000.]

3. [continued from question 1] Treating those five days as the period of running business, your profit was
(A) somewhere between 1,000 and 1,500;
(B) somewhere between 800 and 1,000;
(C) somewhere between 600 and 800;
(D) None of the above is correct.
Ans: B. [Profit was [(100)(3) + (200)(2)](50) - 2,500 - 23,000 = 9,500.]

4. [continued from question 1] Let q be the amount of cups sold daily. Denote C(q) your variable cost (function).
(A) C(100) = C(200);
(B) C(100)/C(200) is about 0.5 ;
(C) C(100)/C(200) is about 0.7;
(D) C(100)/C(200) is about 0.6.
Ans: C. [On Monday, variable cost of producing 100 cups was 1,000 + 2,000 + 3,000/3 = 4,000. Likewise for Tuesday and Wednesday. On Thursday, variable cost of producing 200 cups was 1,000 + 2,000 + 5,000/2 = 5,500. On Friday, variable cost of producing 200 cups was 5,500 as well. Hence C(100) = 4,000 and C(200) = 5,500. Note 40/55 is about 0.73.]

5. [continued from question 1] Let q be the amount of cups sold daily. Your average variable cost
(A) was decreasing;
(B) was increasing;
(C) was increasing and then decreasing;
(D) was decreasing and then increasing.
Ans: A. [Your average variable cost was 4,000/100 = 40 when q = 100; was 5,500/200 = 27.5 when q = 200. We do not know what happens if q is neither 100 nor 200.]

6. [continued from question 5] Why couldn’t his average variable cost remain to be a constant? Reasons exclude
(A) 每日咖啡濃度未必相同;
(B) 咖啡豆售價會波動;
(C) 牛奶售價會波動;
(D) 顧客對咖啡的需求改變。
Ans: D. [Obvious]

7. [continued from question 1] Let q be the amount of cups sold daily. If we have to say something about your supply curve, that will be
(A) it contains the point (100, 50);
(B) it contains the point (200, 50);
(C) it is consistent with P = MC;
(D) it is a vertical ray.
Ans: B. [At P = 50, making 200 cups yields profit (50 - 27.5)(200) - 500, greater than (50 - 40)(100) - 500.]

8. [continued from question 1] Treating those five days as the period of running business. 你的報酬率 (rate of return) 約為
(A) 12%;
(B) 19%;
(C) 37%;
(D) 41%.
Ans: C. [9,500/25,500 is about 0.37.]

9. Suppose that you have NTD200 to be spent on coffee and cherries consumption. Prices are NTD100 for each cup of coffee; NTD50 for each box of cherries. We quantify your satisfaction as follows: one cup of coffee gives you 20 utils; two cups of coffee give you 28 utils; three cups of coffee give you 34 utils; four cups of coffee give you 38 utils; five cups of coffee give you 41 utils; one box of cherries gives you 20 utils; two boxes of cherries give you 35 utils; three boxes of cherries give you 50 utils; four boxes of cherries give you 80 utils; five boxes of cherries give you 85 utils. Your should buy
(A) 2 cups of coffee;
(B) 1 cup of coffee and 2 boxes of cherries;
(C) 4 boxes of cherries;
(D) None of the above is correct.
Ans: C. [80 is the highest utility level you can get.]

10. [continued from question 9] Here we see
(A) how we solve the problem by using MU1/P1 = MU2/P2;
(B) law of diminishing marginal utility holds for coffee only;
(C) law of diminishing marginal utility holds for cherries only;
(D) law of diminishing marginal utility holds for both goods.
Ans: B.

11. [continued from question 9] If you have NTD400, then you should buy
(A) 3 cups of coffee and 2 boxes of cherries;
(B) 2 cups of coffee and 4 boxes of cherries;
(C) 1 cup of coffee and 5 boxes of cherries;
(D) None of the above is correct.
Ans: B. [(1, 5) will cost you 350 and yield 105 utils; (2, 4) will cost you 400 and yield 108 utils; (3, 2) will cost you 400 and yield 69 utils; (4, 0) will cost you 400 and yield 38 utils. Note that (0, 6) is not feasible.]


