Tuesday, April 22, 2008

Midterm Exam -- Math for Mgmt (Spring 2008)

Midterm Examination (Int'l Business, WUCL)
Spring 2008 Instructor: 衛忠欣 (Jong-Shin Wei)
管理數學(Mathematics for Management) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib

10:30 am ~ 11:30 am, Tuesday, April 22, 2008. 另卷作答。三日後公佈解答於e-learning,也歡迎以email函索
Closed books/notes exam. 110 points in 60 minutes; absolutely no talking nor borrowing items during exams. 可使用自己的字典或翻譯機。行動電話若響起,該生扣十分,以強調基本禮貌。務必工整扼要、依序作答。違反規定,視同放棄調分機會。Watch your time and have fun!
Part One: Multiple choice questions. [Choose the most appropriate one from 4 alternatives. 依慣例,答錯不倒扣。] 80 points 每五題成一列,由左至右,逐題標明題號作答。
1. The graph of function f(x) := 5 if x is in [0, 5]; f(x) := x if x > 5 is the same as the graph of
(A) g(x) := Max{x, 5} defined for all non-negative reals x;
(B) g(x) := Min{x, 5} defined for all non-negative reals x;
(C) g(x) := Min{x + 5, x – 5} defined for all non-negative reals x;
(D) g(x) := 5 + Min{x, 5}.
2. How many elements can we find in the set {x is a real: x ≧ 1 and x ≦ 1}?
(A) zero;
(B) one;
(C) two;
(D) None of the above is correct.
3. The incorrect statement about (0, 1) is
(A) it is a point on the first quadrant;
(B) {x is a real: 0 < x < 1};
(C) {(x, y) of R(square): x = 0 and y = 1};
(D) it is a closed interval with endpoints 0 and 1.
4. The set {(x, y) of R2: the slope of the line going thru (x, y) and (1, 2) is 4} is
(A) 4x + y = 6;
(B) 4x - y = 2;
(C) x - 4y = 7;
(D) x + 4y = 9.
5. Choose (x, y) to maximize 2x + y subject to x + y ≦ 5, x ≧ 0, and y ≧ 0.
(A) The solution is (5, 0) only;
(B) The solution is (0, 5) only;
(C) Both (0, 5) and (5, 0) are solutions;
(D) None of the above is correct.
6. [continued from question 5] Which of the following cannot serve as an economic application?
(A) Prices of two consumption goods are 2 and 1 respectively;
(B) Utility function is U(x, y) := 2x + y;
(C) Utility function is U(x, y) := (2x + y)2 + 1;
(D) Disposable income is 10.
7. The set {(x, y) of R2: xy = 1, x > 0, and y > 0} can be
(A) the graph of function f(x, y) := xy for all x > 0 and y > 0;
(B) the graph of function f(x) := 1/x for all x > 0;
(C) the graph of function f(x) := 1/y for all y > 0;
(D) None of the above is correct.
8. 「我對你百分之兩百的支持。」In English, it is better put as
(A) You have my 110% support;
(B) You have my 200% support;
(C) I give you 200% support;
(D) You have my 200 degrees in support.
9. Let f(x) be twice-differentiable (二次微分存在) and be defined for all non-negative reals. If we know that f(x*) is a local maximum, then
(A) x* = 0 is possible;
(B) we can find an interval (a, b) containing x* such that f(x) ≧ f(x*) for all x in (a, b);
(C) The equation df(x)/dx = 0 has only one solution, which is x*;
(D) d2(f(x))/dx2 ≦ 0 for all x > 0.
10. Consider the function f(x) := x4 defined for all real numbers x.
(A) f(0) is the unique local maximum and unique global maximum;
(B) f can be neither maximized nor minimized;
