tag:blogger.com,1999:blog-64406196849766502052020-02-28T23:40:29.913+09:00Coremicro2009coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.comBlogger34125tag:blogger.com,1999:blog-6440619684976650205.post-72188033209653855632009-07-21T14:17:00.002+09:002009-07-21T14:21:43.163+09:00Comment on Problem 2 of hwk 8Solution of problem 2 of hwk 8 is valid only for L=1.<br />When L>1, assume (to the contrary) that x_11 not equal to x_12.<br />Then from strict convexity of preference, we can say that<br />(x_11+x_12)/2 is strictly preferred to x_11 under type 1's preference. <br />(See MWG p.656 Prop. 18.B.2)<br /><br />I thank Matsuda-san for pointing this out.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-69691630258329325852009-07-16T14:06:00.002+09:002009-07-16T14:18:04.974+09:00Answer to question on consumer choiceIn general, if C({x,y})={x}, then x \succsim y & not「y \succsim x」 so that x \succ y holds. ...(*)<br /><br />One student asked me that it seems contradicting to the statement in<br />the first example of p.6 (Section 2.3) in resume:<br />\succsim which rationalizes C(.) s.t. C({x,y})={x}, C({x,y,z})=x<br />is given by ① x \succsim y, x \succsim z, y \succsim z.<br /><br />Using (*), you might think that it should be written as<br />"\succsim which satisfies 「 ①' x \succ y, x \succ z, y \succsim z」 rationalizes C(.). "<br /><br />Here is Prof. Kamiya's reply:<br />In general, binary relation is represented using only \succsim<br />(and not \succ, \sim ...etc). Since ① does NOT contain<br />"y \succsim x", it implies that "y \succsim x" does NOT hold. Hence we can conclude that<br />「x \succsim y & not「y \succsim x」」 so that x \succ y. <br />Thus, representating \succsim by ① is correct.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-47929585938396356972009-07-15T10:55:00.001+09:002009-07-15T10:57:25.537+09:00New version of hwk 13I made corrections to original solution of hwk 13 and new one is available at hp. <br />(I realized that (3-ii) was wrong.) Also, I wrote some comments by Prof. Kamiya regarding questions came up in yesterday's TA session. <br />(ex. BC inequality in Radner eqm, assuming symmetric price in answer sheet...)coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-49721842506074216132009-07-10T10:55:00.002+09:002009-07-10T10:57:15.087+09:00New version of hwk 12's solutionNew version of hwk 12's solution is now available<br />from coremicro 2009's homepage.<br />(Changes are written in blue.)coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-6152935064671946922009-07-10T07:53:00.002+09:002009-07-10T07:56:46.103+09:00Hwk 11-12 GradedI finished grading hwk 11-12. <br />I will return them in today's TA session. <br />Afterwards, I will place them in front of 428.<br />My grading policy:<br />C: incomplete<br />B: Many errors in basic problems or tragic error in Problem 3 of hwk 12<br />A: Most of the problem correct. solve problem 3 of hwk 12 correct.<br />If you have any comments, please contact me.<br />I gave Ino-san A+ for his excellent performance in A-D eqm.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-76000550235573140492009-07-09T17:48:00.002+09:002009-07-09T17:52:47.123+09:00Correction of Hwk11-Problem 4-iiHwk 11 (4-ii)'s solution is wrong. <br />I must show that for all F. <br />(New Answer: Fix arbitrary F. Then from Jensen's inequality,<br />E[u(x)] = E[-x^2 + 6x +1] = E[-x^2] + 6(E[x]) +1<br />< -(E[x])^2 + 6(E[x]) +1 = u(E[x]).)coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-25355200726236297992009-07-03T15:35:00.002+09:002009-07-03T15:40:51.783+09:00Typo in Hwk 12In Hwk 12 Problem (2-iii),<br />Prob[X* (smaller than or equal to) Y*] must be<br />Prob[X* (greater than or equal to) Y*].coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-21622276468253186872009-06-29T11:46:00.002+09:002009-06-29T12:05:43.130+09:00HW 9 & 10 GradedFinished grading HW 9 &10. I will bring them to the class in June 30. If you want them before the class, please come to my office to pick them up. I put them in the mail box in front of room 426 by the class, and after the class.<br /><br />This time, I gave A for 12 students, B for 7 students, and C for 1 students. Kubota, Ino, and Tsukahara received A+ for their excellent performance.<br /><br />I feel you all have done fairly well. Few students made major mistakes. The difference between grade A and B is just whether you can make a clear and convincing argument. Some students only put the answer, and did not exposit the logic to reach it. We less evaluate such a paper.<br /><br />If you had any question, feel free to ask me.