12. [continued from questions 9 and 11] Here we see that an increase in income
(A) shifts down your demand curve of coffee;
(B) shifts up your demand curve of cherries;
(C) makes you consume more cherries;
(D) None of the above is correct.
Ans: D. [For coffee, note the movement from (0, 100) to (2, 100); for cherries, the point remains to be (4, 50). 此題係測試同學對需求曲線之靈活運用。]

13. Question 12 best illustrates the phenomenon which is
(A) 咖啡與櫻桃是互補財;
(B) 供給面因素導致咖啡比櫻桃貴;
(C) 所得增加會使消費者增加購買最喜歡的商品;
(D) 櫻桃是你最喜歡的商品。
Ans: D.

14. Suppose that last year you worked as a (private) English tutor for junior high school students to earn tuition and fees. You charged NTD800 per hour when you had one student; NTD600 per hour when you had two students; NTD500 per hour when you had three students; NTD400 per hour when you had four students. The number of students you tutored fluctuated over time. Tutoring was done on the one-on-one basis; one hour per day for each student. Your supply of labor
(A) satisfied the law of supply;
(B) reflected that the market equilibrium price might be around NTD400 per hour;
(C) reflected that the market equilibrium price might be around NTD800 per hour;
(D) reflected that your opportunity cost of tutoring for one hour was no greater than NTD600.
Ans: B. [If your opportunity cost of tutoring for one hour was over NTD400, it did not make sense for you to teach four hours and earn NTD1,600 only.]

15. [continued from question 14] let C(q) be the your daily operating cost (including commuting and preparing materials) in providing tutorial service for the number of students being q of {1, 2, 3, 4}. Which one of the following makes sense?
(A) C(1) = 600; C(2) = 1,000; C(3) = 1,300; C(4) = 1,500;
(B) C(1) = 600; C(2) = 800; C(3) = 1,100; C(4) = 1,500;
(C) C(1) = 600; C(2) = 1,000; C(3) = 1,600; C(4) = 2,600;
(D) C(1) = 700; C(2) = 1,400; C(3) = 2,100; C(4) = 2,800.
*Ans: A. [Think about the decreasing marginal cost. Note that (A) is better than (B) in light of your willingness of offering reduced rate when q increases.]

16. [continued from question 15] You wished that you could have
(A) four students;
(B) at least two students;
(C) at most two students;
(D) at most three students.
*Ans: D. [For one student, (daily) profit was 800 - 600 = 200; for two students, profit was 1,200 - 1,000 = 200; for three students, profit was 1,500 - 1,300 = 200; for four students, profit was 1,600 - 1,500 = 100.]

17. [continued from question 15] Your best friend at Taipei also served as a tutor similarly. Yet she charged NTD800 per hour when she had one student; NTD900 per hour when she had two students; NTD1,100 per hour when she had three students; NTD1,400 per hour when she had four students. Her function C(q) might be defined such that
(A) C(1) = 800; C(2) = 1,900; C(3) = 2,300; C(4) = 4,000;
(B) C(1) = 900; C(2) = 1,800; C(3) = 2,700; C(4) = 3,600;
(C) C(1) = 600; C(2) = 1,800; C(3) = 3,400; C(4) = 5,000;
(D) C(1) = 500; C(2) = 1,100; C(3) = 2,000; C(4) = 3,000.
*Ans: D. [Key: 800 > 500, 1,800 > 1,100, 3,300 > 2,000, and 5,600 > 3,000.]

18. [continued from question 17] In term of production efficiency, we shall say that
(A) you always spent less time on each session than your best friend did;
(B) having more students reduced your preparation time for each session;
(C) you and your best friend were equally efficient;
(D) efficiency comparison does not make sense since tutorial service is not a manufacturing good.
*Ans: B. [To see why (A) cannot be chosen, notice C(1) = 600 in your case; C(1) = 500 in your friend’s case.]

19. [continued from question 17] Your friend wished that she could have
(A) four students;
(B) three students;
(C) two students;
(D) one student;
Ans: A. [For one student, (daily) profit was 800 - 500 = 300; for two students, profit was 1,800 - 1,100 = 700; for three students, profit was 3,300 - 2,000 = 1,300; for four students, profit was 5,600 - 3,000 = 2,600.]

20. [continued from question 17] The reason we assume that you and your friend were at different cities has to do with
(A) the assumption that college students are all alike;
(B) the assumption that searching for qualified tutors is easy;
(C) jealousy;
(D) equilibrium prices.
Ans: D. [See question 14.]


