DSE 2012 paper discussion-Please join

[kangkan]

My paper series is 01
Question 34...


I am getting B(Y on X) as 1.25 alright but B(X on Y)=0.555 ...option seems to be the only close option..is this a case of approximation?

38

wage=3.73+0.298 exper -0.0061exper^2 ...the t value of the 1st coefficient is coming out to be 7.2 and and t value of the 2nd is coming out to be 6.77.since both the value are >2,shudnt they both be significant...hence the returns shoud increase and then decrease right?but apparently the ans is a...cant figure out why

39. dont know how to approach..is this a max likelihod question

44. Is (0,0) included among a "possible solution)..because the system wont have a non trivial solution when A=[0 1|1 0]..but my ans key says both statements are correct? how


47.Cant figure out the approach

55 and 56

58,59,60- is there are algebric statement for marshall lerner conditions?

[Dreyfus]

For q44.....when system of equations is homogeneous then there can be only two possibilities for solution, a unique solution (x=0) and infinitely many solutions(x≠0)
If A is coefficient matrix and x is variable vector ie Ax=0
This can be only satisfied when x=0 A≠0, the case of unique solution and when x≠0 then A=0 ie the case of infinitely many solutions
Probability of unique solution ie x=0 A≠0 is 6/16
Probability of infinitely many solutions A=0, is 10/16
For atleast one solution,  6/16 +10/16 =1

[kangkan]

thanks vaibhav :)

[Granpa Simpson]

47) Given, g(x)= lim(t→x)[f(c+t)-f(c+x) ]/(t-x),
Let t-x=h,
so, g(x)=lim(h→0)[f(c+x+h)-f(c+x)]/h,
or g(x)=f'(x+c) [By using first principle of derivative].
Again since f(x) is concave in x, sol clearly it will be concave in (x+c) too.
so g'(x)=f''(x)<=0.
So clearly g(x) is decreasing in x.

[kangkan]

ok..thanks subhyanau..i got 55 and 56,but i am not able to solve the marshall lerner wala question.. :(

[neha:)]

How to solve Q. 26.. the Ginni coefficient one?

[The Villain]

@neha..

We know
Gini ceoff=(1/2n^2 mean) sigma ninj(mutual differences)yi-yj
           
here n1=1/2 and n2=1/2
mean is 200+100 divided by 2=150

subs in above formula
(1/2*1^2*150)(1/4(200-100)+1/4(200-100))
=1/6

[neha:)]

Thanks :)

[Akshay Jain]

even if u dont no the formula but no how the lorenz curves are constructed and how gini coeff is related to dem, den u cn easily find out the gini coefficient using area of triangles.......give it a try, its an interesting excercise....

[mrittik]

Dear Akshay, plz explain detail abt Gini Co-eff

[kangkan]

its is twice the area between the 45 degree line and the lorentz curve

[sarawagisruti]

Hi,

Could someone help with question 38

Suppose you have 500 observations and you regress wage
(measured in rupees per hour) on experience in the labour market, exper
(measures in years), and on experience in the labour market squared, (exper^2).
Your estimated OLS equation is
wdage = 3.73+ 0.298 exper - 0.0061 exper^2
              (0.35) (0.041)         (0.0009)
where the standard errors are in brackets. The estimated equation implies
(a) The returns to experience is strictly increasing
(b) The returns to experience is strictly diminishing
(c) The returns to experience is constant
(d) Experience has no statistically signicant effect on wage

[mrittik]

D2(Wage)/D(Experience)2 = -.00122....so returns to experience is strictly diminishing

[kangkan]

thanks mrittick :)

[phelps.phan]

Q 34: I'm also getting the same kangkan.

Q 55: U have the expression from qn 51 option b. at NAIRU expected inflation=actual inflation. Cancel the 1+pi on each side to get F(u,A)=1/(1+mu).
----> (A/u)-1=1/(1+mu). Solve and you'll get ans c.

Q 56: As we can write unemployment in the form u=c*A from qn 55. u has to increase by same percent as of A.

[phelps.phan]

Guys pls clarify my doubts below. Appreciate your help.

Q 2: Why not option a. If he transfers a part of his endowment, he is willing to trade off by market mechanism for another consumption bundle isn't it? So he is better off now after transfering. So his first bundle is not pareto optimal right?? Please can you tell the difference b/w option a and b in affecting pareto optimal condition.

Q 5: pls explain the approach.
Q 24: pls explain the approach.
Q 40: pls explain the approach.

Q 45: Seeing this this two variable optimization we get the determinant f11.f22-f12.f21=-1. So we can't say the function has a maximum or minimum in other words concave or convex. It has a saddle point. How then can we say the sets above it convex?

Q 46: How is the answer 2. FOC for (2+x)^3 gives one local extrm as x=-2. And I don't think u can find one with f`=0 for x^(2/3). I'm getting only one local extrm :(.

[kangkan]

Question 5>Any choice like (6,3) or(3,6) rules cannot be nash equilibrium..cuz here both players will have incentive to change behaviour...but someting like(7,3) or(3,7) or (5,5) will be nash since none of the players will have incentive to change behaviour

[kangkan]

24...here any player will consider putting the swap option only when he gets some number less than 50..now lets consider i get 38...if i decide to put the swap optio i have a (12/50) chance of getting more than 38 and (37/50) chance of getting less ...hence i wudnt take the bet..the other player will also reason the same way..hence no one will put the swap option.

[phelps.phan]

thanks kangkan:)

[kangkan]

Question 40....

Let X be the number of green balls drwan before a red ball is drwa

X=0   p=1/2

X=1   p=1.4

X=2   p=1/8 and so on....

The expected value of X comes out to be 1..hence you will get 1 rupee and pay 1 rupee leaving you with 0 rupess