Thursday, November 22, 2007
為就業學程的「形象包裝」授課自拍
Taking my own photo for the purpose of teaching "Workshop on Professional Image" on 11222007.
當老師的，一定得以身作則。
Wednesday, November 14, 2007
Solution to Midterm -- Microeconomics F2007
★★★ Solution to Midterm Examination (International Business, WUCL) ★★★
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
個體經濟學(Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 13, 2007
Open books/notes exam. 105 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。3:10 pm ~ 4:10 pm, Wednesday, November 14, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過2分鐘。] 75 points
1. An economy consists of three people: Andy, Bill, and Cindy. There are two consumption goods. Andy cares about good one only. Bill cares about both goods but prefers consuming the same amount of both goods to consuming at the unequal amount. Cindy has no preferences over those goods but only wishes Andy to be happy.
(A) The utility function of Andy can be U(x, y) := x2;
(B) The utility function of Andy can be U(x, y) := x + y;
(C) The utility function of Bill can be U(x, y) := Max{x, y};
(D) The utility function of Cindy can be U(x, y) := x - y.
Ans: A. [Recall lectures]
2. [continued from question 1] If each consumer has 10 dollars in budget. Prices are given as P1 = 1 and P2 = 2.
(A) The optimal consumption decision for Andy is (0, 10);
(B) The optimal consumption decision for Bill is (5, 5);
(C) The optimal consumption decision for Bill is (10/3, 10/3);
(D) None of the above is correct.
Ans: C. [Solving x + 2y = 10 and x = y yields (10/3, 10/3).]
3. [continued from question 1] Suppose that Andy and Bill do not know whether Cindy cares about Andy or cares about Bill. Of course, Cindy knows her own preferences. How will Cindy signal?
(A) Yelling “I love you” to Andy;
(B) Purchasing 10 units of good one;
(C) Purchasing nothing at all;
(D) Sitting next to Andy.
*Ans: B. [Recall lectures. 教師的題庫 (test bank) 是不會有這種靈活題目的。]
4. [continued from question 2] What do we know about budget lines?
(A) All three consumers have the same budget line;
(B) Andy’s budget line is given by 2x + y = 10;
(C) Bill’s budget line is given by 2C1 + C2 = 10;
(D) Cindy’s budget line is given by x + 2y ≦ 10.
Ans: A. [Recall lectures]
5. Which of the following is not the reason for male toads (in Frank's text) to croak?
(A) Female toads can not see how big male toads are;
(B) Other male toads can not see how big male toads are;
(C) Croaking is a signal telling others the size of the toad;
(D) Toads must croak before staring a fight.
Ans: D. [Recall lectures]
6. Frank’s toad story illustrates
(A) the problem with information asymmetry on the part of all female toads only;
(B) the problem with information asymmetry on the part of all male toads only;
(C) the problem with information asymmetry on all toads;
(D) the problem with market failure.
Ans: C. [Why not (D)? Since there is no market for toad-mating, we cannot talk about market failure per se.]
7. Examples of cheap talk do not include
(A) “Untie me and let me go home, please. I won't report to the police. You already have my nude photos;”
(B) “I always practice safe sex. Let's get down to it;”
(C) “I will kill myself if I ever lie to you;”
(D) “If you study harder, you will pass the course.”
Ans: A. [Recall lectures]
8. [Credit: Inspirations came from a conversation with Claire, Linda, and Peggy.] 如果學務處要知道「那一個系學會完全沒有投入文藻週活動」，應該如何？
(A)在校園隨機抽問300位學生；
(B)在e-learning platform隨機匿名抽問300位學生；
(C)發電子郵件請教所有的系主任；
(D)召開檢討會，要求每位系學會會長必須出席。
Ans: D. [Common sense]
9. Which of the following meets the “costly-to-fake principle” but fails the “full-disclosure principle”?
(A) Having an expensive treat on the first date to show how serious you are;
(B) Marrying your boyfriend to prove that you love him dearly;
(C) Duplicating your car key and giving it to your boyfriend to show your trust;
(D)買情人裝給男朋友穿。
*Ans: B.
10. Which of the following meets the “full-disclosure principle” but fails the “costly-to-fake principle”?
(A) 在大腿以刺青刻上女友的名字;
(B) 自願幫老師天天買午餐;
(C) 借筆記給女朋友影印;
(D) 買情人裝給男朋友穿。
Ans: C.
11. 阿土伯打電話給總經理：「別的應試者，都面試至少10分鐘。我家寶貝女兒阿花，不到七分鐘就出來啦。搞什麼鬼嘛！」總經理該如何回應？
(A) 面試提前結束，是人事主管在釋放訊號；
(B) 對不起，我們程序失當，下週六重考一次；
(C) 如果問答順暢，用不到10分鐘；
(D) 是您家小姐在釋放訊號啊。
Ans: C. [啟示：不要無限上綱，大小事情都硬套上『訊號』。]
12. Which of the following does not make sense?
(A) 台灣大學的教授，較不會在授課大綱上，註明自己擁有博士學位；
(B) 排名末尾的學校的教授，如果有博士學位，多會註明自己擁有博士學位；
(C) 大學校長在報紙投書時，應該註明自己擁有博士學位；
(D) 高中生參加全國科學展，不該陳列準備階段的生活照。
Ans: C. [Slide no.16, lecture 2]
13. Often college professors are working hard to get papers published. This has little or nothing to do with the fact that
(A) they are signaling their quality;
(B) they simply cannot teach well;
(C) it is hard to evaluate teaching effectiveness;
(D) college administrators let the external peer review help them evaluate professors.
Ans: B.
14. 假設全班同學都無法完成 Assignment One，教師仍然要區分優劣作品。妳/你應該
(A) find some native speaker to polish your letters before you turn it in;
(B) provide the original communication evidence as soon as possible;
(C) open a Word document and make up the reply;
(D) write a nasty letter to those who have not responded.
Ans: B.
15. Let your budget line be 3x + 2y = 10 and your utility function is U(x, y) = (x + y)2.
(A) Your preferences cannot be of the perfect substitution nature;
(B) You may not act as a price-taker;
(C) Your marginal rate of substitution between good X and good Y is 1.5;
(D) Your will buy 5 units of good Y.
Ans: D. [Recall lectures]
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。教師也有權公告具有特色之作答。] 30 points
16. [5 points]
Recall what you wrote on Assignment 2 (about your profile). Carefully point out where in that assignment you “signaled your characteristics (or merits)”. Explain briefly. Of course, you will get zero if you have not turned in your Assignment 2.
17. [5 points]
Recall the on-line auction experiment we conducted on Nov. 7, 2007. Suppose that five people (called bidders) participate in an English auction. Their privately known reservation prices (as potential buyers) are: 100 (dollars) for bidder 1, 150 for bidder 2, 200 for bidder 3, 200 for bidder 4, and 250 for bidder 5. The auctioneer announces (1) each bid incremental must be 5, 10, 15, …. (i.e., 5的倍數) and (2) the auction starts at 50. What follows is the log of bidding process.
Bidder 2: 60
Bidder 1: 65
Bidder 2: 70
Bidder 3: 75
Bidder 4: 90
Bidder 2: 100
Bidder 5: 180
Bidder 4: 190
Bidder 3: 195
Bidder 4: 200
Bidder 5: 220
The winner is bidder 5.
Based on the above information, find the most intelligent (and rational) bidder and the least intelligent one. Briefly explain why you make such choice.
Ans: Bidder 1 is not aggressive. Bidder 2 bids quite rationally. Bidders 3 and 4 are doing fine but bidder 3 does not seem to closely follow the bidding game for some time. Finally bidder 5 truly will regret because that he could have bid 205 to win the auction. The difference between 220 and 205 (i.e., 15) is referred to as the winner’s curse in the literature. To sum up, we can say that bidders 2 and 4 are the most intelligent (and rational) bidders; bidder 5 is the least intelligent bidder.
18. [20 points] 簡答題 [Hint: Think like an economist.]
(i)就經濟學的觀點，學校該如何確定學生認真填答教學評量？如何找出真正的好老師，而不是「對學生好的老師」？
Ans: Generally speaking, students have little incentive to seriously answer those questionnaires. Cannot blame them as they barely have any idea about what this task is for, let alone getting access to those evaluation results. [現在學校辦的大小活動，還有一堆炒冷飯的碩、博士生，也喜歡一窩蜂的要求滿意度問卷，既無填答誘因，也無法保證彙整過程的公信力。我自己也常逆向操作或亂填，測試主事者的智慧。] 教務主管直接了解每位教師的授課情形，成本確實太高。依賴學生來評量，確有其重要性。因為「教師音量大小」、「教師是否上課遲到」、「教師是否親自監考」，這一類的正確資訊，教務單位很容易取得。只要在教學評量問卷上，分散置入此類問題，再對照真實資訊，系統即可篩選掉「情緒性、報復性的填答者」。當然，有作為的資教或電算中心，還可以藉由系統設計，追蹤每位學生在每門課的期中考成績、給教師的評量、期末考成績。分析學生在不同年級(time series)、不同課程(cross section)、系列課程之學習情況與主觀感受。學生如果知道有此機制，應該會較認真填答。耳朵靈光的資深教師，不難有以下的經驗：一位同學每學期都會向不同老師私下表示，這是我遇到最難的課！This is the toughest course I have ever had! 如何找出真正的好老師？除非落實教學實況的透明化、學校能夠區分用功的學生的回饋與打混的學生之意見、認真的學生或是傑出校友能夠建言，現階段由教師的研究績效(假外界專家之手，即同儕評鑑)來評比，也算是次佳解之一吧。
(ii)學校為何不直接公告每位專、兼任教師的教學評量，來幫助學生辨識真正的好老師、也可提供選課參考？
Ans: 頭腦清楚的學校主事者，應該知道無法確保學生認真填答，所以不能單以教學評量，來排序教師的教學表現、甚至開鍘。但是，為了應付(或配合)家長的要求、立委的指責、輿論的關愛，不得不行禮如儀，還要依此辦理優良教師選拔等活動。更諷刺的是，主事者以尊重隱私為由，讓學生完全不知評量結果，當然缺乏認真填寫的誘因。主管教務者，與教師們正處於一種「策略性模糊」的均衡狀態。如果直接公告每位專、兼任教師的教學評量，勢必將喚醒不少獅虎，擴大教師對「評量教學績效」之檢討呼聲。當然，教師以easy grade『換取』較佳的評量分數、爭取選課人數，此類問題，勢必會擴散、加深。
[Any resolution? 如果大多數教師，直接把自己的教學評量，大剌剌地張貼於網頁，會有何衝擊效應呢？]
(iii)一門「教師認真授課、學生嚴肅學習」的課程，該如何釋放訊號，以便與「教師敷衍打混、學生迷糊過關」的課程，有所區隔？
Ans: If the former group is relatively small but not negligible as compared with the latter group, then surely I will recommend professors in the former group to try their best to make all lecture notes, exams and solutions available to the general public, which is consistent to the signaling theory. They can also design courses such that shirking students who got easy grades from courses belonging to the latter group will have a hard time to catch up. Lessons will be well taken. Tough grading is fine as long as those who do relatively well will receive good grades from those serious professors. However, if the former is overwhelmingly dominated by the latter, we have the doomsday.