21. Recall question 9. Your utility function might be
(A) U(C1, C2) = Min{C1, C2};
(B) U(C1, C2) = Max{C1, C2};
(C) U(C1, C2) = f(C1) + g(C2);
(D) U(C1, C2) = 2C1 + 3C2.
Ans: C. [Additively separable! Make sure you know why (D) is false.]

22. Suppose that one (kind of) input is used, under the technology characterized by a continuous and increasing function f, to produce some output. The input price r > 0 is given. Assume no fixed cost, f(0) = 0, and f exhibits decreasing returns to factor (defined in Ch.8; also known as the diminishing marginal product). Let C(q) be the cost of producing q units of output. The graph of function C is
(A) 向下開口、正斜率的拋物線;
(B) 向上開口、正斜率的拋物線;
(C) 向下開口且有最高點的拋物線;
(D) 向上開口且有最低點的拋物線。
Ans: B. [Recall lectures]

23. [continued from question 22]
(A) We need calculus to understand it;
(B) C(0) = 0;
(C) marginal cost curve is U-shaped;
(D) average cost curve is negatively sloped.
Ans: B. [Recall lectures]

24. Suppose that one (kind of) input is used, under the technology characterized by a continuous and increasing function f, to produce some output. The input price r = 1 is given. Assume C(q) = 10 + q0.5 be the (total) cost of producing q ≧ 0 units of output. The graph of function f is
(A) 向下開口、正斜率的拋物線;
(B) 向上開口、正斜率的拋物線;
(C) 向下開口且有最高點的拋物線;
(D) 向上開口且有最低點的拋物線。
Ans: A. [Recall lectures]

25. [continued from question 24]
(A)f(0) = 10;
(B)f(2x) = 2f(x);
(C)f(x) = x0.5;
(D)f(x) = x2.
Ans: D. [Recall lectures. Producing q units of output bears the variable cost q0.5 = (1)(q0.5), meaning that q0.5 units of input must be purchased. Hence, x units of input will produce x2 units of output. Hence, production function is f(x) = x2.]

26. [continued from question 24] Assume this firm takes output price P > 0 as given.
(A) Producing nothing is her unique best output choice;
(B) She has two best output choices;
(C) She cannot have any best output choice;
(D) It all depends on whether P is sufficiently high.
Ans: C. [Obvious. d/dq is positive when q is sufficiently large.]

27. Let variable cost curve be向下開口、正斜率的拋物線for q > 10; becomes 向上開口、正斜率的拋物線 for q > 10。The marginal cost is 6 at q = 10.
(A) It is possible to have MC = AVC at q = 10;
(B) 6 is the minimized marginal cost occurring at q = 10;
(C) AVC is minimized at q = 10;
(D) For q > 10, her AVC is向上開口、正斜率的拋物線;
Ans: B. [Last week I showed by drawing on the chalkboard why (A) is false.]

28. 『我不知道,這是不是你要的答案。我覺得‧‧‧』課堂討論裡,與這句話無關的是
(A) 洪蘭教授;
(B) 鄭同學;
(C) 國企系第一屆與第二屆各一位女性畢業生;
(D) 前任校長。
Ans: A. [Recall lectures. From questions 28 and 29 you might see why we do not really need mandatory attendance checking. 我的焦點與洪蘭教授不同,上課時間啃雞腿的學生有三種:邊啃邊聽課的、邊啃邊放空的、在教室外啃雞腿的。強制點名制度下,第三種不存在。我認為區分前兩者,是教師的基本責任。]

29. Find the correct statement.
(A) 本學期任課教師提供三次 Dollar Auction 實驗;
(B) 本學期任課教師在 Dollar Auction 實驗中,約賠了NTD200;
(C) 上週吳同學授課中途報備尿遁,係由窗戶出去、由前門回來;
(D) 上週蘇同學前來旁聽,被她同學戲稱為「水貨」。
Ans: C. [The idea of making this question is similar to that of question 28.]

30. “The exam consists of 100 questions (皆為四選一的選擇題). Correct answers are equally distributed among A, B, C, and D. I do not care if anyone happens to pick the same answer, say C, for all 100 questions,” announced by Professor John Doe before the exam starts.
(A) Hard-working (and brilliant) students in good standing will benefit (most) from this design;
(B) Unprepared students will benefit (most) from this design;
(C) It now becomes impossible to have anyone scoring under 25 points;
(D) Students with average performance will benefit (most) from this design.
Ans: A. [Such a design actually benefit hard-working (and brilliant) students while penalizing the unprepared students. Why? Does this resemble the open books/notes policy?]

