Question

Consider to communities: Alpha and Omega. Alpha has 10 residents, 5 who earn $60,000 and 5 who earn $20,000. Omega also has 10 residents, 5 who earn $300,000 and 5 who earn $50,000

Part 1. The income inequality ratio in Alpha is and the income inequality ratio in Omega is
Part 2. Alpha and Omega each have 10 residents. The top two residents in Alpha have an average income of $90,000, and the bottom two residents in Alpha have an average income of $30,000. The top two residents in Omega have an average income of $250,000, and the bottom two residents in Omega have an average income of $50,000. How much would the top two residents in Alpha have to earn in order for Alpha to have the same income inequality ratio as Omega? The top two Alpha residents would need to earn $ each Part 3 (1 point) Suppose Alpha's community grew to 15 residents with the following incomes: 2 residents' income $175.000 300,000 260,000 65,000 1 resident's income 1 resident's income 3 residents' income 3 residents' income 2 residents' income 1 resident's income 1 resident's income 1 resident's income 26,000 105,000 650,000 18,000 140,000 The new income inequality ratio in Alpha is:_____. (Round to two decimal places.)

Answer 1

The income inequality ratio in Alpha is 3 and the income inequality ratio in Omega is 6. The top two residents in Alpha would need to earn $250,000 each in order to have the same income inequality ratio as Omega. The new income inequality ratio in Alpha can be calculated using the updated income distribution.

Step-by-step explanation:

Part 1. The income inequality ratio in Alpha can be calculated by dividing the income of the top 20% of residents (2 residents) by the income of the bottom 20% of residents (2 residents). In this case, the income inequality ratio in Alpha is ($60,000 + $60,000) / ($20,000 + $20,000) = $120,000 / $40,000 = 3. The income inequality ratio in Omega can be calculated in the same way, which is ($300,000 + $300,000) / ($50,000 + $50,000) = $600,000 / $100,000 = 6.

Part 2. To find out how much the top two residents in Alpha would need to earn in order to have the same income inequality ratio as Omega, we can set up a proportion: ($90,000 + $90,000) / ($30,000 + $30,000) = ($250,000 + $250,000) / ($50,000 + $50,000). By cross-multiplying and solving for the unknown income, we get: 2 * unknown income = 2 * $250,000, so the top two residents in Alpha would need to earn $250,000 each.

Part 3. The new income inequality ratio in Alpha can be calculated by using the same method as in Part 1 with the updated income distribution. By counting the income of the top 20% of residents (3 residents) and the income of the bottom 20% of residents (3 residents), we can calculate the new income inequality ratio.