(iv)假設一位高職生面臨兩所學校，很難決定究竟應申請那一所。其中一所學校在網頁標榜：本校教師的教學評量平均值為4.2 (依據5分量表；5分係最佳)；另一所學校則不提此類資料。這位高職生該選那一所？何故？
Ans: Of course, it is the latter! To the best of my knowledge, nowadays most universities and colleges alike claim that the average teaching evaluation statistics is above 4 (on the 5-point scale). [Ironically, when the Ministry of Education ranks or accredits universities, this data plays no role for obvious reason.] If University A publicizes such information, it does not really work as signaling. Instead, it might very likely lure people to think: “Is the procedure of obtaining such data transparent and unbiased?” or “Will having 4.5 in a mediocre place be as good as getting 3.5 in some better school?” This is why you will never see elite schools such as MIT, Stanford, Chicago, and Yale brag that their average teaching evaluation statistics are high. Too bad that many university administrators here never open their mind to learn.
(放棄智慧財產權；歡迎全貌下載流傳。)
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
個體經濟學(Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 13, 2007
Open books/notes exam. 105 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。3:10 pm ~ 4:10 pm, Wednesday, November 14, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過2分鐘。] 75 points
1. An economy consists of three people: Andy, Bill, and Cindy. There are two consumption goods. Andy cares about good one only. Bill cares about both goods but prefers consuming the same amount of both goods to consuming at the unequal amount. Cindy has no preferences over those goods but only wishes Andy to be happy.
(A) The utility function of Andy can be U(x, y) := x2;
(B) The utility function of Andy can be U(x, y) := x + y;
(C) The utility function of Bill can be U(x, y) := Max{x, y};
(D) The utility function of Cindy can be U(x, y) := x - y.
Ans: A. [Recall lectures]
2. [continued from question 1] If each consumer has 10 dollars in budget. Prices are given as P1 = 1 and P2 = 2.
(A) The optimal consumption decision for Andy is (0, 10);
(B) The optimal consumption decision for Bill is (5, 5);
(C) The optimal consumption decision for Bill is (10/3, 10/3);
(D) None of the above is correct.
Ans: C. [Solving x + 2y = 10 and x = y yields (10/3, 10/3).]
3. [continued from question 1] Suppose that Andy and Bill do not know whether Cindy cares about Andy or cares about Bill. Of course, Cindy knows her own preferences. How will Cindy signal?
(A) Yelling “I love you” to Andy;
(B) Purchasing 10 units of good one;
(C) Purchasing nothing at all;
(D) Sitting next to Andy.
*Ans: B. [Recall lectures. 教師的題庫 (test bank) 是不會有這種靈活題目的。]
4. [continued from question 2] What do we know about budget lines?
(A) All three consumers have the same budget line;
(B) Andy’s budget line is given by 2x + y = 10;
(C) Bill’s budget line is given by 2C1 + C2 = 10;
(D) Cindy’s budget line is given by x + 2y ≦ 10.
Ans: A. [Recall lectures]
5. Which of the following is not the reason for male toads (in Frank's text) to croak?
(A) Female toads can not see how big male toads are;
(B) Other male toads can not see how big male toads are;
(C) Croaking is a signal telling others the size of the toad;
(D) Toads must croak before staring a fight.
Ans: D. [Recall lectures]
6. Frank’s toad story illustrates
(A) the problem with information asymmetry on the part of all female toads only;
(B) the problem with information asymmetry on the part of all male toads only;
(C) the problem with information asymmetry on all toads;
(D) the problem with market failure.
Ans: C. [Why not (D)? Since there is no market for toad-mating, we cannot talk about market failure per se.]
7. Examples of cheap talk do not include
(A) “Untie me and let me go home, please. I won't report to the police. You already have my nude photos;”
(B) “I always practice safe sex. Let's get down to it;”
(C) “I will kill myself if I ever lie to you;”
(D) “If you study harder, you will pass the course.”
Ans: A. [Recall lectures]
8. [Credit: Inspirations came from a conversation with Claire, Linda, and Peggy.] 如果學務處要知道「那一個系學會完全沒有投入文藻週活動」，應該如何？
(A)在校園隨機抽問300位學生；
(B)在e-learning platform隨機匿名抽問300位學生；
(C)發電子郵件請教所有的系主任；
(D)召開檢討會，要求每位系學會會長必須出席。
Ans: D. [Common sense]
9. Which of the following meets the “costly-to-fake principle” but fails the “full-disclosure principle”?
(A) Having an expensive treat on the first date to show how serious you are;
(B) Marrying your boyfriend to prove that you love him dearly;
(C) Duplicating your car key and giving it to your boyfriend to show your trust;
(D)買情人裝給男朋友穿。
*Ans: B.
10. Which of the following meets the “full-disclosure principle” but fails the “costly-to-fake principle”?
(A) 在大腿以刺青刻上女友的名字;
(B) 自願幫老師天天買午餐;
(C) 借筆記給女朋友影印;
(D) 買情人裝給男朋友穿。
Ans: C.
11. 阿土伯打電話給總經理：「別的應試者，都面試至少10分鐘。我家寶貝女兒阿花，不到七分鐘就出來啦。搞什麼鬼嘛！」總經理該如何回應？
(A) 面試提前結束，是人事主管在釋放訊號；
(B) 對不起，我們程序失當，下週六重考一次；
(C) 如果問答順暢，用不到10分鐘；
(D) 是您家小姐在釋放訊號啊。
Ans: C. [啟示：不要無限上綱，大小事情都硬套上『訊號』。]
12. Which of the following does not make sense?
(A) 台灣大學的教授，較不會在授課大綱上，註明自己擁有博士學位；
(B) 排名末尾的學校的教授，如果有博士學位，多會註明自己擁有博士學位；
(C) 大學校長在報紙投書時，應該註明自己擁有博士學位；
(D) 高中生參加全國科學展，不該陳列準備階段的生活照。
Ans: C. [Slide no.16, lecture 2]
13. Often college professors are working hard to get papers published. This has little or nothing to do with the fact that
(A) they are signaling their quality;
(B) they simply cannot teach well;
(C) it is hard to evaluate teaching effectiveness;
(D) college administrators let the external peer review help them evaluate professors.
Ans: B.
14. 假設全班同學都無法完成 Assignment One，教師仍然要區分優劣作品。妳/你應該
(A) find some native speaker to polish your letters before you turn it in;
(B) provide the original communication evidence as soon as possible;
(C) open a Word document and make up the reply;
(D) write a nasty letter to those who have not responded.
Ans: B.
15. Let your budget line be 3x + 2y = 10 and your utility function is U(x, y) = (x + y)2.
(A) Your preferences cannot be of the perfect substitution nature;
(B) You may not act as a price-taker;
(C) Your marginal rate of substitution between good X and good Y is 1.5;
(D) Your will buy 5 units of good Y.
Ans: D. [Recall lectures]
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。教師也有權公告具有特色之作答。] 30 points
16. [5 points]
Recall what you wrote on Assignment 2 (about your profile). Carefully point out where in that assignment you “signaled your characteristics (or merits)”. Explain briefly. Of course, you will get zero if you have not turned in your Assignment 2.
17. [5 points]
Recall the on-line auction experiment we conducted on Nov. 7, 2007. Suppose that five people (called bidders) participate in an English auction. Their privately known reservation prices (as potential buyers) are: 100 (dollars) for bidder 1, 150 for bidder 2, 200 for bidder 3, 200 for bidder 4, and 250 for bidder 5. The auctioneer announces (1) each bid incremental must be 5, 10, 15, …. (i.e., 5的倍數) and (2) the auction starts at 50. What follows is the log of bidding process.
Bidder 2: 60
Bidder 1: 65
Bidder 2: 70
Bidder 3: 75
Bidder 4: 90
Bidder 2: 100
Bidder 5: 180
Bidder 4: 190
Bidder 3: 195
Bidder 4: 200
Bidder 5: 220
The winner is bidder 5.
Based on the above information, find the most intelligent (and rational) bidder and the least intelligent one. Briefly explain why you make such choice.
Ans: Bidder 1 is not aggressive. Bidder 2 bids quite rationally. Bidders 3 and 4 are doing fine but bidder 3 does not seem to closely follow the bidding game for some time. Finally bidder 5 truly will regret because that he could have bid 205 to win the auction. The difference between 220 and 205 (i.e., 15) is referred to as the winner’s curse in the literature. To sum up, we can say that bidders 2 and 4 are the most intelligent (and rational) bidders; bidder 5 is the least intelligent bidder.