31. You are a price-taking consumer with utility function U(C1, C2) = C1 + C2 defined for all non-negative real numbers C1 and C2. Your budget line is given by
2C1 + C2 = 100.
(i) Precisely depict your indifference map and budget line on C1-C2 space. Find your optimal consumption bundle(s).
(ii) Recall what we did for deriving the (individual) demand curve of good one. Use a diagram to illustrate how, for this case, you find your demand curve of good one on the C1*-P1 space. Hint: Let P2 be fixed at 1 and vary P1.
Ans: skipped; recall lectures and see text.

32. Use an indifference map and budget lines to illustrate why it is possible, for a price-taking consumer in a two-good case, to have the following effects:
P1 = 0, P2 > 0, and M = 0 → C1* < 0 and C1* > 0.
Ans: skipped; recall lectures.

33. [Test how you think like an economist.] The following photo was taken by me during the class break. Here is my recollection. Right before the break, I noticed that the student (Mr. Lee) on that photo was apparently taking a nap for a few minutes. So, during the break I approached him and took my mobile phone out. With his consensus and my properly setting the scene (intentionally showing the textbook cover), I had that photo taken in 10 seconds. According to my background check, that student outscored (or outplayed) most students in that class in the midterm exam.



An unintelligent bystander later commented: “It is silly to publicize that photo. It is YOUR microeconomics text shown in that photo. Professors teaching some other courses might use that photo against you. 讓洪蘭知道,就慘了!”
Why am I, trained in economics, so sure about the above comment being silly or even stupid?
Ans: Information asymmetry is the key issue. People neither can nor wish to know what is going on in each classroom. I have never heard about evaluating universities based on such criterion. When I was an undergraduate student, at that time some universities had strict policies (even mandatory school uniform) but nobody valued those some universities above some others which were much liberal in nature. Nowadays, we know grading can be quite subjective, and even be used to exchange good relationship with students particularly when professors really had little to teach at those courses, nor are they interested in the course materials themselves. That is why good schools (and even MOE here) have to emphasize the research performance. After all, it is a tough battle with much stronger enemies. However, bystanders did make a big scene out of some trivial incidents, e.g., the news about Medical School at NTU and a mini series following the observation made by Prof. Hung. Well, self-disclosure might help a bit. What actually interested me was the immediate comment made by Mr. Lee, “I really want to have the textbook used in XXX (name of another course) shown up on the photo.” Since he was half sleepy while saying that, I have every reason to believe that he was not lying. Also see questions 28 and 29.

Monday, January 11, 2010

Solution to Final Exam -- Micro Principles (F2009, Wenzao)

★★★ Solution to Final Exam (Int’l Business Administration, WUCL) ★★★
Fall 2009 Instructor: 衛忠欣 (Jong-Shin Wei)
經濟學一 (Principles of Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw jsw12011958@gmail.com
3:30 pm ~ 5:00 pm, January 11, 2010 Open books/notes exam. For questions 1 to 30, choose the most appropriate one from four alternatives. Three points for each. Questions 31 and 32 are short-essay or analytical questions (12 points each).
Total: 114 points. 字典與翻譯機,限於 4:00 pm 前使用。題目較靈活、非填鴨式,宜有系統地依序作答。

1. Recently we saw a movie clip about a meeting between a college young man (Todd) and his professor (Dr. Stephen Malley played by Robert Redford) in his office. That meeting took place
(A) in the late afternoon;
(B) at lunch hour;
(C) in the early morning;
(D) in the evening.
Ans: C. [From questions 1 thru 3, you will see why we do not really need mandatory attendance checking. 我的焦點與洪蘭教授不同,上課時間啃雞腿的學生有三種:邊啃邊聽課的、邊啃邊放空的、在教室外啃雞腿的。強制點名制度下,第三種不存在。我認為區分前兩者,是教師的基本責任。]

2. [continued from question 1] The title of that movie is
(A) The Class;
(B) The Emperor's Club;
(C) Charlie Wilson’s War;
(D) Lions for Lambs.
Ans: D. [Chinese title of (D) is 權力風暴;Chinese title of (C) is 蓋世奇才]

