5

PreviousQuestion 11 of 11 (1 point)Find the Gini inder for the = given Lorenz curveJe* Lk) = € +1The Gini inder for the given Lorenz curve is approximatelyRou...

Question

PreviousQuestion 11 of 11 (1 point)Find the Gini inder for the = given Lorenz curveJe* Lk) = € +1The Gini inder for the given Lorenz curve is approximatelyRound your answer t0 four decimal places

Previous Question 11 of 11 (1 point) Find the Gini inder for the = given Lorenz curve Je* Lk) = € +1 The Gini inder for the given Lorenz curve is approximately Round your answer t0 four decimal places



Answers

Find the constant $c$ ( to 2 decimal places) such that the Lorenz curve $f(x)=x^{c}$ has the given Gini index of income concentration. $$ 0.52 $$

Were given the Lorenz curve with the equation. Why is equal to X squared times the to the X minus one, and we're asked to find the Gini index of income concentration. So let's denote, uh, this equation as a function at FedEx, Then the Gini Index is going to be so g is equal to 0.5, minus the integral from 0 to 1 of our function. So which is our Lorenz curve and divided by 0.5? So this tells us me to find this integral first, so let's go ahead and do that on the side. So the integral from 0 to 1 of f of X, which is X squared the to the X minus one it's equal to. And to do that, we're going to need to do integration by parts twice. So the first time we're going to let you be equal to X squared, which means Devi is going to be e to the X minus one DX. So now d'you is too. The X and we is B to the X minus one. So this gives us using our integration by parts formula. This will be X squared E to the X minus one evaluated from 0 to 1, minus the integral from 0 to 1 of the time's D. So that would be you can pull the two to the French, and that would be X B to the X minus one DX. Okay, so now we can see that this part requires us to do integration by parts again. So let's this part. So we're going to let you be equal to X here, which means D V is still e to the X minus one DX and now D U is equal to just the X, and we is still e to the X minus one DX. So now putting that in, we're going to get so we can actually, um, evaluate from 0 to 1 here. So when we put in one, this is one times either the zero, which is just one. And then if you put in zero, that's just zero. So this this part here is equal to one, and this is minus two times and then we'll put this in bracket. So now integration by parts tells us we need new times V. So that's X B to the X minus one from 01 minus the integral of VD. You. So that's e to the X minus one DX. Okay. And now we can evaluate that this is one minus two times and the same thing with him violate this. This is one times either. The zero, which again is just one and then minus. And the integral of E to the X minus one is just e to the X minus one. So this is going to be e to the X minus one evaluated from 0 to 1. So this becomes one minus two times, and this is one minus that we put in one. This is going to give us either the zero. So which is one? And if we put in zero, that's going to give us each a negative one, which is one over eat. Okay, so now if you put this into your calculator, you should get this zero point. If we're up to three decimal, there are 26 4. Check your point. Yes. You are applying to six fortune. Yeah. So now the last thing to do is put that number into our formula to find the Gini Index. So we put this in there. We're going to get this here. So you should end up with G is equal to 0.5 minus zero point to explore all over 0.5. And that ends up being 0.4715 Okay, and that would be our final answer.