18. [20 points] 簡答題 [Hint: Think like an economist.]
(i)就經濟學的觀點，學校該如何確定學生認真填答教學評量？如何找出真正的好老師，而不是「對學生好的老師」？
Ans: Generally speaking, students have little incentive to seriously answer those questionnaires. Cannot blame them as they barely have any idea about what this task is for, let alone getting access to those evaluation results. [現在學校辦的大小活動，還有一堆炒冷飯的碩、博士生，也喜歡一窩蜂的要求滿意度問卷，既無填答誘因，也無法保證彙整過程的公信力。我自己也常逆向操作或亂填，測試主事者的智慧。] 教務主管直接了解每位教師的授課情形，成本確實太高。依賴學生來評量，確有其重要性。因為「教師音量大小」、「教師是否上課遲到」、「教師是否親自監考」，這一類的正確資訊，教務單位很容易取得。只要在教學評量問卷上，分散置入此類問題，再對照真實資訊，系統即可篩選掉「情緒性、報復性的填答者」。當然，有作為的資教或電算中心，還可以藉由系統設計，追蹤每位學生在每門課的期中考成績、給教師的評量、期末考成績。分析學生在不同年級(time series)、不同課程(cross section)、系列課程之學習情況與主觀感受。學生如果知道有此機制，應該會較認真填答。耳朵靈光的資深教師，不難有以下的經驗：一位同學每學期都會向不同老師私下表示，這是我遇到最難的課！This is the toughest course I have ever had! 如何找出真正的好老師？除非落實教學實況的透明化、學校能夠區分用功的學生的回饋與打混的學生之意見、認真的學生或是傑出校友能夠建言，現階段由教師的研究績效(假外界專家之手，即同儕評鑑)來評比，也算是次佳解之一吧。
(ii)學校為何不直接公告每位專、兼任教師的教學評量，來幫助學生辨識真正的好老師、也可提供選課參考？
Ans: 頭腦清楚的學校主事者，應該知道無法確保學生認真填答，所以不能單以教學評量，來排序教師的教學表現、甚至開鍘。但是，為了應付(或配合)家長的要求、立委的指責、輿論的關愛，不得不行禮如儀，還要依此辦理優良教師選拔等活動。更諷刺的是，主事者以尊重隱私為由，讓學生完全不知評量結果，當然缺乏認真填寫的誘因。主管教務者，與教師們正處於一種「策略性模糊」的均衡狀態。如果直接公告每位專、兼任教師的教學評量，勢必將喚醒不少獅虎，擴大教師對「評量教學績效」之檢討呼聲。當然，教師以easy grade『換取』較佳的評量分數、爭取選課人數，此類問題，勢必會擴散、加深。
[Any resolution? 如果大多數教師，直接把自己的教學評量，大剌剌地張貼於網頁，會有何衝擊效應呢？]
(iii)一門「教師認真授課、學生嚴肅學習」的課程，該如何釋放訊號，以便與「教師敷衍打混、學生迷糊過關」的課程，有所區隔？
Ans: If the former group is relatively small but not negligible as compared with the latter group, then surely I will recommend professors in the former group to try their best to make all lecture notes, exams and solutions available to the general public, which is consistent to the signaling theory. They can also design courses such that shirking students who got easy grades from courses belonging to the latter group will have a hard time to catch up. Lessons will be well taken. Tough grading is fine as long as those who do relatively well will receive good grades from those serious professors. However, if the former is overwhelmingly dominated by the latter, we have the doomsday.
(iv)假設一位高職生面臨兩所學校，很難決定究竟應申請那一所。其中一所學校在網頁標榜：本校教師的教學評量平均值為4.2 (依據5分量表；5分係最佳)；另一所學校則不提此類資料。這位高職生該選那一所？何故？
Ans: Of course, it is the latter! To the best of my knowledge, nowadays most universities and colleges alike claim that the average teaching evaluation statistics is above 4 (on the 5-point scale). [Ironically, when the Ministry of Education ranks or accredits universities, this data plays no role for obvious reason.] If University A publicizes such information, it does not really work as signaling. Instead, it might very likely lure people to think: “Is the procedure of obtaining such data transparent and unbiased?” or “Will having 4.5 in a mediocre place be as good as getting 3.5 in some better school?” This is why you will never see elite schools such as MIT, Stanford, Chicago, and Yale brag that their average teaching evaluation statistics are high. Too bad that many university administrators here never open their mind to learn.
(放棄智慧財產權；歡迎全貌下載流傳。)
Tuesday, November 13, 2007
Solution to Midterm -- Introductory Calculus F2007
★★★★ Solution to Midterm Examination (International Business, WUCL) ★★★★
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
微積分(Introductory Calculus) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 13, 2007
Closed books/notes exam. 104 points in 70 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。10:10 am ~ 11:20 am, Tuesday, November 13, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過100秒。] 80 points
1. Let the market demand curve be given by P = -0.01Q2 - 0.2Q + 8; the market supply curve be given by P = 0.01Q2 + 0.1Q + 3, where P is the price and Q is the quantity. At market equilibrium, quantity demanded equals quantity supplied.
(A) The equilibrium price is 10;
(B) The equilibrium price is 5;
(C) The equilibrium quantity is 25;
(D) None of the above is correct.
Ans: B. [See p.83, text.]
2. [continued from question 1]
(A) The market demand function is P = f(Q) := -0.01Q2 - 0.2Q + 8;
(B) The market supply function is P = f(Q) := 0.01Q2 + 0.1Q + 3;
(C) Market demand curve and market supply curve only intersect once;
(D) The slope of demand curve is a negative constant.
Ans: C. [Straightforward]
3. If the graph of a function on the x-y place is simply the 45-degree ray starting at (0, 0), then
(A) the function must be f(x) := x for all non-negative reals;
(B) the function must be a constant function;
(C) the function must be f(x, y) := x + y;
(D) the function must be f(x) := 1/x for all positive reals.
Ans: A. [Trivial]
4. If the graph of a function on the x-y plane is the set {(0, 0), (1, 1), (2, 2), (3, 3)}, then
(A) the function must be f(x) := x for all non-negative reals;
(B) the range (set) of this function can be the set of all reals;
(C) the image set of this function must be the set of non-negative reals;
(D) the image of f at 4 is 4.
Ans: B. [Recall lectures]
5. The set {(1, 2), (3, 4), (5, 1)}
(A) can not be a graph;
(B) can not be a domain;
(C) can not be a range (set);
(D) is a subset of the plane.
Ans: D. [Recall lectures]
6. On the plane, consider two circles with different centers but with the same radius 3.
(A) they can only intersect once;
(B) they can only intersect twice;
(C) they can not intersect;
(D) the area inside each circle is 9.
Ans: D. [Trivial]
7. Connecting points (2, 0), (0, 2), and (2, 4) to get a triangle.
(A) the area within the triangle is 6;
(B) the area within the triangle is 8;
(C) the length of the boundary is 4(1 + 20.5);
(D) None of the above is correct.
Ans: C. [The area within the triangle is 4; the length of the boundary is 2(22 + 22)0.5 + 4.]
8. 4x(x + 1)0.5 – 2x2(0.5)(x + 1)-0.5 =
(A) (x + 1)0.5;
(B) x(x + 1)0.5(3x + 4) ;
(C) x(x + 1)-0.5(4x + 3) ;
(D) x(x + 1)-0.5(3x + 4).
Ans: D. [Straightforward ; p.13, text]
9. Let a and b be real numbers. The distance between a and the origin (i.e., 0) adds the distance between b and 0 must be no smaller than the distance between a + b and 0.
(A) This is called 畢氏定理；
(B) This is called 三角不等式；
(C) This is called 柯西定理；
(D) This is called 白努利不等式。
Ans: B. [p.5, text]
*10. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters.
(A) This equation may have no solution;
(B) This equation may have (0, 0) as the unique solution;
(C) This equation can not have infinitely many solutions;
(D) This equation may have (1, 1) as the unique solution.
Ans: A. [Consider the case where a = b = 0 yet c ≠ 0.]
11. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is a line with slope -1, then we must have
(A) a = b ≠ 0 and c ≠ 0;
(B) a = b > 0 and c ≠ 0;
(C) a = b and abc ≠ 0;
(D) a = b ≠ 0.
Ans: D. [By -a/b = -1 we know a = b ≠ 0. It goes thru the origin if and only if c = 0.]
12. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is the graph of a function f: R → R on the x-y plane, we must have
(A) a ≠ 0;
(B) b ≠ 0;
(C) ac ≠ 0;
(D) bc ≠ 0.
Ans: B. [f(x) := c/b - ax/b.]
13. The equation representing a line going thru points (1, 2) and (3, 4) is
(A) x + y = 3 ;
(B) 2x - y = 0 ;
(C) x - y = 1 ;
(D) x - y = -1.
Ans: D. [It follows immediately from (y - 2)/(x - 1) = (4 - 2)/(3 - 1), yielding x - y = -1.]
14. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is associated with a function f(x, y), then at each solution (x*, y*),
(A) we say that the image of (x*, y*) under f is c;
(B) we say that the image of c under f is (x*, y*);
(C) we say that the image of x* under f is y*;
(D) None of the above is correct.
Ans: A. [Recall lectures]
15. [continued from question 14] Which of the following can not be a nice economic interpretation (or meaning) of f?
(A) x and y are amount of inputs used in production;
(B) x and y are amount of consumption goods;
(C) x is price while y is quantity;
(D) x and y are amount of goods produced in an economy.
Ans: C. [For A, think about the production function; for B, think about the utility function; for D, think about the production possibility frontier (or curve). The function f(P, Q) does not mean much in economics.]
