ISI-2008 ME 2 Discussion

[Dr. Strange]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/msqe2008.pdf

Please help me out with Q3 and Q4 (b) part of ME2.

[Akash]

3.
Max (a-(q1+q2))q1-10(40-q1)
Wrt q1

q1=( a+10-q2)/2 if a+10-80<0
      40 if                a+10-80>=0 his marginal revenue is always +vet so he sells everything

Similarly
q2= ( a+10-q1)/2 if a+ 10-160<0
       80 if a+ 10-160>0


Use these to get response for a=100 and 200
100 hasq1,q2=  40,35

200 has 40,80

[Akash]

I am pretty confused by 4. Does the production function mean 1 of X AND 1 of Y for each L or 1 of X OR 1 of Y for each L. Also how we decide prices? Using marginal product = wage?

Can you please give your solution?

[Dr. Strange]

Q3. Thanks a lot Akash for replying.

For a=200 I am also getting 40,80 as yours.

For a=100 I don't think q1=40,q2=35 can be an answer because :
del(profit 1)/del q1 = a-2q1-q2+10 if you put q1=40 and q2=35 and a=100 we get
del(profit 1)/del q1 =-5 which we means we can increase profit by decreasing q1

Solving reaction curves for both I am getting q1=q2= 110/3 for a=100

However in question it is given firm 2 always destroys a part of produce even if a=200 which is not in our case.

Please have a look.

[Dr. Strange]

I am having trouble in (b) part of Q4. If you are facing problem in (a) part let me know.

[Akash]

Yeah you are correct in second case. I made an error in copying from one page to the next in my notebook.

I had a problem with a part and the general approach to such questions for 4. I'll be thankful if you could share your solution

[urvashi]

I did not understand the conditions the logic behind why the firms are responding that way to the inequality conditions pls explain

[Dr. Strange]

4(A) Demand Side:
Consumer demands 50/px of x and 50/py of y

Supply side:

Since everything is competitive
so profit=0

So in x industry, profit=0 i.e px=w
for y, py=w

Now net demand =net supply
so 50/px of x requires 50/px of labour
similarly 50/py of y requires 50/py of labour
since px=py=w and total labour=10 so px=py=w=10

[Dr. Strange]

4 B) Optimum production requires K=L
NOW assuming all K is used K=L=100
This gives w=2
since net profit =0
so assuming price=p and rental rate=r we get a relation p=2+r

I can't find rental rate.

[Dr. Strange]

3)

Akash:

 Question 3 states firm 2 always has to destroy a part of its produce which is not coming in our case.Is the question statement Wrong or we made a mistake somewhere?

Urvashi :

  Profit of firm 1=(a-q1-q2)q1 - cost of destroying unutilised goods
                          = (a-q1-q2)q1 - 10(40-q1)
optimise wrt q1

Similarly do this for q2 and solve 2 conditions simultaneously for answer

[duck]

Hi.. :)

Amit Sir has posted solution to ISI 2008 Q3.

ISI 2008 - Q3

Thanks

[Dr. Strange]

Thanks a lot.

[duck]

Hi.. :)

Amit Sir has posted solution to ISI 2008 - Q4(b).

ISI 2008 - Q4(b)

Thanks