(C) d2(f(x))/dx2 > 0 for all x;
(D) The local minimum is also the global minimum.
11. Recall the kissing problem (and experiment). If there are 50 kids, then there will be
(A) 100 kissing activities to be performed;
(B) 1,225 kissing activities to be performed;
(C) 1,250 kissing activities to be performed;
(D) None of the above is correct.
*12. [continued from question 11] Recall the paper “Having Fun with Organized Kissing” which you can find on e-learning. By using the proposed method (or scheme) and assuming that each kiss takes 10 seconds, how long does it take to complete the process?
(A) 1,850 seconds;
(B) 1,470 seconds;
(C) 1,180 seconds;
(D) None of the above is correct.
13. [Jump to question 21] In this scenario,
(A) the disutility of hard-working is w - 10;
(B) the rate of unemployment is 1/4;
(C) the rate of unemployment is 0.05;
(D) the unemployment benefit is 6.
14. [continued from question 13] Which of the following will increase the efficiency wage?
(A) A decrease in the disutility of hard-working;
(B) An increase in the rate of unemployment;
(C) An increase in the probability of getting caught while shirking;
(D) An increase in the wage at the next available job.
15. Recall lecture 1. There are three workers, indexed by A, B, and C, ready to accomplish a labor-intensive job of which the amount is normalized to 1, that is, k = 1. Assume fixed productivity, perfect divisibility, and the absence of externalities. Suppose that it takes 10 days if A and B work together (while C does not work at all); if takes 10 days if A and C work together (while B does not work at all); if takes 8 days if B and C work together (while A does not work at all). Denote by x the amount of work done by A working for one day. Similarly y and z represent the amount of work done by B and C working for one day respectively. Obviously,
(A) A is the most efficient or productive;
(B) C is the most efficient or productive;
(C) B is the least efficient or productive;
(D) None of the above is correct.
16. [continued from question 15] How many days does A need if A works alone?
(A) 20 days;
(B) 70/3 days;
(C) 80/3 days;
(D) None of the above is correct.
17. [continued from question 15] How many days does B need if B works alone?
(A) 16 days;
(B) 15 days;
(C) 14 days;
(D) None of the above is correct.
18. [continued from question 15] If three workers work together, then how many days do they need to finish this job?
(A) 4 days;
(B) 70/13 days;
(C) 80/11 days;
(D) None of the above is correct.
19. 本棟大樓的每間教室,皆被分配一個號碼(如506)。此一real-valued function
(A) does not have any local maximum;
(B) does not have any global maximum;
(C) cannot be minimized;
(D) is continuous but not differentiable.
20. (Now it is time to find out who have paid adequate attention to lecturing.) 瀏覽97.03.24網路新聞「張正傑新竹彈三角戀鬧美猴王」之用意是
(A) 修習管理數學可以訓練作戰策略;
(B) 數學訓練可以培養精確性;
(C) 示範沒有備課的教師,如何打發時間;
(D) 誘使大家指出誰是班上最調皮的同學。