16. Let a and b be real numbers. If ∣a + b∣ < ∣a ∣+ ∣b∣, then
(A) ab < 0;
(B) ab ≠ 0;
(C) a < 0 and b < 0;
(D) None of the above is correct.
*Ans: A. [∣a + b∣ < ∣a ∣+ ∣b∣holds only when a and b are of opposite signs.]
17. Which of the following piecewise-defined functions is actually a standard function (defined by a single rule)?
(A) f(x) := -x if x < 0 and f(x) := (x)0.5 if x ≧ 0;
(B) f(x) := x if x ≧ 0 and f(x) := -x-1 if x < 0;
(C) f(x) := x3 if x ≧ 0 and f(x) := -(-x)3 if x < 0;
(D) f(x) := x2 if x ≧ 0 and f(x) := -x2 if x < 0.
Ans: C. [It is simply f(x) := x3 for all real numbers x.]
18. Which of the following best serves as an illustration of the notion of function?
(A) marriage;
(B) dating;
(C) indexing room numbers;
(D) college admission application.
Ans: C. [To see why (A) fails, think of those who are in the domain but not married. Since a person may date more than one person of the opposite sex, (B) is incorrect.]
19. Let f and g be two functions defined by f(x) := x + 1 for all non-negative reals and g(x) := x2 for all non-negative reals. The composition of g and f is
(A) (g ○ f)(x) := (x + 1)2 defined for all non-negative reals;
(B) (g ○ f)(x) := x2 + 1 defined for all non-negative reals;
(C) (g ○ f)(x) = (f ○ g)(x) defined for all non-negative reals;
(D) (f ○ g)(x) := (x + 1)2 defined for all non-negative reals.
Ans: A. [(g ○ f)(x) := g(f(x)) = (x + 1)2 defined for all non-negative reals; (f ○ g)(x) := f(g(x)) = x2 + 1 defined for all non-negative reals.]
*20. Let f and g be two functions defined by f(x) := x2 for all reals and g(x) := x-2 for all non-zero reals. The domain of the composition of g and f is
(A) the set of real numbers;
(B) the set of non-zero real numbers;
(C) the set of positive real numbers;
(D) the set of non-negative real numbers.
Ans: B. [Recall slide no.12 of Lecture 3. Each element x in the domain of g ○ f must be in the domain of f such that f(x) lies in the domain of g. This is also in your text.]
Part Two: Analytical questions. [皆是數學應用題。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。] 24 points
21. [10 points] Recall the problem with organizing kissing raised by Professor Harbaugh at the Univ. of Oregon (Lecture 1).
(i) For a class of 35 kids, exactly how many kissing must be done?
Ans: C(35, 2) = (35)(35 - 1)/2 = 595.
*(ii) Suggest a way to efficiently make all these kissing take place in a short period of time.
Ans: [I posed this entertaining yet educational puzzle on the lecture notes for you to think it over for several weeks. Now let’s see who did it and who failed to do so.] What follows is what I got after thinking for 10 minutes or so. 將學生(little girls at some French school)編號，由1到35。依據我的教學經驗，行動緩慢、興趣缺缺、聽力較差與習慣性觀望者，當然會得到較大的號碼。小女孩依號碼圍成一圓圈坐下。No.1起身，由 No.2、No.3、… 依序逐一親吻臉頰。大約在No.1走向No.4之時，No.2應起身，由 No.3、No.4、… 逐一親吻臉頰。大約在No.2走向No.5之時，No.3起身，由 No.4、No.5、… 逐一親吻臉頰。以此類推，很快地，35位小女孩將井然有序地完成此任務。當然，No.1親吻No.35的臉頰後，應該迅速由邊緣離開該圈，去喝水或洗臉之類。No.2親吻No.35的臉頰後，應該撤出該圈，去喝水或洗臉。… 此設計還有兩項特色：(1)團體的任務，不會被行動緩慢、興趣缺缺、聽力較差與習慣性觀望者所延宕；(2)積極主動的小女孩，編號較小，將可以較早離席，不必乾等。Of course, I am always open to any better solution. [During the semester break, I will mail my solution (in English) to Prof. Harbaugh and see how he thinks about it.]
Remarks:
(1) If each kiss takes 10 seconds, then my proposed procedure will take 670 seconds (slightly over 11 minutes) to complete. Can you prove it?
*(2) Any other applications or extensions? 假設有35支球隊，每兩隊要比賽一場，賽事可以同時進行。如果採用上述流程，大會需提供多少座球場？Hint: Figure out the peak load.
22. [7 points]
給你一條繩子，長度為k > 0. 你可以圍成一個正方形，或是圓形，目標是面積極大化。假設極大後的面積是a，當然，a將是k 的函數。接著，在面積是a的新限制下，你可以圍成一個正方形，或是圓形，這一回目標是週邊長度極大化。請算出極大後的長度。Hint: Of course, your final answer will be expressed as a function of k only.
Ans: From slide no.16 in lecture 1, we know that a circle has more area than the square does. So, the maximized area is a = [k/(2pi)]2 = k2/(4pi). Next, from slide no.18, we know that the maximized length is 4[k2/(4pi)]0.5 = 2k(pi)-0.5 > k.
23. [7 points]
你需要桌面的面積是a > 0. 你可以製作一個方桌，或是圓桌，目標是週邊長度極大化。假設極大後的週邊長度是k，當然，k將是a 的函數。接著，在週邊長度是k的新限制下，你可以圍成一個正方形，或是圓形，這一回目標是面積極大化。請算出極大後的面積。Hint: Of course, your final answer will be expressed as a function of a only.
Ans: From slide no.18 in lecture 1, we know that a square is better than a circle. So, the maximized boundary is k = 4(a)0.5Next, from slide no.16, we know that the maximized area is [4(a)0.5/(2pi)]2 =[2(a)0.5/pi]2 = 4a(pi)-1 > a.
**N.B. Compare questions 22 with 23, what can you possibly learn? This is a real challenge for brave soul.
(放棄智慧財產權；歡迎全貌下載流傳。)
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
微積分(Introductory Calculus) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 13, 2007
Closed books/notes exam. 104 points in 70 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。10:10 am ~ 11:20 am, Tuesday, November 13, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過100秒。] 80 points
1. Let the market demand curve be given by P = -0.01Q2 - 0.2Q + 8; the market supply curve be given by P = 0.01Q2 + 0.1Q + 3, where P is the price and Q is the quantity. At market equilibrium, quantity demanded equals quantity supplied.
(A) The equilibrium price is 10;
(B) The equilibrium price is 5;
(C) The equilibrium quantity is 25;
(D) None of the above is correct.
Ans: B. [See p.83, text.]
2. [continued from question 1]
(A) The market demand function is P = f(Q) := -0.01Q2 - 0.2Q + 8;
(B) The market supply function is P = f(Q) := 0.01Q2 + 0.1Q + 3;
(C) Market demand curve and market supply curve only intersect once;
(D) The slope of demand curve is a negative constant.
Ans: C. [Straightforward]
3. If the graph of a function on the x-y place is simply the 45-degree ray starting at (0, 0), then
(A) the function must be f(x) := x for all non-negative reals;
(B) the function must be a constant function;
(C) the function must be f(x, y) := x + y;
(D) the function must be f(x) := 1/x for all positive reals.
Ans: A. [Trivial]
4. If the graph of a function on the x-y plane is the set {(0, 0), (1, 1), (2, 2), (3, 3)}, then
(A) the function must be f(x) := x for all non-negative reals;
(B) the range (set) of this function can be the set of all reals;
(C) the image set of this function must be the set of non-negative reals;
(D) the image of f at 4 is 4.
Ans: B. [Recall lectures]
5. The set {(1, 2), (3, 4), (5, 1)}
(A) can not be a graph;
(B) can not be a domain;
(C) can not be a range (set);
(D) is a subset of the plane.
Ans: D. [Recall lectures]
6. On the plane, consider two circles with different centers but with the same radius 3.
(A) they can only intersect once;
(B) they can only intersect twice;
(C) they can not intersect;
(D) the area inside each circle is 9.
Ans: D. [Trivial]
7. Connecting points (2, 0), (0, 2), and (2, 4) to get a triangle.
(A) the area within the triangle is 6;
(B) the area within the triangle is 8;
(C) the length of the boundary is 4(1 + 20.5);
(D) None of the above is correct.
Ans: C. [The area within the triangle is 4; the length of the boundary is 2(22 + 22)0.5 + 4.]
8. 4x(x + 1)0.5 – 2x2(0.5)(x + 1)-0.5 =
(A) (x + 1)0.5;
(B) x(x + 1)0.5(3x + 4) ;
(C) x(x + 1)-0.5(4x + 3) ;
(D) x(x + 1)-0.5(3x + 4).
Ans: D. [Straightforward ; p.13, text]
9. Let a and b be real numbers. The distance between a and the origin (i.e., 0) adds the distance between b and 0 must be no smaller than the distance between a + b and 0.
(A) This is called 畢氏定理；
(B) This is called 三角不等式；
(C) This is called 柯西定理；
(D) This is called 白努利不等式。
Ans: B. [p.5, text]
*10. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters.
(A) This equation may have no solution;
(B) This equation may have (0, 0) as the unique solution;
(C) This equation can not have infinitely many solutions;
(D) This equation may have (1, 1) as the unique solution.
Ans: A. [Consider the case where a = b = 0 yet c ≠ 0.]
11. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is a line with slope -1, then we must have
(A) a = b ≠ 0 and c ≠ 0;
(B) a = b > 0 and c ≠ 0;
(C) a = b and abc ≠ 0;
(D) a = b ≠ 0.
Ans: D. [By -a/b = -1 we know a = b ≠ 0. It goes thru the origin if and only if c = 0.]
12. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is the graph of a function f: R → R on the x-y plane, we must have
(A) a ≠ 0;
(B) b ≠ 0;
(C) ac ≠ 0;
(D) bc ≠ 0.
