★★★★ 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.