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。如昔,教師有權公告具有特色之作答。] 30 points
21. [20 points] Recall lecture 2. This is about the determination of efficiency wage that provides an incentive for a worker to work hard, not to shirk. A worker is paid at wage w > 0. If he works hard (as expected), his utility is w - 10. If he shirks, then with probability 1/4, he will be caught. Once being caught, he will be fired at once (and getting no pay). After being fired, with probability 0.05, he will remain unemployed and will be entitled to receiving unemployment benefit, which is 2. And with probability 0.95, he will be getting a new job at wage 6. If he shirks, then with probability 3/4, he will not be caught and his utility will be w.
(i) Use a decision tree to illustrate this worker’s decision-making.
(ii) Find the minimal wage providing an incentive for him to work hard. In other words, find the efficiency wage w.

22. [10 points] Suppose that you and I are playing the scissors-rock-paper game. We both show our choices simultaneously. The loser gives $1 to the winner. Nobody pays if there is a tie. Carefully draw a game tree to describe it.

(放棄智慧財產權;歡迎全貌下載流傳。)

Monday, April 21, 2008

Midterm Exam -- Macro Principles (Spring 2008)

Midterm Examination (Int'l Business, WUCL)
Spring 2008 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 http://www.wtuc.edu.tw/ib

4:00 pm ~ 5:00 pm, Monday, April 21, 2008. 另卷作答。三日後公佈解答於e-learning,也歡迎以email函索
Open books/notes exam. 110 points in 60 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。務必工整扼要、依序作答。違反規定,視同放棄調分機會。平日無閱讀英文教材習慣的同學,想必會有時間壓力。Watch your time and have fun!
Part One: Multiple choice questions. [Choose the most appropriate one from 4 alternatives. 依慣例,答錯不倒扣。] 80 points 每五題成一列,由左至右,逐題標明題號作答。
1. Nowadays the best single measure of an economy’s well-being or performance is
(A) inflation rate;
(B) rate of unemployment;
(C) trade deficit;
(D) gross domestic product.
2. Which of the following does not imply that there is an increase of GDP by 100 dollars?
(A) Anna paid Bob 100 dollars to mow her lawn;
(B) Andy stole 100 dollars from Becky’s purse;
(C) Adam borrowed 100 dollars from a bank to improve the operation of his store;
(D) None of the above is correct.
3. Which of the following best describes the connection between microeconomics and macroeconomics?
(A) One cannot learn macroeconomics without learning microeconomics first;
(B) One cannot learn microeconomics without learning macroeconomics first;
(C) Households and firms are interacting in many markets;
(D) Nobel prizes in economics have never been awarded to economists for their contributions to microeconomics.
4. Find the incorrect statement about GDP.
(A) The market value of owner-occupied housing is included in GDP;
(B) The market value of tomatoes Mary grew and consumed from her backyard is included in GDP;
(C) The market value of illegal drugs is not included in GDP;
(D) The market value of (illegal) prostitution services is not included in GDP.
5. Suppose that Hallmark (which is an internationally well-known greeting card supplier) purchased 10 tons of paper in January 2007 (in USA). Hallmark used 8 tons to make greeting cards. At the end of 2007, Hallmark put 2 tons of paper in her warehouse and treated them as inventory. Accordingly, for USA,
(A) the market value of these 2 tons of paper is included in GDP in 2007;
(B) the market value of these 8 tons of paper in included in GDP in 2007;
(C) the market value of these 2 tons of paper will be included in GDP in 2008;
(D) None of the above is correct.
6. Which of the following is included in GDP?
(A) Diana sold her used car to the dealer at the price of 5,000 dollars;
(B) Edward sold his stocks (股票) and got 100,000 dollars in cash;
(C) Frank, an English teacher from UK, made 5,000 dollars last month for his teaching at Wenzao;
(D) George bet on professional baseball games and won 10,000 dollars.
7. Let’s now examine the components of GDP. Find the incorrect statement.
(A) Your tuition and fees should be included in C;
(B) Increase in the inventory should be included in I;
(C) Unemployment benefits should be included in G;
(D) President’s (總統的) salary should be included in G.