Ans: B. [f(x) := c/b - ax/b.]
13. The equation representing a line going thru points (1, 2) and (3, 4) is
(A) x + y = 3 ;
(B) 2x - y = 0 ;
(C) x - y = 1 ;
(D) x - y = -1.
Ans: D. [It follows immediately from (y - 2)/(x - 1) = (4 - 2)/(3 - 1), yielding x - y = -1.]
14. Consider an equation ax + by = c, where a, b, and c are real numbers as parameters. If it is associated with a function f(x, y), then at each solution (x*, y*),
(A) we say that the image of (x*, y*) under f is c;
(B) we say that the image of c under f is (x*, y*);
(C) we say that the image of x* under f is y*;
(D) None of the above is correct.
Ans: A. [Recall lectures]
15. [continued from question 14] Which of the following can not be a nice economic interpretation (or meaning) of f?
(A) x and y are amount of inputs used in production;
(B) x and y are amount of consumption goods;
(C) x is price while y is quantity;
(D) x and y are amount of goods produced in an economy.
Ans: C. [For A, think about the production function; for B, think about the utility function; for D, think about the production possibility frontier (or curve). The function f(P, Q) does not mean much in economics.]
16. Let a and b be real numbers. If ∣a + b∣ < ∣a ∣+ ∣b∣, then
(A) ab < 0;
(B) ab ≠ 0;
(C) a < 0 and b < 0;
(D) None of the above is correct.
*Ans: A. [∣a + b∣ < ∣a ∣+ ∣b∣holds only when a and b are of opposite signs.]
17. Which of the following piecewise-defined functions is actually a standard function (defined by a single rule)?
(A) f(x) := -x if x < 0 and f(x) := (x)0.5 if x ≧ 0;
(B) f(x) := x if x ≧ 0 and f(x) := -x-1 if x < 0;
(C) f(x) := x3 if x ≧ 0 and f(x) := -(-x)3 if x < 0;
(D) f(x) := x2 if x ≧ 0 and f(x) := -x2 if x < 0.
Ans: C. [It is simply f(x) := x3 for all real numbers x.]
18. Which of the following best serves as an illustration of the notion of function?
(A) marriage;
(B) dating;
(C) indexing room numbers;
(D) college admission application.
Ans: C. [To see why (A) fails, think of those who are in the domain but not married. Since a person may date more than one person of the opposite sex, (B) is incorrect.]
19. Let f and g be two functions defined by f(x) := x + 1 for all non-negative reals and g(x) := x2 for all non-negative reals. The composition of g and f is
(A) (g ○ f)(x) := (x + 1)2 defined for all non-negative reals;
(B) (g ○ f)(x) := x2 + 1 defined for all non-negative reals;
(C) (g ○ f)(x) = (f ○ g)(x) defined for all non-negative reals;
(D) (f ○ g)(x) := (x + 1)2 defined for all non-negative reals.
Ans: A. [(g ○ f)(x) := g(f(x)) = (x + 1)2 defined for all non-negative reals; (f ○ g)(x) := f(g(x)) = x2 + 1 defined for all non-negative reals.]
*20. Let f and g be two functions defined by f(x) := x2 for all reals and g(x) := x-2 for all non-zero reals. The domain of the composition of g and f is
(A) the set of real numbers;
(B) the set of non-zero real numbers;
(C) the set of positive real numbers;
(D) the set of non-negative real numbers.
Ans: B. [Recall slide no.12 of Lecture 3. Each element x in the domain of g ○ f must be in the domain of f such that f(x) lies in the domain of g. This is also in your text.]
Part Two: Analytical questions. [皆是數學應用題。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。] 24 points
21. [10 points] Recall the problem with organizing kissing raised by Professor Harbaugh at the Univ. of Oregon (Lecture 1).
(i) For a class of 35 kids, exactly how many kissing must be done?
Ans: C(35, 2) = (35)(35 - 1)/2 = 595.
*(ii) Suggest a way to efficiently make all these kissing take place in a short period of time.
Ans: [I posed this entertaining yet educational puzzle on the lecture notes for you to think it over for several weeks. Now let’s see who did it and who failed to do so.] What follows is what I got after thinking for 10 minutes or so. 將學生(little girls at some French school)編號，由1到35。依據我的教學經驗，行動緩慢、興趣缺缺、聽力較差與習慣性觀望者，當然會得到較大的號碼。小女孩依號碼圍成一圓圈坐下。No.1起身，由 No.2、No.3、… 依序逐一親吻臉頰。大約在No.1走向No.4之時，No.2應起身，由 No.3、No.4、… 逐一親吻臉頰。大約在No.2走向No.5之時，No.3起身，由 No.4、No.5、… 逐一親吻臉頰。以此類推，很快地，35位小女孩將井然有序地完成此任務。當然，No.1親吻No.35的臉頰後，應該迅速由邊緣離開該圈，去喝水或洗臉之類。No.2親吻No.35的臉頰後，應該撤出該圈，去喝水或洗臉。… 此設計還有兩項特色：(1)團體的任務，不會被行動緩慢、興趣缺缺、聽力較差與習慣性觀望者所延宕；(2)積極主動的小女孩，編號較小，將可以較早離席，不必乾等。Of course, I am always open to any better solution. [During the semester break, I will mail my solution (in English) to Prof. Harbaugh and see how he thinks about it.]
Remarks:
(1) If each kiss takes 10 seconds, then my proposed procedure will take 670 seconds (slightly over 11 minutes) to complete. Can you prove it?
*(2) Any other applications or extensions? 假設有35支球隊，每兩隊要比賽一場，賽事可以同時進行。如果採用上述流程，大會需提供多少座球場？Hint: Figure out the peak load.
22. [7 points]
給你一條繩子，長度為k > 0. 你可以圍成一個正方形，或是圓形，目標是面積極大化。假設極大後的面積是a，當然，a將是k 的函數。接著，在面積是a的新限制下，你可以圍成一個正方形，或是圓形，這一回目標是週邊長度極大化。請算出極大後的長度。Hint: Of course, your final answer will be expressed as a function of k only.
Ans: From slide no.16 in lecture 1, we know that a circle has more area than the square does. So, the maximized area is a = [k/(2pi)]2 = k2/(4pi). Next, from slide no.18, we know that the maximized length is 4[k2/(4pi)]0.5 = 2k(pi)-0.5 > k.
23. [7 points]
你需要桌面的面積是a > 0. 你可以製作一個方桌，或是圓桌，目標是週邊長度極大化。假設極大後的週邊長度是k，當然，k將是a 的函數。接著，在週邊長度是k的新限制下，你可以圍成一個正方形，或是圓形，這一回目標是面積極大化。請算出極大後的面積。Hint: Of course, your final answer will be expressed as a function of a only.
Ans: From slide no.18 in lecture 1, we know that a square is better than a circle. So, the maximized boundary is k = 4(a)0.5Next, from slide no.16, we know that the maximized area is [4(a)0.5/(2pi)]2 =[2(a)0.5/pi]2 = 4a(pi)-1 > a.
**N.B. Compare questions 22 with 23, what can you possibly learn? This is a real challenge for brave soul.
(放棄智慧財產權；歡迎全貌下載流傳。)
Monday, November 12, 2007
Solution to Midterm -- Micro Principles F2007
★★★★ Detailed Solution to Midterm Examination (International Business, WUCL) ★★★★
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
個體經濟學原理(Principles of Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 12, 2007
Open books/notes exam. 110 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。3:10 pm ~ 4:20 pm, Monday, November 12, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過2分鐘。] 80 points
1. A society consists of three people: Ann, Becky, and Cindy. Ann prefers apple to orange; prefers orange to banana. Becky prefers apple to banana; prefers banana to orange. Cindy has no preferences over those fruits but just wants to see Ann be happy. Suppose that Ann has one orange and nothing else; Becky has one banana and nothing else; Cindy has one apple and nothing else. We call it the initial endowment or the status quo (at autarky). Fruits can be traded among them but are indivisible (不可切割細分).
(A) The initial endowment is Pareto efficient;
(B) Ann and Becky will trade and the term of trade is one;
(C) Becky and Cindy will trade and the term of trade is one;
(D) None of the above is true.
Ans: C. [To see why (A) is false, letting Ann and Cindy trade, leading to a Pareto efficient allocation. Since Cindy is indifferent while Becky prefers apple to banana, when it comes to the bilateral trade, we know that Cindy and Becky can make the trade. Since one unit of good is exchanged for one unit of another good, the term of trade is, of course, one.]
2. [continued from question 1] Which one of the following (allocation分配) is Pareto efficient?
(A) Ann has one orange, Becky has one apple and Cindy has one banana;
(B) Ann has one apple, Becky has one orange and Cindy has one banana;
(C) Ann has one banana, Becky has one orange and Cindy has one apple;
(D) Ann has one banana, Becky has one apple and Cindy has one orange.
Ans: A. [Straightforward. 教師的題庫 (test bank) 是不會有這種靈活題目的。]
3. We can say that the society enhances efficiency at the cost of equity if
(A)重視國防、犧牲民生；
(B)不讓「對候選人不了解的選民」行使投票權；
(C)不讓油價上漲；
(D)推動公投。
Ans: B. [Obvious.]
4. We can say that the society enhances equity at the cost of efficiency if
(A)針對單身貴族課重稅、補貼低所得家庭之育嬰開支；
(B)重點補助研究型大學、淘汰區域性教學型大學；
(C)立法要求所有新車車主需有停車位證明；
(D)學校明文要求「每門課至少五分之一同學成績不及格」。
Ans: A. [Obvious.]