3. [continued from question 1] What we can learn from that clip include
(A) students can gain by bribing professors;
(B) students can gain by threatening professors;
(C) opportunity costs;
(D) social costs of cheating on exams.
Ans: C. [Also 差別取價(price discrimination)與自我選擇(self selection). http://www.aliran.com/index.php?option=com_content&view=article&id=427:on-robert-redfords-new-film-lions-for-lambs&catid=53:200710&Itemid=10 ]

4. Lessons we learn from rainfall data in California and New Mexico are
(A) 陳菊市長透過垃圾車廣播呼籲大家節約用水是有效的;
(B) 自來水公司應該視地區制定水費費率;
(C) 自來水公司應該由大陸進口自來水;;
(D) 政府應補貼獎勵大家抽取地下水。
Ans: B. [p.126, text]

5. [continued from question 4] Bad policies include
(A) 針對公立學校推動「一校一泳池」,減少民營游泳池之供給;
(B) 對洗車業實施總量管制;
(C) 檢討用水量龐大的工廠之水費費率與輔導遷徙;
(D) 對游泳池與三溫暖業者實施給水總量管制。
Ans: A.

6. The notion of utilometer
(A) was proposed by Adam Smith;
(B) was proposed by Jeremy Bentham;
(C) was proposed by Thorstein Veblen;
(D) was proposed to measure output thru input usages.
Ans: B. [p.126, text]

7. Examples of violating the law of diminishing marginal utility include
(A) 咖啡續杯半價;
(B) 90分鐘的協同教學的聽眾意見回饋通常比一學期的教學評量為佳;
(C) Most prefer spending NTD240 to see the movie Avatar now to buying its DVD at NTD299 six months later;
(D) Unfamiliar songs may become your favorite songs.
Ans: D. [p.126, text]

8. Suppose that you have NTD200 to be spent on coffee and strawberries consumption. Prices are NTD100 for each cup of coffee; NTD50 for each box of strawberries. We quantify your satisfaction as follows: one cup of coffee gives you 10 utils; two cups of coffee give you 18 utils; three cups of coffee give you 22 utils; four cups of coffee give you 24 utils; five cups of coffee give you 25 utils; one box of strawberries give you 20 utils; two boxes of strawberries give you 35 utils; three boxes of strawberries give you 45 utils; four boxes of strawberries give you 50 utils; five boxes of strawberries give you 51 utils. Your should buy
(A) 1 cup of coffee and 2 boxes of strawberries;
(B) 2 cups of coffee;
(C) 4 boxes of strawberries;
(D) None of the above is correct.
Ans: C. [50 is the highest utility level you can get. See pp.127-133, text]

9. [continued from question 8] Here we see
(A) how the formula MU1/P1 = MU2/P2 works;
(B) law of diminishing marginal utility holds for coffee only;
(C) law of diminishing marginal utility holds for strawberries only;
(D) law of diminishing marginal utility holds for both goods.
Ans: D. [Judging from 10 > 8 > 4 > 2 > 1 and 20 > 15 > 10 > 5 > 1]

10. [continued from question 8] If you have NTD300, then you should buy
(A) 3 cups of coffee;
(B) 2 cups of coffee and 2 boxes of strawberries;
(C) 1 cup of coffee and 4 boxes of strawberries;
(D) None of the above is correct.
Ans: C. [60 is the highest utility level you can get. See pp.127-133, text]

11. [continued from questions 8 and 10] Here we see that an increase in income
(A) shifts your demand curve of coffee to the right;
(B) shifts your demand curve of strawberries to the right;
(C) makes you consume less of coffee;
(D) makes you consume less of strawberries.
Ans: A. [For coffee, note the movement from (0, 100) to (1, 100); for strawberries, the point remains to be (4, 50). 此題係測試同學對需求曲線之靈活運用。]

12. Question 11 best illustrates the phenomenon which is
(A) 咖啡與草莓是互補財;
(B) 供給面因素導致咖啡比草莓貴;
(C) 所得增加會使消費者增加購買最喜歡的商品;
(D) 你是理性的消費者。
Ans: D. [草莓是你最喜歡的商品]

13. According to Chapter 5,
(A) 建商應該在台北信義區興建大坪數的高樓住宅;
(B) 建商應該在屏東地區興建小坪數的高樓住宅;
(C) 由好市多(Costo)試吃的大排長龍,可推知主客群所得水準下降;
(D) 由好市多(Costo)試吃的大排長龍,可推知顧客滿意度增加。
Ans: C. [pp.136-138, text]