8. Suppose that our government spent 1 million dollars last year in purchasing Boeing aircrafts from USA. This made our
(A) G increase by 1 million dollars last year;
(B) NX increase by 1 million dollars last year;
(C) GDP increase by 1 million dollars last year;
(D) C increase by 1 million dollars last year.
9. 『愛用國貨』這句口號,可以與下列何者,搭配在教學上?
(A) GDP is a flow variable;
(B) GDP := C + I + G + NX;
(C) GDP is measured in current prices;
(D) The increase in inventory is a part of I.
10. If we look at a recent year GDP data for USA, we shall see that
(A) G/GDP is over 1/2;
(B) C < I + G;
(C) C per person is about NTD600,000;
(D) NX is always negative.
11. Examples of externalities do not include
(A) Dioxin is a by-product of producing paper;
(B) A dog barks at mid-nights;
(C) Getting hurt in our green vs. red experiment conducted during lectures;
(D) Research into new technology for mankind.
12. From the social planner’s point of view, in the presence of a negative externality in production, at social optimum
(A) the price should be below the market equilibrium price;
(B) the price should be the same as the market equilibrium price;
(C) the quantity should be below the market equilibrium quantity;
(D) None of the following is correct.
13. From the social planner’s point of view, in the presence of a positive externality in consumption, at social optimum
(A) the price should be above the market equilibrium price;
(B) the price should be the same as the market equilibrium price;
(C) the quantity should be the same as the market equilibrium quantity;
(D) None of the following is correct.
14. In the presence of a negative externality in production, the social planner can achieve the socially optimal outcome by
(A) imposing a unit tax on suppliers;
(B) imposing a unit subsidy on suppliers;
(C) imposing an income tax on consumers;
(D) reducing the income tax.
15. Which of the following best captures the so-called Coase theorem?
(A) Even if the bargaining is costly, private economic agents can solve the problem of externalities on their own regardless of the initial distribution of property rights.
(B) Private economic agents can solve the problem of externalities on their own only when the initial distribution of property rights is correct;
(C) Private economic agents cannot solve the problem of externalities on their own
unless there is justice in the initial distribution of property rights;
(D) If the transaction cost is zero, private economic agents can solve the problem of externalities on their own regardless of the initial distribution of property rights.
16. Coase theorem tells us that
(A) 情場失意人一定會有美好姻緣;
(B) 落跑員工不該輕率發信批評老闆與同仁;
(C) 上課頻跑廁所的同學將來一定不會有好工作;
(D) 學校不必統一規定每間教室的冷氣使用與收費辦法。
17. Examples of reducing the transaction costs do not include
(A) 本課程教師徵求義工,負責教室管理;
(B) Anna 寫匿名信給 Bob,表達愛意;
(C) 房東在「城市租屋族」網站登錄;
(D) 學校雇用司機、買校車,取消租用校車。
18. Lessons from the idea (or examples) of the tragedy of commons do not include
(A) 系辦公室吵鬧情況,日趨嚴重;
(B) 市民呼籲以付費停車場,取代部份的公有免費停車場;
(C) 很多學校限制住宿生之網路下載容量;
(D) 國企系學生應該享有Z0507 (即國企系資源教室)之免費列印權。
19. 消弭the tragedy of commons的作法,不包含
(A) 限制田徑場跑道之慢跑動線,單日為順時針、雙日為逆時針;
(B) 圖書館限制校外人士之使用權限;
(C) 推動全系同學票選系主任、全校師生票選校長;
(D) 學校禁止同學使用講台的電腦。
20. A good example illustrating being excludable yet not rival is
(A) 學生使用學生活動中心;
(B) 救生員的保護泳客安全;
(C) 傍晚時段由10號高速公路駛向文藻;
(D) 清明節期間行駛中山高。

Part Two: Analytical or short-essay 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。援例,教師有權公告具有特色之作答。] 30 points
21. [10 points] (Obviously, now it is time to find out who have not read text with care and patience.) Recall the London plan made by Mayor Ken Livingstone. 在你我的周遭環境裡,找出一個實例,扼要說明兩者的相似處。
22. [10 points] When it comes to the debate on market-based policies toward negative externalities (such as pollution), some economists prefer selling pollution permits to levying the so-called Pigovian taxes. Why?
23. [10 points] (實用題) After reading ‘In the News – Should Yellowstone Charge as Much as Disney World?’ in your text, you might apply it to the following question: Why is the dining room (學生餐廳at the basement of the dormitory at Wenzao) always crowded at noon? Yet, students kept complaining about the service; providers of food services may also complain about not making good profits. 該如何改善學生餐廳的營運呢?

(放棄智慧財產權;歡迎全貌下載流傳。)