Question
In: Statistics and Probability
Depict the income data on a Lorenz curve for country A Depict the income data on...
Depict the income data on a Lorenz curve for country A
Depict the income data on a Lorenz curve for country B
Find the Gini-coefficient index for country A
Find the Gini-Coefficient index for country B
Interpret the index value
| INCOME | POPULATION COUNTRY A | POPULATION COUNTRY B |
| 10000 | 1000 | 4000 |
| 20000 | 5000 | 5000 |
| 30000 | 4000 | 6000 |
| 40000 | 12000 | 6500 |
| 50000 | 10000 | 5200 |
| 60000 | 6000 | 4600 |
| 70000 | 4500 | 5200 |
| 80000 | 3500 | 6500 |
| 90000 | 2500 | 3400 |
| 100000 | 1500 | 3600 |
Solutions
Expert Solution
COUNTRY A
| INCOME | POPULATION COUNTRY A | PER CAPITAL INCOME | ACENDING ORDER PER CAPITAL INCOME | POPULATION AS A PERCAPITAL INCOME (X) | INCOME AS A POPULATION (Y) | % OF X | % OF Y | CUMULATIVE % OF X | CUMULATIE % OF Y | X*(Y+I) | Y*(X+1) | |
|
10000 |
1000 | 10 | 3.33333 | 12000 | 40000 | 16.66666667 | 7.27273 | 16.66666667 | 7.27272727 | 181.818182 | 171.717172 | |
| 20000 | 5000 | 4 | 4 | 5000 | 20000 | 6.944444444 | 3.63636 | 23.6111111 | 10.9090909 | 472.222222 | 409.090909 | |
| 30000 | 4000 | 7.5 | 5 | 10000 | 50000 | 13.88888889 | 9.09091 | 37.5 | 20 | 954.545455 | 861.111111 | |
| 40000 | 12000 | 3.33333 | 7.5 | 4000 | 30000 | 5.555555556 | 5.45455 | 43.0555556 | 25.4545455 | 1174.24242 | 1131.31313 | |
| 50000 | 10000 | 5 | 10 | 1000 | 10000 | 1.388888889 | 1.81818 | 44.4444444 | 27.2727273 | 1696.9697 | 1439.39394 | |
| 60000 | 6000 | 10 | 10 | 6000 | 60000 |
|
10.9091 | 52.7777778 | 38.1818182 | 2686.86869 | 2386.36364 | |
| 70000 | 4500 | 15.5556 | 15.5556 | 7000 | 70000 | 9.722222222 | 12.7273 | 62.5 | 50.9090909 | 4090.90909 | 3747.47475 | |
| 80000 | 3500 | 22.8571 | 22.8571 | 8000 | 80000 | 11.11111111 | 14.5455 | 73.6111111 | 65.4545455 | 6022.72727 | 5636.36364 | |
| 90000 | 2500 | 36 | 36 | 9000 | 90000 | 12.5 | 16.3636 | 86.1111111 | 81.8181818 | 8611.11111 | 8181.81818 | |
| 100000 | 1500 | 66.6667 | 66.6667 | 10000 |
|
13.88888889 | 18.1818 | 100 | 100 | |||
| SUM | 72000 | 550000 | 100 | 100 | 25891.4141 | 23964.6465 |
GINI COEFFICIENT =
| [SUM OF X*(Y+I) - SUM OF Y*(X+1)]/10000 |
= 0.1926
COUNTRY B
| INCOME | POPULATION COUNTRY B | PER CAPITAL INCOME | ACENDING ORDER PER CAPITAL INCOME | POPULATION AS A PERCAPITAL INCOME (X) | INCOME AS A POPULATION (Y) | % OF X | % OF Y | CUMULATIVE % OF X | CUMULATIE % OF Y | X*(Y+I) | Y*(X+1) | |
|
10000 |
2.5 | 4000 | 10000 | 8 | 1.81818 | 8 | 1.81818182 | 43.63636364 | 32.72727 | |||
| 4 | 5000 | 20000 | 10 | 3.63636 | 18 | 5.45454545 | 196.3636364 | 163.6364 | ||||
| 5 | 6000 | 30000 | 12 | 5.45455 | 30 | 10.9090909 | 545.4545455 | 469.0909 | ||||
| 6.15385 | 6500 | 40000 | 13 | 7.27273 | 43 | 18.1818182 | 1172.727273 | 970.9091 | ||||
| 9.61538 | 5200 | 50000 | 10.4 | 9.09091 | 53.4 | 27.2727273 | 2038.909091 | 1707.273 | ||||
| 13.0435 | 4600 | 60000 | 9.2 | 10.9091 | 62.6 | 38.1818182 | 3186.909091 | 2787.273 | ||||
| 70000 | 5200 | 13.4615 | 13.4615 | 5200 | 70000 | 10.4 | 12.7273 | 73 | 50.9090909 | 4778.181818 | 4378.182 | |
| 80000 | 6500 | 12.3077 | 12.3077 | 6500 | 80000 | 13 | 14.5455 | 86 | 65.4545455 | 7036.363636 | 6074.182 | |
| 90000 | 3400 | 26.4706 | 26.4706 | 3400 | 90000 | 6.8 | 16.3636 | 92.8 | 81.8181818 | 9280 | 8181.818 | |
| 100000 | 3600 | 27.7778 | 27.7778 | 3600 | 100000 | 7.2 | 18.1818 | 100 | 100 | |||
| SUM | 50000 | 50000 | 550000 | 100 | 100 | 28278.54545 | 24765.09 |
GINI COEEFICIENT =
| [SUM OF X*(Y+I) - SUM OF Y*(X+1)]/1000 |
= 0.3514
INTERPRETATION: In the country, a Gini coefficient is 0.1926 and country b Gini coefficient is 0.3514 so, country b is more unequal distribution of income than country a.
orchestra answered 1 year agoRelated Solutions
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