<br /><br />Regards,<br />Koheicoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-37424425828111096022009-06-18T13:45:00.002+09:002009-06-18T13:52:28.713+09:00Murooka's last OHDear all,<br /><br />TA Murooka's last Office Hour will be held on June 24.<br /><br />If you have any question to me,<br />please send E-mail by the next week, or visit on June 24.<br /><br />Best regards,<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-81869697024428328142009-06-15T20:51:00.000+09:002009-06-15T20:52:44.301+09:00HW 9 & 10We have uploaded both HW 9 and 10. The due date is June 23, in next week.<br />Feel free to come to my office if you found any typos and mistakes.<br /><br />Regards,<br />Koheicoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-50599957973431786332009-06-12T07:58:00.003+09:002009-06-12T08:04:34.799+09:00Hwk 7-8 gradedI finished grading hwk 7-8. I will return them in today's TA session. Afterwards, I will place them in front of room 428. <br />My general grading policy is<br />C: did not do Problem 3 of hwk 8<br />B: at least try Problem 3 of hwk 8 but incorrect answers in basic problems<br />A-: Problem 3 (i),(ii) of hwk 8 is correct( or with minor errors) but incorrect answers in basic problems<br />A: Solve all of them with minor errors. Correct Problem 3(iii).<br />A+: Excellent performance.<br /><br />If you have any questions about your grade, please feel free to<br />ask me for explanation.<br /><br />Nakajimacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-89471400154897739872009-06-03T10:46:00.002+09:002009-06-03T10:50:36.217+09:00Additional assumption for hwk 8- (3-3)Please note that in (3-3), x_h^i denote the demand of good h for consumer i.<br />There may be several ways to solve this problem. <br />If you need to assume u_{12}^2, u_{21}^2>0, please do so.<br />(where u_{12}^2 =\frac{\partial^2 u^2 (x_1^2,x_2^2;a)}{\partial x_1^2 \partial x_2^2}.)<br /><br />Nakajimacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-82872439562625727262009-05-31T14:00:00.003+09:002009-05-31T14:11:50.042+09:00Corrections in Hwk 7-(1-v)In the social planner's problem,<br />z_1^1,z_1^2,z_2^1,z_2^2 in the<br />objective function must be<br />x_1^1,x_1^2,x_2^1,x_2^2. <br />Also, please assume that Pareto weights satisfy \lamba_i>0 for both i.<br />Lastly, please ignore "From Claim 1."<br /><br />I apologize if I confused you and thank Kubota-san for letting me know.<br /><br />P.S. Other minor typos are:<br />1) problem after (2-iii) must be (2-iv)<br />2) Pareto otimal, locally nonsatiated. (comma is needed in-between .)<br /><br />Nakajimacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-23531603110206978242009-05-28T22:02:00.005+09:002009-05-28T23:56:37.936+09:00About HW5&6I marked all your HW 5&6 answer sheets.<br /><br />In HW 5&6, 5 students got A+, 11 students got A, 4 students got B, and 7 students got C.<br /><br />I marked A if you could have solved about 75% of problems or more, and marked B if 50% or more.<br /><br />I awarded Hiraki, Ino, Konishi, Kubota, Matsuda as A+ by their excellent performance.<br /><br /><br />Comment:<br />I want to mention that this year's average performance in these HW is significantly improved (maybe equal or silightly higher than last year's average performance).<br />I continue suggesting you to review all your mistakes.<br /><br />Anyone who has a question should come to my office.<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-36864994920427209072009-05-28T22:01:00.000+09:002009-05-28T22:02:07.404+09:00TA session on 5/29Next TA session will be held on 5/29, 1st slot.<br />I will return homework 5&6 in the TA session.<br /><br />If you can not attend TA session,<br />please pick up your homework from room 426 mail box<br />after 5/29.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-78515690906017575772009-05-28T17:33:00.003+09:002009-05-28T17:41:23.371+09:00Comment on Hwk 7-(1-vii)Regarding the phrase " if we choose $\lambda_1,\lambda_2,\theta_1,\theta_2$ appropriately",<br />I did not mean that these parameters can be chosen independently. <br />This question just asks you to chose these parameters which is consistent with<br />FOCs for social planner's problem and brings FOCs in (1-iv) coincide with FOCs in (1-ii).<br /><br /><strong></strong>coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-48681866840067593312009-05-28T10:47:00.002+09:002009-05-28T10:53:05.285+09:00Comments on homework 7There was a misleading statement in Problem 1 of hwk 7.<br />Since there is no producer in this economy,<br />I should have written "pure endowment economy" instead<br />of "private ownership economy."