DSE 2010 Disucssion-Please joim

[kangkan]

Hi..i have series 4...i am stuck with these questions..please help
http://econdse.org/wp-content/uploads/2012/04/2010-Option-A.pdf

question 16...

Question 24..i am getting option C..please confirm

Questio 52. i am getting option C

Question 54.i am getting option b.

54. c

58. How can the prices be different?

[mrittik]

52. idea is very simple the only transaction happens with the 2nd one....so she thinks how to distribute....she has 2 of first one....she needs only 1 one second to stay the original utility level....so px/py=1.

54. option b is the level of starting....but whether the distribution or walrasian equilibrium reached? think...the answer is nope....so the set is empty

58. Prices r different....because price fighting leads to monopolize the market in respect to price....for more idea on Bertrand Duopoly plz peruse 'POLICONOMICS'

16. a

[Spiti]

How to approach q57

[kangkan]

Hi Spiti for 57....the effective price for good X= p/2(since ita buy get one free)...Dx= 1/2 *m/2px which is greateer than p*..but the demand for y is independent of price of x..so yd=y*

:)

[kangkan]

yes 54 is c accd to me too..i marked it wrong..it shu be empty...@mrtittick..can you please explain 58...wuould really help..thanks

[kangkan]

and for 16..how did you establish the transitivity

[Spiti]

For 57, Well i thought so too, but Amit sirs answer key says answer is d, xd=x* and yd=y*.

[mrittik]

54. The logic is simple: if the price set by both firms is the same but the marginal cost is lower, there will be an incentive for both firms to lower their prices and seize the market. Therefore, the only equilibrium in which none of the firms will be willing to deviate is when price equals marginal cost.

16. X>=Y, Y=Z, so from transitivity of >= we can conclude that X=Z. understood?

[mrittik]

basic logic of need of both the goods more....it has this kind of Utility curve...Budget Line is going to be changed...it is becoming flatter because the price of good X is now Px/2....so the consumer needs more of good x because of the less price....but only staying at the previous consumption bundle it has been matched with the previous utility level at lesser Income...so Xd=X*...understood?

[The Villain]

I'm getting 52 as c...
how is it a...i still didnt get it.

[Granpa Simpson]

Still I dint get how to use POLINOMICS in this case..anyhow the answer will be option d, this is because in both the cases i.e if p2=3 or p2=2 the profit of firm 2 will remain at same level i.e 1.5, so firm 2 will be indifferent between p2=2 or p2=3, hence option d...in any case it wud be grt if u give us the basic idea regarding working with POLINOMICS.

[Granpa Simpson]

for Q52 just use the concept that for any point which is Pareto Efficient the monetary value of the excess demand will be zero..this condition gives leads to the condition that the market gets cleared, so competitive a competitive price ratio will clear the market...now the question remains how to find that price ratio..under the assumption that the preferences are monotone, complete and convex a Pareto efficient bundle leads to a competitive equilibrium (second theorem of welfare economics)..now we know that a Lexicographic preference ordering is monotone, complete and convex so a choose a Pareto Efficient point and compare..in this case in the previous question we have found that (1,0) is a pareto efficient bundle for A. put this in the excess demand function of A and set its monetary value equal to 0. This gives.
px*1+py*0=px*0+py*1.
or, px=py.
or, px/py=1.
Hope this helps.

[Granpa Simpson]

For Q54)
Option A: Cannot be Pareto Efficient because A is worse off as compared to the initial endowment bundle, since A strictly prefers bundle with more of y (lexicographicaly prefers y to x) so putting him/her to (1,0) makes her worse off as compared to (0,1). So a cannot be the answer.
Option B: Consider reallocation (1,1) for A and (1,0) for B..clearly A can be made better off as compared to the bundle (0,1) keeping B's utility constant at 0.
Option D: Cannot be the answer by the logic used for option b.
Option C: is the right answer.

[kangkan]

@Spiti- i think we wud be consuming 2X* ,hence he will be buying X*...hence Xd=X*

[kangkan]

Thnaks mrittick..i ignored the positive integer part

[phelps.phan]

guys pls explain qns 35,36,37,40 (series4). thanks

[rongmon]

Anyone for Q 48, 49, 50. Series 04.

Thanks.

[rongmon]

Q10 as well!

[jack]

@48.
integrate o to 5(kX) + integrate 5 to 10{ k(10-X)}
solve it  
you get K=1/25

@49
p(B)= integrate 3 to 5(kx) + integrate 5 to 8 {k(10-X)}
p(A intersection B)=integrate 5 to 8 {k(10-X)}
then find P(A/B)
you get 21/37

@50. not indepentdent
P(A) is not = to P(B)

[Granpa Simpson]

Q48) Integrate kx over [0,5], k*(10-x) over [5,10] and equate the sum equal to 1, you will get an equation of the form, k*(25/2)+{(100*k-50*k-50*k+(25/2)*k}=1,
or, k*25=1,
or, k=1/25.
Q49) P(AGivenB)=Pr(X>=5 intersection X=[3,5])/Pr(X=[3,5])={integration (1/25)*(10-x) over [5,8]}/{integration (1/25)*x over [3,5]+(1/25)*(10-x) over [5,8]} from this the numerator will be (21/50) and the denominator will be (37/50), hence the required probability will be (21/37).