Comment on Problem 2 of hwk 8

Solution of problem 2 of hwk 8 is valid only for L=1.
When L>1, assume (to the contrary) that x_11 not equal to x_12.
Then from strict convexity of preference, we can say that
(x_11+x_12)/2 is strictly preferred to x_11 under type 1's preference.
(See MWG p.656 Prop. 18.B.2)

I thank Matsuda-san for pointing this out.

Answer to question on consumer choice

In general, if C({x,y})={x}, then x \succsim y & not「y \succsim x」 so that x \succ y holds. ...(*)

One student asked me that it seems contradicting to the statement in
the first example of p.6 (Section 2.3) in resume:
\succsim which rationalizes C(.) s.t. C({x,y})={x}, C({x,y,z})=x
is given by ① x \succsim y, x \succsim z, y \succsim z.

Using (*), you might think that it should be written as
"\succsim which satisfies 「 ①' x \succ y, x \succ z, y \succsim z」 rationalizes C(.). "

Here is Prof. Kamiya's reply:
In general, binary relation is represented using only \succsim
(and not \succ, \sim ...etc). Since ① does NOT contain
"y \succsim x", it implies that "y \succsim x" does NOT hold. Hence we can conclude that
「x \succsim y & not「y \succsim x」」 so that x \succ y.
Thus, representating \succsim by ① is correct.

New version of hwk 13

I made corrections to original solution of hwk 13 and new one is available at hp.
(I realized that (3-ii) was wrong.) Also, I wrote some comments by Prof. Kamiya regarding questions came up in yesterday's TA session.
(ex. BC inequality in Radner eqm, assuming symmetric price in answer sheet...)

New version of hwk 12's solution

New version of hwk 12's solution is now available
from coremicro 2009's homepage.
(Changes are written in blue.)

Hwk 11-12 Graded

I finished grading hwk 11-12.
I will return them in today's TA session.
Afterwards, I will place them in front of 428.
My grading policy:
C: incomplete
B: Many errors in basic problems or tragic error in Problem 3 of hwk 12
A: Most of the problem correct. solve problem 3 of hwk 12 correct.
If you have any comments, please contact me.
I gave Ino-san A+ for his excellent performance in A-D eqm.

Correction of Hwk11-Problem 4-ii

Hwk 11 (4-ii)'s solution is wrong.
I must show that for all F.
(New Answer: Fix arbitrary F. Then from Jensen's inequality,
E[u(x)] = E[-x^2 + 6x +1] = E[-x^2] + 6(E[x]) +1
< -(E[x])^2 + 6(E[x]) +1 = u(E[x]).)

Typo in Hwk 12

In Hwk 12 Problem (2-iii),
Prob[X* (smaller than or equal to) Y*] must be
Prob[X* (greater than or equal to) Y*].

HW 9 & 10 Graded

Finished 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.

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.

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.

If you had any question, feel free to ask me.

Regards,
Kohei

Murooka's last OH

Dear all,

TA Murooka's last Office Hour will be held on June 24.

If you have any question to me,
please send E-mail by the next week, or visit on June 24.

Best regards,

Murooka

HW 9 & 10

We have uploaded both HW 9 and 10. The due date is June 23, in next week.
Feel free to come to my office if you found any typos and mistakes.

Regards,
Kohei

Hwk 7-8 graded

I finished grading hwk 7-8. I will return them in today's TA session. Afterwards, I will place them in front of room 428.
My general grading policy is
C: did not do Problem 3 of hwk 8
B: at least try Problem 3 of hwk 8 but incorrect answers in basic problems
A-: Problem 3 (i),(ii) of hwk 8 is correct( or with minor errors) but incorrect answers in basic problems
A: Solve all of them with minor errors. Correct Problem 3(iii).
A+: Excellent performance.

If you have any questions about your grade, please feel free to
ask me for explanation.

Nakajima

Additional assumption for hwk 8- (3-3)

Please note that in (3-3), x_h^i denote the demand of good h for consumer i.
There may be several ways to solve this problem.
If you need to assume u_{12}^2, u_{21}^2>0, please do so.
(where u_{12}^2 =\frac{\partial^2 u^2 (x_1^2,x_2^2;a)}{\partial x_1^2 \partial x_2^2}.)

Nakajima

Corrections in Hwk 7-(1-v)

In the social planner's problem,
z_1^1,z_1^2,z_2^1,z_2^2 in the
objective function must be
x_1^1,x_1^2,x_2^1,x_2^2.
Also, please assume that Pareto weights satisfy \lamba_i>0 for both i.
Lastly, please ignore "From Claim 1."

I apologize if I confused you and thank Kubota-san for letting me know.

P.S. Other minor typos are:
1) problem after (2-iii) must be (2-iv)
2) Pareto otimal, locally nonsatiated. (comma is needed in-between .)

Nakajima

About HW5&6

I marked all your HW 5&6 answer sheets.

In HW 5&6, 5 students got A+, 11 students got A, 4 students got B, and 7 students got C.

I marked A if you could have solved about 75% of problems or more, and marked B if 50% or more.

I awarded Hiraki, Ino, Konishi, Kubota, Matsuda as A+ by their excellent performance.


Comment:
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).
I continue suggesting you to review all your mistakes.

Anyone who has a question should come to my office.

Murooka

TA session on 5/29

Next TA session will be held on 5/29, 1st slot.
I will return homework 5&6 in the TA session.