5. Suppose that you like to see movies and you also do not want to waste time while waiting to get into the theater. At 7 pm you arrive at the theater’s ticket counter (or window). Movie #1 will start at 7:30 pm; movie #2 will start at 7:30 pm; movie #3 will start at 8:00 pm. All movies have the same admission charge. Assume that you like movie #3 most while movie #1 is at the bottom of your priority list. If you finally decide to see movie #2, then the opportunity cost of doing so is
(A) the value of movie #3;
(B) the value of movie #3 minus (the utility derived from) the 30-minute waiting time saved;
(C) the value of movie #1 plus the value of movie #3
(D) the value of saving 30 minutes in waiting.
*Ans: B. [pp.5-6, text]
*6. Suppose that you like to see movies and you also do not want to waste time while waiting to get into the theater. At 7 pm you arrive at the theater’s ticket counter (or window). Movie #1 will start at 7:30 pm; movie #2 will start at 7:30 pm; movie #3 will start at 8:00 pm. All movies have the same admission charge. Assume that you like movie #3 most while movie #1 is at the bottom of your priority list.
(A) You will definitely choose to see movie #1;
(B) You will definitely not see movie #1;
(C) You will definitely choose to see movie #3;
(D) You will definitely choose to see movie #2.
Ans: B. [Notice that a rational consumer will reject movie #1 in light of the choice of movie #2. Can you figure out the opportunity cost of seeing movie #3?]
7. Examples of not thinking at the margin include:
(A) You saw NTD100 bill (紙鈔) on the sand beach before dark and did not pick it up;
(B) Explaining why water is much cheaper than diamond;
(C)教室若有空座位，學校要求教師不得拒絕增加學生；
(D)一家人買數種麥當勞套餐，然後各取所需。
Ans: A. [pp.6-7, text. 週六球場的20元無主硬幣，是(A)的靈感。]
8. Examples of people responding to incentives do not include:
(A) College professors should not announce the “all pass” policy;
(B) Average and above-average students tend to study more seriously for open book exams;
(C) I intentionally made you have some time pressure on this exam;
(D)認真填答文藻週的國際企業畢業專題展之問卷。
Ans: D. [Obvious.]
9. When economists study the short-run effects of some policy, they often assume that
(A) quantities are fixed;
(B) prices are fixed;
(C) labor inputs are fixed;
(D) people have no time to respond rationally.
Ans: B. [p.21, text]
10. Which of the following is not related to the notion of production possibility frontier?
(A) efficiency;
(B) technology constraints;
(C) scarce resources;
(D) Pareto efficiency.
Ans: D. [pp.24-26, text]
11. According to the bowed shaped (or negatively-sloped concave-shaped) production possibility frontier in your text, for an economy producing good X and Y, at larger x (i.e., the amount of good X produced),
(A) the opportunity cost for the society in producing X is higher;
(B) the opportunity cost for the society in producing X is lower;
(C) the opportunity cost for the society in producing Y is higher;
(D) the opportunity costs of producing X and Y are equal.
Ans: A. [p.25, text]
12. According to the production possibility frontier presented during lectures (concerning agents Frank and Robert), for an economy producing good X and Y, at larger x (i.e., the amount of good X produced),
(A) the opportunity cost for the society in producing X is higher;
(B) the opportunity cost for the society in producing X is lower;
(C) the opportunity costs of producing X and Y are equal;
(D) None of the above is correct.
Ans: D. [The PPF is linear in this case.]
13. This question does nothing but test whether you did read the textbook. Which person of the following did not major in economics at college?
(A) Arnold Schwarzenegger (the Governor of California);
(B) Mick Jagger (singer for the Rolling Stones);
(C) Condoleezza Rice (U.S. Secretary of State);
(D) Cate Blanchett (actress).
Ans: C. [Dr. C. Rice majored in political science. See p.27, text.]
14. The proposition that relatively more economists in a survey disagreed is
(A)租金管制會降低租屋的數量與品質；
(B)制定最低工資會增加年輕人的失業；
(C)實施進口關稅會減少本國福利；
(D)政府不應在(會計)年度內要求預算平衡。
Ans: B. [See p.34, text. You will find that 93% (approval) for A; 79% for B; 93% for C; 85% for D.]
15. Mr. Robert D. McTeer, Jr., the former president of the Federal Reserve Bank of Dallas wrote an article for the Wall Street Journal in 2003. His point regarding the so-called “broken window fallacy” is similar to
(A)制定最低工資會增加就業率；
(B) 921大地震有助於振興總體需求；
(C)修讀經濟學無助於政策的制定；
(D)最聰明的學生應該就讀醫科。
Ans: B. [See p.35, text. Test your reading comprehension.]
16. Suppose that there are only two consumers, A and B, in the market whose market demand curve is given by P + 2Q = 10. Assume that A demands 2 units of that good when the price is 5; demands 3 units when the price is 4.
(A) The demand of B for that good fails to satisfy the law of demand;
(B) The market demand for that good fails to satisfy the law of demand;
(C) At price 5, B will demand nothing;
(D) At price 6, A will demand nothing.
Ans: A. [At price 5, A will demand 2 units while B will demand 0.5 [= (10 - 5)/2 - 2] unit. At price 4, A will demand 3 units while B will demand nothing. See p.67, text. Key: the reverse of horizontal aggregation or summation.]
17. Let the market supply of soy bean (黃豆) be P - Q = 10. Suppose that the price of crude oil suddenly goes up,
(A) the demand for soy bean will fall;
(B) the demand for soy bean will rise;
(C) the supply of soy bean may become P - Q = 12;
(D) the supply of soy bean may become P - Q = 8.
Ans: C. [Crude oil price increases, increasing the transportation cost, hence making the supply curve of soy bean shift upward.]
18. Let the market supply of soy bean (黃豆) be P - Q = 10. Let the market demand for soy bean be 0.5P + Q = 10. At market equilibrium,
(A) the price is 12;
(B) the quantity is 10;
(C) the price is 15;
(D) None of the above is correct.
Ans: D. [By P - 10 = 10 - 0.5P we solve for P* = 40/3, hence Q* = 10/3.]
19. [continued from question 18] Suppose that crude oil price rose suddenly and that consumers were so panic that many bought more soy beans than what they usually do and stored them at home. As a result, the government officials might observe that
(A) a fall in equilibrium price but a rise in equilibrium quantity;
(B) a fall in equilibrium price and also a fall in equilibrium quantity;
(C) a rise in equilibrium price but a fall in equilibrium quantity;
(D) the same equilibrium price but a fall in equilibrium quantity.
Ans: C. [Shifting up both the supply curve and the demand curve leads to three possible outcomes: higher P* and higher Q*; higher P* and lower Q*; higher P* but Q* being unchanged.]
20. [continued from question 18] Suppose that both the equilibrium price and the equilibrium quantity fall. What might be the reason on the demand side for it?
(A) The price of milk rises dramatically;
(B) The price of milk falls dramatically;
(C) The price of crude oil rises dramatically;
(D) A recent scientific finding proves that soy beans are good for preventing cancers.
Ans: B. [When the price of milk falls dramatically, people consume more milk and less soy bean milk, hence we can see a decrease in the demand for soy bean.]
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。教師也有權公告具有特色之作答。] 30 points
21. [10 points]
Suppose that each agent has 4 hours to spend on the production of goods X and Y, whose quantities are denoted by x and y respectively. The PPF (productivity possibility frontier) of agent A is given by x/4 + y = 4; the PPF of agent B is given by x + y/4 = 4.
(a) For producing one unit of good X, how many hours does A need to spend?
Ans: By x/4 + y = 4 we see that it takes A 1/4 hour (or 15 minutes) to produce 1 unit of good X.
(b) Before the trade takes place, suppose that each agent concentrates on the
production of the good which she has the comparative advantage in producing. After production is realized, allow both agents to trade. Carefully use a diagram to illustrate what the range (範圍) of the relative price of good one is.
Ans: A has the comparative advantage in producing good X and B has the comparative advantage in producing good Y. At the full specification scenario, the production plan for A is (16, 0), the production plan for B is (0, 16). When we open up the trade, the relative (world) price of good one will be somewhere between 1/4 and 4, making both agents better off (as compared with autarky). When I grade the exam papers, I am expecting to see lines x/4 + y = 4 and x + y/4 = 4 precisely drawn on the x-y plane. Of course, (16, 0) and (0, 16) ought to be highlighted.
Note: Also see the Solution to Midterm Exam, Summer 2007.
22. [16 points]
宗輔中心的一份刊物寫道：「學生要的不是好老師，而是對他(她)好的老師。」
(i) From the point of information asymmetry, explain why this statement makes sense.
Ans: Good professors serve the university, not individual students, best. For a student, if his/her professor is nice to him/her in a conceivable way, of course, he/she might be happy to live with that. Why cannot professors strive for being kind to all students? The opportunity costs of doing so is simply too high for us to bear.