So if we want to find what Ecstasy needs to be to give us a genie index of 0.23 I went ahead and first just run out. What the equation was that you can just find this in the book. Um and then I said that he would appoint to three and then I made that substitution of f of X is equal to X to the sea. Now the first thing I'm going to do is actually divide each side by two, just so we get that number by itself. So if we do point to three divided by two, that would give us 0.115 is equal to the integral from 0 to 1 of X minus six to C D X. Now, if we just go ahead and integrate this and then evaluate, that should go ahead and give us, um, something that we can hopefully solve for C. So first we use power rule. For both of these, who would be X squared over two minus. So this would be X to the C plus one oversee plus one, and we evaluate from 0 to 1. So if we go ahead and plug it. One that gives us one half minus, uh would be one to the C plus one, which would actually leave us with just one over C plus one and then minus 12 to plus and zero. That gives us zero. So now this is going to be able to one point 115 and so we can go ahead and subtract over 0.5. So that would be negative. 0.385 is equal to negative one over C plus one. So we just multiply each side by negative one. And then I'm going to reciprocate each side so we would do one divided by, um, 0.385 which would give us something around 200 over 77. And then over here, if I reciprocate this side, that is going to be C plus one, right? And then I can go ahead and subtract one over, which would give 123 over 77 as you could see. But they said that they wanted us to approximate this to two decimal points, so it would be about 1.597 But if I round that to two decimal places. It would just give us 1.6. So, I mean, over here is technically the exact answer. Um, and then this is our approximate answer. So, I mean, if you want to exactly right that or the approximation to two decimal points that works as well.

If we want to try to find what gives us the Gini Index that 0.29 given our Lauren's curve being this ecstasy here, um, I first just went ahead and wrote out the equation that they give us in the book. And now let's actually first divide this by 2.29 divided by two is going to be 0.145 Now we have the integral from 0 to 1 of X minus X two c d X. Now we can integrate this using powerful, which is going to give us so X squared over two minus X to the C plus one over C plus one, and then we evaluate from 0 to 1. And now, if we plug in one now, just give us one half minus. Uh, here it would be one to the C plus one, which is just gonna be one and then just be overseas. Plus one. Uh, and if we were to plug in zero, that just gives us zero. So this is equal to 0.145 so we can go ahead and subtract one half. We're just going to give us negative 0.355 which would be equal to negative one over C plus one. We can multiply each side by a negative, reciprocate each side so it would be one over 0.355 on the left side, which gives, uh, 200 over 71 and then over here on the right side. If we reciprocate that, that just gives a C plus one. So now we can go ahead and subtract one from each side. That would be 1 20 not 79 over 71 is good to see. So that's the exact answer or says they want us to round to two decimal places. This would be approximately 1.81 so six, But then we round to two decimal places. That would be 1.82 So this here is technically the exact answer. But since they wanted us to round to two decimal points, I just want to head in, rounded it

So if we want to determine what would give us a genie index of 0.65 when our Lorenz curve is this X to the C term, the first thing I would do is just go ahead and divide each side by two just to get rid of that. So this would give us 0.3 to 5 to the integral from 0 to 1 of X minus ecstasy DX. Now, we can just come over here and integrate this and then plug in 011 and hope we get something that we can actually solve for C. So integrating ex, we'd use power rule and then next to the sea. Same thing power rules. So we add one to the power and then divide by the new power violate from 0 to 1. If we plug in one, that would just be one half minus. Will one to the C plus one is just going to be one and then see, plus one, um, and the number and then if we plug in, zero would get zero minus zero, which is just zero. So this is going to be equal to 3.25 So first we subtracted, tied by 0.5, which would give negative 0.175 is even negative one over C plus one. We multiply each side by a negative, and now we're going to reciprocate each side. It will be one over 10.175 on the left side, which would give 40/7. And then on the right side, that would be just C plus one. Then we can go ahead and subtract one from each side, which is going to give us 33/7 is C. So that's going to be the exact answer. But they told us to approximate this to to desperate places, so that would be 4.71 after rounding. So technically, these are both the correct answer. If you want the exact it's 33/7 or the round it is 4.71


