Gini Coefficient Questions!!!!

[Sumit]

Q1.(a) There are 5 individuals in an economy n1, n2, n3, n4, n5 and their incomes are 5,11,18,25,41 respectively..
where n1=poorer person
n5=richest person
find The Gini coefficient of inequality for this economy??

(b) Now suppose due to progressive transfer (i.e richest person remains richest and poorer person remains poorer) richest persons transfer 5 unit of his income to poorer person, Now the new income of individuals  are as follows:
n1=10
n2=11
n3=18
n4=25
n5=36
Now calculate the new Gini coefficient of inequality????Also state whether the inequality has reduce or increases???
 

[laracroft]

i think the ans (a) is 0.294

(b) 0.26

So, Inequality has reduced.

[Sumit]

Answer is. a)0.444  b)0.244 n yes inequality has reduced..

[maahi]

Q1.(a) There are 5 individuals in an economy n1, n2, n3, n4, n5 and their incomes are 5,11,18,25,41 respectively..
where n1=poorer person
n5=richest person
find The Gini coefficient of inequality for this economy??



q1) ginni coeff= ginni mean difference / 2mean
ginni mean difference = sum of the mutual differences/{n(n-1)/2} {(11-5 )+(18-5) +(25-5)+(41-5)+(41-11)+(25-11)+(18-11)+(25-18)+(41-18)+(41-25) }= 172
sum of the mutual differences  {(11-5 )+(18-5) +(25-5)+(41-5)+(41-11)+(25-11)+(18-11)+(25-18)+(41-18)+(41-25) }= 172
5*4/2=10
ginni mean difference= 17.2
mean = 20
ginni coeff= 17.2 /40 =

[Sumit]

@Maahi: n what will be the answer of question-26 DSE 2012 by this method????? Are u getting the correct answer????

[maahi]

i did it by other method . in the above problem number of people in d different income categories are not specified . in 26 q the number is specified .
lets say d total population is 1  which has two income  categories :100 and 200 . 1/2 people in category 1 and other half in 2 . i used this formula given in debraj ray

ginni coeff = sigma ninj(mutual differences)/2n^2*mean
ni = number of people in category 1
nj = no. of ppl in category 2

g= sigma 1/2*1/2(100)/2*1*150 =1/6
 :-)

[Sumit]

@maahi: plz read above question carefully it is clearly specified that there are 5 individuals in an economy & all of them hv different income which mean there are only 5 income group....n yes, for this we need to assume that there is only five people in economy then only we can calculate the gini coefficient of economy(you can't calculate the gini coefficient of an economy if you hv income of a few people or in absolute words all the income group+ the no.of people in each income group in that economy).

n yes I also know both the formulas, I asked the above q26 answer  bcoz if you calculate its answer by the formula given in  S.c gupta...you will get different answer.than calculate it by dabraj ray formula...Actually I didn't get the formula given in S.c gupta...why there is discrepancy n both the formulas????

I actually found that dabraj formula is better and can be applied to all the problems..

Note: If you calculate the answer of a) by debraj ray formula you will get 0.444 to be precise...whereas by S.c gupta formula you'll get 0.43.

[vandita24x7]

what is d formula given in Debraj Ray? and pls also give the formula given in S.c . gupta

[vandita24x7]

Sumit, pls provide both the formulae here...m so confused

[vandita24x7]

how to find gini coefficient here? which formula to use??????

[maahi]

ya i realized my mistake after posting it
i dunno d difference b/w d two formulas
 can u show your working for d 5 ppl ques . i didn't get its answer by debraj method

[wolverine]

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&ved=0CEgQFjAD&url=http%3A%2F%2Fwww3.nccu.edu.tw%2F~jthuang%2FGini.pdf&ei=U7iAUbqpFcWtrAfMzIG4Ag&usg=AFQjCNGVWoGjtfl4ohZvSnOk8LbjthtbWw&bvm=bv.45921128,d.bmk

chck the above link.

[Sumit]

@vandita24x7 and maahi: For dabraj ray formula look for page no.188 to190....in below link...If found any problem then you can ask me.

http://books.google.co.in/books?id=GKr5RxWT4uAC&printsec=frontcover#v=onepage&q&f=false

@vandita24x7:  Answer of your question is b)G5<G1=G2=G3=G6<G4
where G1=G2=G3=G6=0.25, G5=0, G4>0.25( not calculated it bcoz It must be greater than all .....can be seen by examine the yellow type people income which is increasing, so the inequality must also increase).

Note: Guys don't get confuse,,,, If you will consider both the formulas you'll definitely get confused like I did when I get to know both the formulas..
I found simple solution for this,
1)consider only debraj ray formula bcoz it applied to all the problem I faced till now n got all the answers correct.
2)Including Debraj ray formula understand lorenz curve utterly bcoz gini coefficient is nothing but the ratio of the area btw 45 degree line and lorenz curve to the area of triangle below 45 degree line.

Also I get to know two things while doing questions which will help you to solve gini coefficient question using debraj ray formula.
1)If the different income of all the income group is multiplied by a same +ive real number then the gini coefficient will remain same.
2)If the no. of people in each income group is multiplied by a same +ive integer then again gini coefficient remain same.

You can verify above two results by using Lorenz curve........you can also verify the above results from the question given by vandita24x7 above...plz let me know if you found any difficulty...


 

[vandita24x7]

can u pls just show the working of that question.. for which u have given the answer  b)G5<G1=G2=G3=G6<G4  ????

[vandita24x7]

Sumit can't follow the formula... wat is ninj meaning here? pls show the working.. for G1 G4 and G6

[vandita24x7]

Sumit can't follow the formula... wat is ninj meaning here? pls show the working.. for G1 G4 and G6

[Sumit]

@vandita24x7: I'm attaching 2 images hv a look....all of the questions can be done like this....but remember one thing whenever there is a same no. of people in each income group treat them like a case where you hv only 1 people in each income group...then only you will get correct answer reason of this is that cumulative population share of each income group is same......check G6 for validation of this statement....G4 can be done like I did G1....If still found any problem feel free to ask me....

For formula:this is the same formula as debraj ray only difference is that we didn't divide it by 2 bcoz we are taking sum of all +ive difference of diff. income group...


calculation of G1:

[vandita24x7]

Thanks a ton Sumit means a lot to me... actually i was dividing by2 also.. coz as u said to do like d formula..
one more question if u could pls help...
If saving propensity is 14% and incremental capital output ratio is 4 and population rate of growth is 3%, there is CRS and no technical progress

a)warranted rate of growth is > than natural rate of growth
b)"              "      "    "          <  "        "         "          "
c)economy will always grow at 3% rate of growth
d)"             "     "        "      " > 3% "      "    "

[Sumit]

sorry vandita 24x7 I hvn't done growth models yet....

[Akshay Jain]

Guys have a look at the above conversation....its a thread from past year and i guess its helpful fo those hu are having problems in gini coefficient.....