14. During the last 30 years or so, we see fast growth in manufacturing industries while the service industries tend to grow slowly. Yet we see that real wages in both categories have risen substantially. One explanation is
(A) opportunity cost;
(B) government regulation;
(C) that nowadays it is more difficult to obtain licenses in service industries;
(D) that nowadays service industries have less employees.
Ans: A. [pp.147-148, text]

15. Suppose that you have worked as a (private) English tutor for junior high school students to earn tuition and fees. You charge NTD800 per hour if you have one student; NTD600 per hour if you have two students; NTD500 per hour if you have three students; NTD400 per hour if you have four students. Tutoring is done on the one-on-one basis; one hour per day for each student. Your supply of labor
(A) satisfies the law of supply;
(B) reflects that the market equilibrium price must be around NTD400 per hour;
(C) reflects that the market equilibrium price must be around NTD500 per hour;
(D) reflects that your opportunity cost of tutoring for one hour is no greater than NTD400.
Ans: D. [If your opportunity cost of tutoring for one hour is over NTD400, it does not make sense for you to teach four hours and earn NTD1,600 only.]

16. [continued from question 15] let C(q) be the your daily operating cost (including commuting and preparing materials) in providing tutorial service for the number of students being q of {1, 2, 3, 4}. Which one of the following makes sense?
(A) C(1) = 800; C(2) = 1,200; C(3) = 1,500; C(4) = 1,800;
(B) C(1) = 500; C(2) = 700; C(3) = 900; C(4) = 1,000;
(C) C(1) = 600; C(2) = 1,200; C(3) = 1,800; C(4) = 2,400;
(D) C(1) = 600; C(2) = 800; C(3) = 1,200; C(4) = 1,600.
*Ans: B. [Think about the non-increasing or decreasing marginal cost]

17. [continued from question 15] You wish that you can have
(A) four students;
(B) three students;
(C) at most two students;
(D) at least three students.
*Ans: D. [For one student, (daily) profit is 800 - 500 = 300; for two students, profit is 1,200 - 700 = 400; for three students, profit is 1,500 - 900 = 600; for four students, profit is 1,600 - 1,000 = 600.]

18. [continued from question 16] Your best friend also serves as a tutor similarly. Yet she charges NTD800 per hour if she has one student; NTD900 per hour if she has two students; NTD1,100 per hour if she has three students; NTD1,400 per hour if she has four students. Her function C(q) might be defined such that
(A) C(1) = 800; C(2) = 1,600; C(3) = 3,000; C(4) = 5,600;
(B) C(1) = 900; C(2) = 1,800; C(3) = 2,700; C(4) = 3,600;
(C) C(1) = 700; C(2) = 1,500; C(3) = 3,000; C(4) = 5,000;
(D) C(1) = 600; C(2) = 1,200; C(3) = 1,800; C(4) = 2,400.
*Ans: C.

19. [continued from question 18] In term of production efficiency, we shall say that
(A) you are more efficient than your best friend is;
(B) you are less efficient than your best friend is;
(C) you and your best friend are equally efficient;
(D) efficiency comparison does not make sense since tutorial service is not a manufacturing good.
Ans: A.

20. Borrow the example of Harry’s collecting recycled cans detailed in Chapter 6. Let q be the amount of cans he find; P be the redemption price (which is how much Harry can get for each collected recycled can). Suppose q = 600 (measured in cans daily) if P = 1 (cent per can); q = 1,000 if P = 1.5; q = 1,300 if P = 2; q = 1,500 if P = 3; q = 1,600 if P = 5. Stories behind this exclude
(A) Harry has more incentive to collect cans when P is higher;
(B) It becomes more difficult to collect cans when P is higher;
(C) Collecting more cans make Harry work more efficiently;
(D) More people start collecting cans when P is higher.
Ans: C. [Recall lectures]

21. [continued from question 20] Those (q, P) pairs are best interpreted as
(A) Harry’s demand curve as a price-taking consumer;
(B) The market supply curve of recycled cans;
(C) Harry’s supply curve as a price-taking producer;
(D) Harry’s supply curve as a price-making producer.
Ans: C. [Obvious]

22. The text has an example showing that each resident is willing to pay 6 cents (thru taxes) for each container removed from local environment. If the community has 60,000 citizens, then the benefit of removing one container becomes (6/60,000 =) 0.0001 cent per person! By the similar reasoning, when library spends NTD400,000 on subscribing e-journals or e-books but, on record, only 400 (檢索與下載人次) out of 8,000 people actually use them,
(A) we should pay attention to 400,000/8,000;
(B) we should pay attention to 400,000/400;
(C) we should stop subscribing them and subsidizing those 400 people or less;
(D)其意義與大量印發便民手冊與勞服宣導手冊相同。
Ans: A. [Think of the nature of public goods. See pp.164-165, text.]