If you can not attend TA session,
please pick up your homework from room 426 mail box
after 5/29.

Comment on Hwk 7-(1-vii)

Regarding the phrase " if we choose $\lambda_1,\lambda_2,\theta_1,\theta_2$ appropriately",
I did not mean that these parameters can be chosen independently.
This question just asks you to chose these parameters which is consistent with
FOCs for social planner's problem and brings FOCs in (1-iv) coincide with FOCs in (1-ii).

Comments on homework 7

There was a misleading statement in Problem 1 of hwk 7.
Since there is no producer in this economy,
I should have written "pure endowment economy" instead
of "private ownership economy."

I thank Nobara-san for pointing this out.

Correction for HW5

(i) In remarks, "with the answer sheet of HW4" is wrong.
Please staple with the answer sheet of HW6.

(ii) In problem 2, also assume x_1,x_2 \in R_{+}, and
f(0,k)=f(k,0)=0 for all k \in R.

Murooka

Correction about TA session on 5/15

In HW4 problem 4 (ii), my explanation was misleading in the TA session.

Regarding the proof of upper-hemicontinuity, the proof of MWG (p.93) is correct.
However, you can't use just same argument
if you want to prove continuity of demand function.
(In other word, "The same argument also establishes continuity ..."
in MWG p.94 is incorrect.)

Thanks to Kubota for letting me know.

Best regards,

Murooka

About HW 3&4

I marked all your HW 3&4 answer sheets.

In HW 3&4, 5 students got A+, 7 students got A, 14 students got B, and 16 students got C.

I marked A if you could have solved about 75% of problems or more, and marked B if 50% or more.

I awarded Ino, Kobayashi, Kanazawa, Konishi, Tsukahara as A+ by their excellent performance.


Comment:
Though some people understand the content very well, it seems that this year's average performance is significantly less than last year's.
I strongly recommend you to review all your mistakes thoroughly.

Anyone who has a question should come to my office.

Murooka

TA session on 5/15

Next TA session will be held on 5/15, 1st slot.
I will return homework 3&4 in the TA session.

If you can not attend TA session,
please pick up your homework from room 426 mail box
after 5/15.

OH on May 6 and May 13: Murooka

(i) Since May 6 is a holiday, there is no OH.

(ii) On May 13, TA Murooka's OH will be held at 10:20-12:00,
not at 15:00-16:40. Please keep in mind.

Murooka

Source Codes for HW1&2

Some students asked me to publish source codes for the homework. Here are those of HW1&2. Use them for reference.

HW1 Problem Set

HW2 Problem Set

HW1 Solution Manual

HW2 Solution Manual

Return HW1&2

I 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.

Sorry for my great delay.

In HW1&2, 10 students got A, 14 students got B, and 16 students got C.

I awarded Tsukahara and Ino A+, since they showed excellence especially in solving optimization problem, some optional problems, and made few mistakes.

Anyone has a question about the rate come to my office.

Regards,
Kohei

Correction for Solution Manual to HW1

I 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.

I might have made some other such mistakes...

Regards,
Kohei

Correction for Solution Manual to HW2

As is mentioned in the last TA session, I made some mistake in solving HW2 5(a)(iii).

I uploaded the revised version in the course web site, so please refer to it.

Thanks Igarashi for letting me know.

Regards,
Kohei

Correction for HW3

Found the following typos in HW3.

Problem 4: "... if X is finite ..." should be replaced to "... if |X| is finite ...",
where |X| represents a cardinality of X.

Thanks to Kobayashi and Kubota for pointing it out.

HW1&2: Solution Manual

We have uploaded solution manual to HW1&2.
Please download and check it.

Regards,
Kohei

Next TA Session: HW1 & 2

We hold a TA session tomorrow 4/24:8:30-10:10 at room 3.
We soon upload the solution manual to the homework, so please bring it to the session.

I must apologize that I cannot return HW tomorrow because I have a full schedule.
I will return the HW at next Wednesday. Sorry for the delay.

Regards,

Kohwi

Correction for HW2

Found ambiguous description in HW2, so correct it as follows:

3. (b)

Wrong: "you can show that the constraints never bind with equality in this optimization problem"
↓
Correct: "you can show that the constraints c_t, c_t+1, s_t >= 0 never bind with equality at the optimum point in this optimization problem"

Kohei

Correction for HW1

We found another mistake in HW1.

3.(a)(iii)

wrong: Is this open in R2? Is this closed in R2?
↓
correct: Let define A={x in R2 | a < x1 < b, x2=0} Is this open in R2? Is this closed in R2?

Thanks Kubota, Takashima, and Fukuda for letting me know.

For precise description, please refer to this.

Kohei

HW2 Uploaded

We have uploaded HW2.
Please download and try it.

Kohei

Next TA Session: TeX lecture

Next TA session is held on April 10, 8:30-10:10 in room 3.
We make a brief lecture on TeX.

By then, anyone who has notepad PC should install TeX and bring it to the room.
We do not hand out the resume in the class, so please download and print it.

Thanks,

Kohei

Correction for HW1

Found the following typos in HW1.

• 1. (a) (iii) wrong: "less than three"→correct: "equal or less than"
• 2. (d) (iii) (T2') wrong: "A_1∩A_2"→correct: "A_1∪A_2"

Already uploaded the corrected version in microeconomics homepage.

Thanks Kanazawa and Ino for pointing it out.

Kohei