Similar Solved Questions

4 answers
Try again13PreviousNextYour answer is incorrect:point)Consider the graph given above: Give an Euler circuit through the graph by listing the vertices in the order visited. LNOMKLAnswersAnswerScoreL,N,O,M,K,L0 / 1Incorrect edge included0 / 1
Try again 13 Previous Next Your answer is incorrect: point) Consider the graph given above: Give an Euler circuit through the graph by listing the vertices in the order visited. LNOMKL Answers Answer Score L,N,O,M,K,L 0 / 1 Incorrect edge included 0 / 1...
5 answers
NuvAxyu czon tmu Ph Remnal scd M St Aux ntly ST dJwhat is the difference between density and specific gravity?
Nuv Axyu czon tmu Ph Remnal scd M St Aux ntly ST dJwhat is the difference between density and specific gravity?...
5 answers
Complete the following table:Compound CyclohexeneMWmmodensityBromine0.205EtherXXXXXXXXXXXXXXXDraw the products of bromine addition cyclohexene making sure clearly shov stereochemistry. Indicate RIS each stereocenterCalculate the theoretical yield of the product for this reaction.Cquiv
Complete the following table: Compound Cyclohexene MW mmo density Bromine 0.205 Ether XXX XXX XXX XXX XXX Draw the products of bromine addition cyclohexene making sure clearly shov stereochemistry. Indicate RIS each stereocenter Calculate the theoretical yield of the product for this reaction. Cquiv...
5 answers
Exercise 6.66: Problems Chemical Formulas as Conversion FactorsCalculate the number of grams of sodium in 3.8 g of each of the following sodium-containing tood additivesPart DNazCoHOz (sodium hydrogen citrale) Express your answer using two significant figures_
Exercise 6.66: Problems Chemical Formulas as Conversion Factors Calculate the number of grams of sodium in 3.8 g of each of the following sodium-containing tood additives Part D NazCoHOz (sodium hydrogen citrale) Express your answer using two significant figures_...
1 answers
JMI| G4ual J %MLjO PIo 1cteWa aswio; meclsrsizci fos the follwig Luncicu , UM YJJEAMO ) 20n1zjun JJ 3/01T)mt2714241n7 0/ "YJJuti)A707 51
JMI| G4ual J %MLjO PIo 1cte Wa aswio; meclsrsizci fos the follwig Luncicu , UM YJJEAMO ) 20n1zjun JJ 3/01T)mt2714241n7 0/ "YJJuti) A707 51...
5 answers
We consider the sequence{an}oo n=l {10/3,40/9,100/27,340/81,940/243,2852/729,...} a) Determine the general formula for the terms an of the sequence_anb) Find the limit of the sequence.lim an n-00Number
We consider the sequence {an}oo n=l {10/3,40/9,100/27,340/81,940/243,2852/729,...} a) Determine the general formula for the terms an of the sequence_ an b) Find the limit of the sequence. lim an n-00 Number...
5 answers
AssuMino Stanoard conditions, and considering table of standard reduction potentials for half-reactions, given Your text, rank the following species according agents_ For example, the most powerful reducing agent would be given rank und the leasttheir relative strengthreducing
AssuMino Stanoard conditions, and considering table of standard reduction potentials for half-reactions, given Your text, rank the following species according agents_ For example, the most powerful reducing agent would be given rank und the least their relative strength reducing...
5 answers
Find the indefinite integra as indicated_K6+4+6)(x" + 4x2 +6) dx=
Find the indefinite integra as indicated_ K6+4+6) (x" + 4x2 +6) dx=...
1 answers
Sketch the region comprising points whose polar coordinates satisfy the given conditions. $1 \leq r \leq 3, \quad-\frac{2}{6} \leq \theta \leq \frac{\pi}{6}$
