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