23. The text raises an interesting point regarding financial analysts spending money and time on having superior forecasting models. Which of the following is not true?
(A) There are too many smart people working as corporate earning forecasters;
(B) Any one individual analyst spends less, he can be sure that the winning forecast will not be his;
(C) The society as a whole suffers little if all analysts spent less money on their forecasting models;
(D) Competition among those analysts leads to social optimum.
Ans: D. [See p.189, text]

24. A monopolist faces the market demand function f(P) = a - bP (with a > 0 and b > 0).
(A) Her marginal revenue curve (on Q-MR space) is 正斜率的直線。
(B) Her marginal revenue curve (on Q-MR space) is 負斜率的直線;
(C) Her revenue curve (on Q-R space) is 向上開口、正斜率的拋物線;
(D) Her revenue curve (on Q-R space) is 向下開口、正斜率的拋物線。
Ans: B. [Q = a - bP we have R = PQ = (a/b)Q - Q2/b, hence MR = a/b - (2/b)Q. See p.218, text]

25. [continued from question 24] Her revenue is maximized when
(A) Q is a;
(B) Q is a/2;
(C) Q is a/3;
(D) None of the above is correct.
Ans: B. [Q = a/2 maximizes R = PQ = (a/b)Q - Q2/b. Why? Note also that MR = 0 when Q = a/2.]

26. A firm takes output price P > 0 as given. Her variable cost is 0 at q = 0; 10 at q = 1; 15 at q = 2; 16 at q = 3; 20 at q = 4. Producing nothing is her unique best output decision if
(A) P = 4;
(B) P = 5.6;
(C) P = 6;
(D) P = 10.
Ans: A. [Her minimal average variable cost is 5 at Q = 4. Note profit is Q(P - AVC) - FC.]

27. [continued from question 26] Let P = 5.
(A) She can not maximize her profit;
(B) q = 5 is her best output decision;
(C) She cannot shut down production;
(D) She will choose q such that her marginal cost equals 5.
Ans: B. [At P = 5, she can choose either q = 0 or q = 4, yielding maximized profit as -FC. Hence we see the shut-down option. Marginal cost is not defined here.]

28. Suppose that both AVC and MC curves are U-shaped. MC is minimized at q = 3; AVC is minimized at q = 8; MC = AVC at q = 8 only.
(A) For q < 3, her VC is向下開口、正斜率的拋物線;
(B) For q > 3, her AVC is向上開口、正斜率的拋物線;
(C) For q < 8, her MC is向上開口、正斜率的拋物線;
(D) For q > 3, her MC > AVC.
Ans: A. [For q < 3, her VC is向下開口、正斜率的拋物線。For q > 3, her VC is向上開口、正斜率的拋物線。]

29. Let market demand and supply curves be Q = 3 - P and Q = P - 1 respectively.
If government decides to impose a unit tax, $1, and let sellers collect taxes on behalf of the government. At the new equilibrium (Q*, P*), we see
(A) consumers’ surplus is 1/8;
(B) consumers’ surplus is 1/4;
(C) producers’ surplus exceeds consumers’ surplus;
(D) None of the above is correct.
Ans: A. [Before tax, the equilibrium price is 2 and the equilibrium quantity is 1. Imposing unit tax on sellers’ side makes the supply curve shift to P = 1 + Q + 1 = 2 + Q. By Q = 3 - P and Q = P - 2, we get P* = 2.5 and Q* = 0.5. Keep in mind that sellers have to render tax money (= (1)(0.5)) to the government. It is easy to calculate CS = PS = (1/2)(1/2)(1/2) = 1/8.]

30. Let market demand and supply curves be Q = 3 - P and Q = P - 1 respectively.
If government decides to impose a unit tax, $1, directly on consumers.
(A) The new demand curve is Q = 4 - P;
(B) The new demand curve is Q = 2 - P;
(C) The new equilibrium quantity is 1;
(D) The new producers’ surplus is 1/4.
Ans: B. [The new demand curve is P = 3 - Q - 1 = 2 - Q. By P = 2 - Q and P = 1 + Q, we get Q** = 0.5 and P** = 1.5. Here, CS = PS = 1/8.]