(ii)就經濟學的觀點，學校該如何確定學生認真填答教學評量？如何找出真正的好老師，而不是「對學生好的老師」？
*Ans: Generally speaking, students have little incentive to seriously answer those questionnaires. Cannot blame them as they barely have any idea about what this task is for, let alone getting access to those evaluation results. [現在學校辦的大小活動，還有一堆炒冷飯的碩、博士生，也喜歡一窩蜂的要求滿意度問卷，既無填答誘因，也無法保證彙整過程的公信力。我自己也常逆向操作或亂填，測試主事者的智慧。] 教務主管直接了解每位教師是否認真授課，成本確實太高。依賴學生來評量，其重要性不可否認。因為「教師音量大小」、「教師是否上課遲到」、「教師是否親自監考」，這一類的正確資訊，教務單位很容易取得。只要在問卷上，分散置入此類問題，再對照真實資訊，系統即可篩選掉「情緒性、報復性的填答者」。當然，有作為的資教或電算中心，還可以藉由系統設計，追蹤每位學生在每門課的期中考成績、給教師的評量、期末考成績。分析學生在不同年級(time series)、不同課程(cross section)、系列課程之學習情況與主觀感受。學生如果知道有此機制，應該會較認真填答。耳朵靈光的資深教師，不難有以下的經驗：一位同學每學期都會向不同老師私下表示，這是我遇到最難的課！This is the toughest course I have ever had! 如何找出真正的好老師？除非落實教學實況的透明化、學校能夠區分用功的學生的回饋與打混的學生之意見，由教師的研究績效(假外界專家之手，即同儕評鑑)來評比，也算是次佳解之一吧。
Note: Here is another example of screening: 利用 questions 13 thru 15，我可以找出那些同學，能夠有效地閱讀英文版教科書。
(iii)學校為何不直接公告每位專、兼任教師的教學評量，來幫助學生辨識真正的好老師？
Ans: 頭腦清楚的學校主事者，應該知道無法確保學生認真填答，所以不能單以教學評量，來排序教師的教學表現、甚至開鍘。但是，為了應付(或配合)家長的要求、立委的指責、輿論的關愛，不得不行禮如儀，還要依此辦理優良教師選拔等活動。更諷刺的是，主事者以尊重隱私為由，讓學生完全不知評量結果，當然缺乏認真填寫的誘因。主管教務者，與教師們正處於一種「策略性模糊」的均衡狀態。如果直接公告每位專、兼任教師的教學評量，勢必將喚醒不少獅虎，擴大教師對「評量教學績效」之檢討呼聲。當然，教師以easy grade『換取』較佳的評量分數、爭取選課人數，此類問題，勢必會擴散、加深。
[Any resolution? 如果大多數教師，直接把自己的教學評量，大剌剌地張貼於網頁，會有何衝擊效應呢？]
(iv)行政院院長為何不依據媒體或國會所製的施政滿意度，針對各部會首長，實施「退場機制」呢？
Ans: Recall the trade-off between efficiency and equity in text. 正如學校不可能以教學評量分數的高低，發給教師薪資。各部會的職掌不同，放在一面放大鏡下檢視，確實不公平。[否則，教育部長早就換人啦。啟示：不要老是把「退場機制」掛在嘴邊！]
[Hint: Think like an economist.]
23. [4 points]
假設我遇到一位不太熟的朋友，請她順道幫我繳電話費900元。轉念之間，我該如何迅速地確保她會真的如期代繳呢？
Ans: Just take out a 1,000 dollar paper bill and tear it into two pieces. [Recall lectures.] Give her one piece and tell her that when I see the receipt she will have the other piece. Hence, if she keeps her words, she will earn 100 dollars as a token showing my appreciation. [But what if she does not come back (and obviously she won’t go to the cashier)? Well, in that case, I will lose 1,000 dollars (plus getting the late payment penalty) while she just misses the chance of earning 100 dollars. If I want to feel safe, I might ask her to leave me with some money now.]
(放棄智慧財產權；歡迎全貌下載流傳。)
Fall 2007 Instructor: 衛忠欣 (Jong-Shin Wei)
個體經濟學原理(Principles of Microeconomics) (07)342-6031 ext.6222
93001@mail.wtuc.edu.tw http://www.wtuc.edu.tw/ib
November 12, 2007
Open books/notes exam. 110 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。3:10 pm ~ 4:20 pm, Monday, November 12, 2007. Watch your time and good luck! 務必工整扼要、依序作答。Watch your time and have fun!
Part One: 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. I did encounter some less intelligent folks who confused it with “複選題”. 依慣例，答錯不倒扣！平均每題不該超過2分鐘。] 80 points
1. A society consists of three people: Ann, Becky, and Cindy. Ann prefers apple to orange; prefers orange to banana. Becky prefers apple to banana; prefers banana to orange. Cindy has no preferences over those fruits but just wants to see Ann be happy. Suppose that Ann has one orange and nothing else; Becky has one banana and nothing else; Cindy has one apple and nothing else. We call it the initial endowment or the status quo (at autarky). Fruits can be traded among them but are indivisible (不可切割細分).
(A) The initial endowment is Pareto efficient;
(B) Ann and Becky will trade and the term of trade is one;
(C) Becky and Cindy will trade and the term of trade is one;
(D) None of the above is true.
Ans: C. [To see why (A) is false, letting Ann and Cindy trade, leading to a Pareto efficient allocation. Since Cindy is indifferent while Becky prefers apple to banana, when it comes to the bilateral trade, we know that Cindy and Becky can make the trade. Since one unit of good is exchanged for one unit of another good, the term of trade is, of course, one.]
2. [continued from question 1] Which one of the following (allocation分配) is Pareto efficient?
(A) Ann has one orange, Becky has one apple and Cindy has one banana;
(B) Ann has one apple, Becky has one orange and Cindy has one banana;
(C) Ann has one banana, Becky has one orange and Cindy has one apple;
(D) Ann has one banana, Becky has one apple and Cindy has one orange.
Ans: A. [Straightforward. 教師的題庫 (test bank) 是不會有這種靈活題目的。]
3. We can say that the society enhances efficiency at the cost of equity if
(A)重視國防、犧牲民生；
(B)不讓「對候選人不了解的選民」行使投票權；
(C)不讓油價上漲；
(D)推動公投。
Ans: B. [Obvious.]
4. We can say that the society enhances equity at the cost of efficiency if
(A)針對單身貴族課重稅、補貼低所得家庭之育嬰開支；
(B)重點補助研究型大學、淘汰區域性教學型大學；
(C)立法要求所有新車車主需有停車位證明；
(D)學校明文要求「每門課至少五分之一同學成績不及格」。
Ans: A. [Obvious.]
5. Suppose that you like to see movies and you also do not want to waste time while waiting to get into the theater. At 7 pm you arrive at the theater’s ticket counter (or window). Movie #1 will start at 7:30 pm; movie #2 will start at 7:30 pm; movie #3 will start at 8:00 pm. All movies have the same admission charge. Assume that you like movie #3 most while movie #1 is at the bottom of your priority list. If you finally decide to see movie #2, then the opportunity cost of doing so is
(A) the value of movie #3;
(B) the value of movie #3 minus (the utility derived from) the 30-minute waiting time saved;
(C) the value of movie #1 plus the value of movie #3
(D) the value of saving 30 minutes in waiting.
*Ans: B. [pp.5-6, text]
*6. Suppose that you like to see movies and you also do not want to waste time while waiting to get into the theater. At 7 pm you arrive at the theater’s ticket counter (or window). Movie #1 will start at 7:30 pm; movie #2 will start at 7:30 pm; movie #3 will start at 8:00 pm. All movies have the same admission charge. Assume that you like movie #3 most while movie #1 is at the bottom of your priority list.
(A) You will definitely choose to see movie #1;
(B) You will definitely not see movie #1;
(C) You will definitely choose to see movie #3;
(D) You will definitely choose to see movie #2.
Ans: B. [Notice that a rational consumer will reject movie #1 in light of the choice of movie #2. Can you figure out the opportunity cost of seeing movie #3?]
7. Examples of not thinking at the margin include:
(A) You saw NTD100 bill (紙鈔) on the sand beach before dark and did not pick it up;
(B) Explaining why water is much cheaper than diamond;
(C)教室若有空座位，學校要求教師不得拒絕增加學生；
(D)一家人買數種麥當勞套餐，然後各取所需。
Ans: A. [pp.6-7, text. 週六球場的20元無主硬幣，是(A)的靈感。]
8. Examples of people responding to incentives do not include:
(A) College professors should not announce the “all pass” policy;
(B) Average and above-average students tend to study more seriously for open book exams;
(C) I intentionally made you have some time pressure on this exam;
(D)認真填答文藻週的國際企業畢業專題展之問卷。
Ans: D. [Obvious.]
9. When economists study the short-run effects of some policy, they often assume that
(A) quantities are fixed;
(B) prices are fixed;
(C) labor inputs are fixed;
(D) people have no time to respond rationally.
Ans: B. [p.21, text]
10. Which of the following is not related to the notion of production possibility frontier?
(A) efficiency;
(B) technology constraints;
(C) scarce resources;
(D) Pareto efficiency.
Ans: D. [pp.24-26, text]
11. According to the bowed shaped (or negatively-sloped concave-shaped) production possibility frontier in your text, for an economy producing good X and Y, at larger x (i.e., the amount of good X produced),
(A) the opportunity cost for the society in producing X is higher;
(B) the opportunity cost for the society in producing X is lower;
(C) the opportunity cost for the society in producing Y is higher;
(D) the opportunity costs of producing X and Y are equal.
Ans: A. [p.25, text]
12. According to the production possibility frontier presented during lectures (concerning agents Frank and Robert), for an economy producing good X and Y, at larger x (i.e., the amount of good X produced),
(A) the opportunity cost for the society in producing X is higher;
(B) the opportunity cost for the society in producing X is lower;
(C) the opportunity costs of producing X and Y are equal;
(D) None of the above is correct.
Ans: D. [The PPF is linear in this case.]
13. This question does nothing but test whether you did read the textbook. Which person of the following did not major in economics at college?
(A) Arnold Schwarzenegger (the Governor of California);
(B) Mick Jagger (singer for the Rolling Stones);
(C) Condoleezza Rice (U.S. Secretary of State);
(D) Cate Blanchett (actress).
Ans: C. [Dr. C. Rice majored in political science. See p.27, text.]
14. The proposition that relatively more economists in a survey disagreed is
(A)租金管制會降低租屋的數量與品質；
(B)制定最低工資會增加年輕人的失業；
(C)實施進口關稅會減少本國福利；
(D)政府不應在(會計)年度內要求預算平衡。
Ans: B. [See p.34, text. You will find that 93% (approval) for A; 79% for B; 93% for C; 85% for D.]
15. Mr. Robert D. McTeer, Jr., the former president of the Federal Reserve Bank of Dallas wrote an article for the Wall Street Journal in 2003. His point regarding the so-called “broken window fallacy” is similar to
(A)制定最低工資會增加就業率；
(B) 921大地震有助於振興總體需求；
(C)修讀經濟學無助於政策的制定；
(D)最聰明的學生應該就讀醫科。
Ans: B. [See p.35, text. Test your reading comprehension.]