Sketch the region comprising points whose polar coordinates satisfy the given conditions. $1 \leq r \leq 3, \quad-\frac{2}{6} \leq \theta \leq \frac{\pi}{6}$...
5 answers
26r' 7x+37 (2x-1)(4x'+9) "d)f cos" (Tx)dx
26r' 7x+37 (2x-1)(4x'+9) " d) f cos" (Tx)dx...
1 answers
General logarithmic and exponential derivatives Compute the following derivatives. Use logarithmic differentiation where appropriate. $$\frac{d}{d x}\left(x^{\left(x^{10}\right)}\right)$$
General logarithmic and exponential derivatives Compute the following derivatives. Use logarithmic differentiation where appropriate. $$\frac{d}{d x}\left(x^{\left(x^{10}\right)}\right)$$...
1 answers
Find a. $(f \circ g)(x)$ b. $(g \circ f)(x)$ c. $(f \circ g)(2)$ d. $(g \circ f)(2)$ $$f(x)=5 x-2, g(x)=-x^{2}+4 x-1$$
Find a. $(f \circ g)(x)$ b. $(g \circ f)(x)$ c. $(f \circ g)(2)$ d. $(g \circ f)(2)$ $$f(x)=5 x-2, g(x)=-x^{2}+4 x-1$$...
5 answers
Graph each ellipse.$$ rac{(x-2)^{2}}{16}+ rac{(y-1)^{2}}{9}=1$$
Graph each ellipse. $$ \frac{(x-2)^{2}}{16}+\frac{(y-1)^{2}}{9}=1 $$...
4 answers
10 pointsLct R' R? be linear transformation yiven bT() = ( ? _' )v Evaluate the following(i) T(ii) Nullity of TNV(T) (iii) Rang" of T R(T)Add file
10 points Lct R' R? be linear transformation yiven bT() = ( ? _' )v Evaluate the following (i) T (ii) Nullity of TNV(T) (iii) Rang" of T R(T) Add file...
5 answers
Total revenue function of a good is given by:𝑇𝑅 = −2𝑄2 + 20𝑄 and total cost function is 𝑇𝐶 =𝑄3 − 8𝑄2 + 20𝑄 + 5. Calculate the maximum profit and thevalue of Q at which it is achieved.
Total revenue function of a good is given by: 𝑇𝑅 = −2𝑄2 + 20𝑄 and total cost function is 𝑇𝐶 = 𝑄3 − 8𝑄2 + 20𝑄 + 5. Calculate the maximum profit and the value of Q at which it is achieved....
5 answers
Two values denoted by A and B have not been entered into the following divided difference table: f(xi)0.880.52.56-0.741.620.754793 0.392189 22781 0.4756211.751.5 1.136090.76Determine the two missing entries in the divided difference table: Enter your answers correct to four decimal placesA =
Two values denoted by A and B have not been entered into the following divided difference table: f(xi) 0.88 0.52.56 -0.74 1.62 0.754793 0.392189 22781 0.475621 1.75 1.5 1.13609 0.76 Determine the two missing entries in the divided difference table: Enter your answers correct to four decimal places A...
5 answers
QI: Subjects in psychological study were timed while completing certain task: Draw continuous frequency distribution along with the relative and cumulative frequencies. I3 Points] 7.6. 84_ 9.2, 6.8, 5.9, 6.2, 6.1, 5.8. 73, 4.28 8.1_ 8.8, 7.4, 7.7, 8.2, 3.2, 85, 10.25, 15.20, 5.7
QI: Subjects in psychological study were timed while completing certain task: Draw continuous frequency distribution along with the relative and cumulative frequencies. I3 Points] 7.6. 84_ 9.2, 6.8, 5.9, 6.2, 6.1, 5.8. 73, 4.28 8.1_ 8.8, 7.4, 7.7, 8.2, 3.2, 85, 10.25, 15.20, 5.7...
5 answers
Aluminium PlateRing Dedektorproton beam
Aluminium Plate Ring Dedektor proton beam...
5 answers
In Problem 3-4, find all singular points of the given equation and determine whether each one is regular Or irregular.3. [2 pts] zy" + (2 - x)y' + xy = 0. 4. [2 pts] ~(1 - 22)3y" + x(1 - 22)2y + 5(1 + x)y = 0.
In Problem 3-4, find all singular points of the given equation and determine whether each one is regular Or irregular. 3. [2 pts] zy" + (2 - x)y' + xy = 0. 4. [2 pts] ~(1 - 22)3y" + x(1 - 22)2y + 5(1 + x)y = 0....

-- 0.021079--