31. Nowadays most countries do not have beverage container deposit laws (that require prices must be marked up to include the container deposit). Yet containers (especially aluminum cans) are well recycled by market force. In all universities in Taiwan, professors are required to hold (at least) 4 hours per week as office hours. Students are also asked in end-of-term teaching evaluations about whether they find professors helpful outside the classrooms. Ironically, students, definitely including mine, generally do not make use of office hours. Can you use demand and supply curves to analyze the “market” for office hours? Identify what price and quantity are. Can we say that there is a market failure here? What can we do to increase the demand (and/or supply) of advising time provided by the office hours policy? Will lifting (or abandoning) the office hours policy make students use more office hours? Can we say that students in better universities use office hours more often?
Ans: (skipped here)

32. Consider two countries, A and B. Suppose that each country has 10 hours to spend on producing goods. Assume that for one hour in the production of (good) X, A can produce 4 units of good X; for one hour in the production of (good) Y, A can produce 6 units of good Y. Assume that for one hour in the production of X, B can produce 2 units of good X; for one hour in the production of Y, B can produce 4 units of good Y. As we did in class, perfect divisibility and fixed technology are assumed throughout.
(i) Precisely depict the PPC (or PPF) for A on the x-y plane. You must also write down the equation, indicate the intercepts and slope.
Ans: The PPF for A is (1/4)x + (1/6)y = 10 or 3x + 2y = 120. Vertical intercept is 60, horizontal intercept is 40, and the slope is -1.5. [The PPF for B is (1/2)x + (1/4)y = 10 or 2x + y = 40. Vertical intercept is 40, horizontal intercept is 20, and the slope is -2.]

(ii) Does any country have the absolute advantage in producing some good? Carefully explain.
Ans: For one hour in the production of (good) X, A can produce 4 units of good X, B can produce 2 units of good X, hence A has the absolute advantage in producing X.
Likewise, by 6 > 4, A also has the absolute advantage in producing good Y.

(iii) What is A’s opportunity cost of producing good X? What is B’s opportunity cost of producing good X? Does any have the comparative advantage in producing some good?
Ans: The PPF for A is 3x + 2y = 120; the PPF for B is (1/2)x + (1/4)y = 10 or 2x + y = 40. Hence, A’s opportunity cost of producing one unit of good X is 1.5 units of good Y. B’s opportunity cost of producing one unit of good X is 2 units of good Y. We see that A has the lower opportunity cost in producing good X (than B does), hence A has the comparative advantage in producing good X. Of course, B has the comparative advantage in producing good Y.

(iv) After each country specializes on producing some good according to the comparative advantage, a free trade takes place. Name a reasonable relative price of good X for them to trade. Which country is the exporter of good X?
Ans: Any number between 1.5 and 2 will do. Country A will export good X and import good Y.

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Also posted on my blog at http://jsw12011958.blogspot.com/

Last update on January 10, 2010

Friday, January 01, 2010

A random thought to end 2009

After teaching for over 20 years, former students came back once in a while. Some would talk about some good/bad experience in old days, right before I am unconsciously getting those out of my mind (which is a hard disk with limited memory space). What I really want to say is that 4 years actually amount to a very tiny portion in their entire life span. Life does go on.

In recent years, I tried (but in vain) to advise my students to see an old movie "The Emperor's Club" (天之驕子) which, in my opinion, truly reflects what former teachers like myself might have while facing students of different generations across the time zone.

好的老師從沒有自身的成就,他們傾一生之力灌注在學生的生命裡。原先他們(自以為)像是樑柱,撐起學校的一片天。建築物汰舊換新時,少有人會注意到當初的樑柱 -- But what happens if the new building proves to be a lemon good。

"A man's character is his fate."

"We are here to teach students and offer them a chance to excel themselves even against their (initial) will. Yet, some will never learn, for better or for worse. After all, teachers cannot mold students. And possibly no one can! The best we can do probably is to set up some timely examples and provide the best resources we can. The rest is out of our hands. Luckily the service we provide here does not have the life-time warranty. Otherwise, the college might go bankruptcy." If the latter is valid, MOE has no reason to care about 退場機制