16. Suppose that there are only two consumers, A and B, in the market whose market demand curve is given by P + 2Q = 10. Assume that A demands 2 units of that good when the price is 5; demands 3 units when the price is 4.
(A) The demand of B for that good fails to satisfy the law of demand;
(B) The market demand for that good fails to satisfy the law of demand;
(C) At price 5, B will demand nothing;
(D) At price 6, A will demand nothing.
Ans: A. [At price 5, A will demand 2 units while B will demand 0.5 [= (10 - 5)/2 - 2] unit. At price 4, A will demand 3 units while B will demand nothing. See p.67, text. Key: the reverse of horizontal aggregation or summation.]
17. Let the market supply of soy bean (黃豆) be P - Q = 10. Suppose that the price of crude oil suddenly goes up,
(A) the demand for soy bean will fall;
(B) the demand for soy bean will rise;
(C) the supply of soy bean may become P - Q = 12;
(D) the supply of soy bean may become P - Q = 8.
Ans: C. [Crude oil price increases, increasing the transportation cost, hence making the supply curve of soy bean shift upward.]
18. Let the market supply of soy bean (黃豆) be P - Q = 10. Let the market demand for soy bean be 0.5P + Q = 10. At market equilibrium,
(A) the price is 12;
(B) the quantity is 10;
(C) the price is 15;
(D) None of the above is correct.
Ans: D. [By P - 10 = 10 - 0.5P we solve for P* = 40/3, hence Q* = 10/3.]
19. [continued from question 18] Suppose that crude oil price rose suddenly and that consumers were so panic that many bought more soy beans than what they usually do and stored them at home. As a result, the government officials might observe that
(A) a fall in equilibrium price but a rise in equilibrium quantity;
(B) a fall in equilibrium price and also a fall in equilibrium quantity;
(C) a rise in equilibrium price but a fall in equilibrium quantity;
(D) the same equilibrium price but a fall in equilibrium quantity.
Ans: C. [Shifting up both the supply curve and the demand curve leads to three possible outcomes: higher P* and higher Q*; higher P* and lower Q*; higher P* but Q* being unchanged.]
20. [continued from question 18] Suppose that both the equilibrium price and the equilibrium quantity fall. What might be the reason on the demand side for it?
(A) The price of milk rises dramatically;
(B) The price of milk falls dramatically;
(C) The price of crude oil rises dramatically;
(D) A recent scientific finding proves that soy beans are good for preventing cancers.
Ans: B. [When the price of milk falls dramatically, people consume more milk and less soy bean milk, hence we can see a decrease in the demand for soy bean.]
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。教師也有權公告具有特色之作答。] 30 points
21. [10 points]
Suppose that each agent has 4 hours to spend on the production of goods X and Y, whose quantities are denoted by x and y respectively. The PPF (productivity possibility frontier) of agent A is given by x/4 + y = 4; the PPF of agent B is given by x + y/4 = 4.
(a) For producing one unit of good X, how many hours does A need to spend?
Ans: By x/4 + y = 4 we see that it takes A 1/4 hour (or 15 minutes) to produce 1 unit of good X.
(b) Before the trade takes place, suppose that each agent concentrates on the
production of the good which she has the comparative advantage in producing. After production is realized, allow both agents to trade. Carefully use a diagram to illustrate what the range (範圍) of the relative price of good one is.
Ans: A has the comparative advantage in producing good X and B has the comparative advantage in producing good Y. At the full specification scenario, the production plan for A is (16, 0), the production plan for B is (0, 16). When we open up the trade, the relative (world) price of good one will be somewhere between 1/4 and 4, making both agents better off (as compared with autarky). When I grade the exam papers, I am expecting to see lines x/4 + y = 4 and x + y/4 = 4 precisely drawn on the x-y plane. Of course, (16, 0) and (0, 16) ought to be highlighted.
Note: Also see the Solution to Midterm Exam, Summer 2007.
22. [16 points]
宗輔中心的一份刊物寫道：「學生要的不是好老師，而是對他(她)好的老師。」
(i) From the point of information asymmetry, explain why this statement makes sense.
Ans: Good professors serve the university, not individual students, best. For a student, if his/her professor is nice to him/her in a conceivable way, of course, he/she might be happy to live with that. Why cannot professors strive for being kind to all students? The opportunity costs of doing so is simply too high for us to bear.
(ii)就經濟學的觀點，學校該如何確定學生認真填答教學評量？如何找出真正的好老師，而不是「對學生好的老師」？
*Ans: Generally speaking, students have little incentive to seriously answer those questionnaires. Cannot blame them as they barely have any idea about what this task is for, let alone getting access to those evaluation results. [現在學校辦的大小活動，還有一堆炒冷飯的碩、博士生，也喜歡一窩蜂的要求滿意度問卷，既無填答誘因，也無法保證彙整過程的公信力。我自己也常逆向操作或亂填，測試主事者的智慧。] 教務主管直接了解每位教師是否認真授課，成本確實太高。依賴學生來評量，其重要性不可否認。因為「教師音量大小」、「教師是否上課遲到」、「教師是否親自監考」，這一類的正確資訊，教務單位很容易取得。只要在問卷上，分散置入此類問題，再對照真實資訊，系統即可篩選掉「情緒性、報復性的填答者」。當然，有作為的資教或電算中心，還可以藉由系統設計，追蹤每位學生在每門課的期中考成績、給教師的評量、期末考成績。分析學生在不同年級(time series)、不同課程(cross section)、系列課程之學習情況與主觀感受。學生如果知道有此機制，應該會較認真填答。耳朵靈光的資深教師，不難有以下的經驗：一位同學每學期都會向不同老師私下表示，這是我遇到最難的課！This is the toughest course I have ever had! 如何找出真正的好老師？除非落實教學實況的透明化、學校能夠區分用功的學生的回饋與打混的學生之意見，由教師的研究績效(假外界專家之手，即同儕評鑑)來評比，也算是次佳解之一吧。
Note: Here is another example of screening: 利用 questions 13 thru 15，我可以找出那些同學，能夠有效地閱讀英文版教科書。
(iii)學校為何不直接公告每位專、兼任教師的教學評量，來幫助學生辨識真正的好老師？
Ans: 頭腦清楚的學校主事者，應該知道無法確保學生認真填答，所以不能單以教學評量，來排序教師的教學表現、甚至開鍘。但是，為了應付(或配合)家長的要求、立委的指責、輿論的關愛，不得不行禮如儀，還要依此辦理優良教師選拔等活動。更諷刺的是，主事者以尊重隱私為由，讓學生完全不知評量結果，當然缺乏認真填寫的誘因。主管教務者，與教師們正處於一種「策略性模糊」的均衡狀態。如果直接公告每位專、兼任教師的教學評量，勢必將喚醒不少獅虎，擴大教師對「評量教學績效」之檢討呼聲。當然，教師以easy grade『換取』較佳的評量分數、爭取選課人數，此類問題，勢必會擴散、加深。
[Any resolution? 如果大多數教師，直接把自己的教學評量，大剌剌地張貼於網頁，會有何衝擊效應呢？]
(iv)行政院院長為何不依據媒體或國會所製的施政滿意度，針對各部會首長，實施「退場機制」呢？
Ans: Recall the trade-off between efficiency and equity in text. 正如學校不可能以教學評量分數的高低，發給教師薪資。各部會的職掌不同，放在一面放大鏡下檢視，確實不公平。[否則，教育部長早就換人啦。啟示：不要老是把「退場機制」掛在嘴邊！]
[Hint: Think like an economist.]
23. [4 points]
假設我遇到一位不太熟的朋友，請她順道幫我繳電話費900元。轉念之間，我該如何迅速地確保她會真的如期代繳呢？
Ans: Just take out a 1,000 dollar paper bill and tear it into two pieces. [Recall lectures.] Give her one piece and tell her that when I see the receipt she will have the other piece. Hence, if she keeps her words, she will earn 100 dollars as a token showing my appreciation. [But what if she does not come back (and obviously she won’t go to the cashier)? Well, in that case, I will lose 1,000 dollars (plus getting the late payment penalty) while she just misses the chance of earning 100 dollars. If I want to feel safe, I might ask her to leave me with some money now.]
(放棄智慧財產權；歡迎全貌下載流傳。)
Monday, November 05, 2007
better take caution in making the signature file
Why?
Recently I was so impressed by a working paper entitled "False Modesty" that I even asked my senior group to write a senior thesis along that line. Can they do a good job? Who knows? Anyway they can just be modest in everything....... By the way,
I bet that this working paper will appear in some top econ journal some day soon.
Just got an email from my young and restless pal, Jerry.
This time he did not put Ph.D. right after his full name. [Gee! He might have monitored my moves all the time.]
Instead, he did something creative and down-to-earth.
He put: Jerry the Research Oriented assistant-Professor
I always enjoy learning from my younger friends, not necessarily including my students.
So, maybe my signature file can be:
John
the profit-oriented Associate Professor
and
asshole (according to my numerous diehard enemies)
哈利路亞！
Recently I was so impressed by a working paper entitled "False Modesty" that I even asked my senior group to write a senior thesis along that line. Can they do a good job? Who knows? Anyway they can just be modest in everything....... By the way,
I bet that this working paper will appear in some top econ journal some day soon.
Just got an email from my young and restless pal, Jerry.
This time he did not put Ph.D. right after his full name. [Gee! He might have monitored my moves all the time.]
Instead, he did something creative and down-to-earth.
He put: Jerry the Research Oriented assistant-Professor
I always enjoy learning from my younger friends, not necessarily including my students.
So, maybe my signature file can be:
John
the profit-oriented Associate Professor
and
asshole (according to my numerous diehard enemies)
哈利路亞！
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