<br /><br />I thank Nobara-san for pointing this out.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-56285278350618262482009-05-15T15:37:00.002+09:002009-05-15T15:41:43.582+09:00Correction for HW5(i) In remarks, "with the answer sheet of HW4" is wrong.<br /> Please staple with the answer sheet of HW6.<br /><br />(ii) In problem 2, also assume x_1,x_2 \in R_{+}, and<br /> f(0,k)=f(k,0)=0 for all k \in R.<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-71117169163050043652009-05-15T15:24:00.002+09:002009-05-15T15:35:35.197+09:00Correction about TA session on 5/15In HW4 problem 4 (ii), my explanation was misleading in the TA session.<br /><br />Regarding the proof of upper-hemicontinuity, the proof of MWG (p.93) is correct.<br />However, you can't use just same argument <br />if you want to prove continuity of demand function.<br />(In other word, "The same argument also establishes continuity ..."<br /> in MWG p.94 is incorrect.)<br /><br />Thanks to Kubota for letting me know.<br /><br />Best regards,<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-12356696290250086982009-05-14T03:19:00.004+09:002009-05-14T03:38:58.301+09:00About HW 3&4I marked all your HW 3&4 answer sheets.<br /><br />In HW 3&4, 5 students got A+, 7 students got A, 14 students got B, and 16 students got C.<br /><br />I marked A if you could have solved about 75% of problems or more, and marked B if 50% or more.<br /><br />I awarded Ino, Kobayashi, Kanazawa, Konishi, Tsukahara as A+ by their excellent performance.<br /><br /><br />Comment: <br />Though some people understand the content very well, it seems that this year's average performance is significantly less than last year's.<br />I strongly recommend you to review all your mistakes thoroughly.<br /><br />Anyone who has a question should come to my office.<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-59189832461402256252009-05-13T13:41:00.002+09:002009-05-13T13:44:30.206+09:00TA session on 5/15Next TA session will be held on 5/15, 1st slot.<br />I will return homework 3&4 in the TA session.<br /><br />If you can not attend TA session,<br />please pick up your homework from room 426 mail box<br />after 5/15.coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-88639846476693545692009-05-02T13:02:00.003+09:002009-05-02T13:11:24.491+09:00OH on May 6 and May 13: Murooka(i) Since May 6 is a holiday, there is no OH.<br /><br />(ii) On May 13, TA Murooka's OH will be held at 10:20-12:00,<br />not at 15:00-16:40. Please keep in mind.<br /><br />Murookacoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-24484524727724792262009-04-29T10:38:00.002+09:002009-04-29T10:40:50.056+09:00Source Codes for HW1&2Some students asked me to publish source codes for the homework. Here are those of HW1&2. Use them for reference.<br /><br /><a href="http://sites.google.com/site/coremicro2009/file-box/Micro_HW1.tex?attredirects=0">HW1 Problem Set</a><br /><br /><a href="http://sites.google.com/site/coremicro2009/file-box/Micro_HW2.tex?attredirects=0">HW2 Problem Set</a><br /><br /><a href="http://sites.google.com/site/coremicro2009/file-box/Micro_HW1_SolutionManual.tex?attredirects=0">HW1 Solution Manual</a><br /><br /><a href="http://sites.google.com/site/coremicro2009/file-box/Micro_HW2_SolutionManual.tex?attredirects=0">HW2 Solution Manual</a>coremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-73935749435268624802009-04-29T10:23:00.006+09:002009-04-29T15:14:16.856+09:00Return HW1&2I marked all your HW1&2 answer sheets and put them in the mail box in front of my office, room 426. Please come to take them.<br /><br />Sorry for my great delay.<br /><br />In HW1&2, 10 students got A, 14 students got B, and 16 students got C.<br /><br />I awarded Tsukahara and Ino A+, since they showed excellence especially in solving optimization problem, some optional problems, and made few mistakes.<br /><br />Anyone has a question about the rate come to my office.<br /><br />Regards,<br />Koheicoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0tag:blogger.com,1999:blog-6440619684976650205.post-27192032705530298022009-04-28T17:20:00.003+09:002009-04-29T09:45:39.946+09:00Correction for Solution Manual to HW1I found an error in the solution manual to HW1(a)(i). There, I argued that A is not closed since it is open, but it is an insufficient argument. That we can take a convergent sequence to b which is not in A is the reason that it is not closed.<br /><br />I might have made some other such mistakes...<br /><br />Regards,<br />Koheicoremicro2009http://www.blogger.com/profile/06853819455572271092noreply@blogger.com0