# Chapter 15. Question 15

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Question 15
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You must read each slide, and complete any questions on the slide, in sequence.

Use the two different distributions of income in the table below to answer the questions that follow.

 Quintile A B Poorest 10.5 2.5 Second 13.2 6.8 Middle 21.6 13.9 Fourth 26.4 24.2 Richest 28.3 52.6
A. Answer the following questions about how to graph these Lorenz Curves:

### Question

A1. On the graph for the Lorenz Curve, the vertical axis is 1Zm5cQZNmHrAKxqE/BEjpt5ApAqGpCfrGUlNOdOJ4c6jYmq3anRTlZ/CFU8mhfUR0d2FKQ== and the values are KoA80zmQ4C0JTnosl9Xa3n5XXJ8ZGiQzaGTWoFU1BQU=, and the horizontal axis is the s/Wrv8xUDR3jRLQJbR73SK0iwfsw4Xfvj1zDjnXbvFYhvuHdEm4H5JH+w3sTN0Q9V0ZG+g== and the values are KoA80zmQ4C0JTnosl9Xa3n5XXJ8ZGiQzaGTWoFU1BQU=.
Incorrect! The vertical axis represents percentage of income, and the horizontal axis represents the percentage of households. Both are cumulative, and include the current quintile as well as lower quintiles.
Correct! The vertical axis represents percentage of income, and the horizontal axis represents the percentage of households. Both are cumulative, and include the current quintile as well as lower quintiles.

### Question

A2. Fill in the table for cumulative income distribution:
 Quintile A Cumulative B Cumulative Poorest 10.5 4dtNmqXeVHM= 2.5 +jEDcWw2tUQ= Second 13.2 yc6CmW1ealA= 6.8 7dANGMEJsXo= Middle 21.6 8rUim+dg3UM= 13.9 rT0BGNTKi8g= Fourth 26.4 t7r464veRcs= 24.2 5/FpzP4PNfc= Richest 28.3 b0g0iQ1whKk= 52.6 b0g0iQ1whKk=
Incorrect! For the lowest quintile, the cumulative value is the value for that quintile. For every other quintile, the cumulative value is calculated by adding the previous cumulative value and the quintile’s non-cumulative value. For example, Country A’s second quintile cumulative value includes the first quintile as well as the second quintile’s (non-cumulative) value. 10.5 + 13.2 = 23.7. This is done for all cells. Since there is no previous value to add for the poorest quintile, the cumulative and non-cumulative values are the same.
Correct! For the lowest quintile, the cumulative value is the value for that quintile. For every other quintile, the cumulative value is calculated by adding the previous cumulative value and the quintile’s non-cumulative value. For example, Country A’s second quintile cumulative value includes the first quintile as well as the second quintile’s (non-cumulative) value. 10.5 + 13.2 = 23.7. This is done for all cells. Since there is no previous value to add for the poorest quintile, the cumulative and non-cumulative values are the same.

### Question

A3. On the graph below, Country A’s Lorenz curve is depicted cjhXe/UDDFpZykaj7nxw8BGveIy36V0LM0hFaghdOQ9NZDhtqh96Og== and Country B’s Lorenz curve is depicted by 0GoepZlPt1t7LncS2KwGR8GDKtNW2SlJDaV/+ewbGiGKHHlOd3JhPw==.
Incorrect! Lines #2 and #3 correspond to Country A and Country B’s cumulative income distributions point by point. For example, A’s first two points, in x-y format, would be (20, 10.5) and (40, 23.7). Line #4 represents an income distribution that is more unequal than either of the provided countries.
Correct! Lines #2 and #3 correspond to Country A and Country B’s cumulative income distributions point by point. For example, A’s first two points, in x-y format, would be (20, 10.5) and (40, 23.7). Line #4 represents an income distribution that is more unequal than either of the provided countries.

### Question

B. Which curve has a more equal distribution? kxeqpWJuMf4=
Incorrect! A’s Lorenz curve is much closer to the equal distribution line than is B’s Lorenz curve. In addition, in Country B each quintile except the richest has a greater share of income in Country A.
Correct! A’s Lorenz curve is much closer to the equal distribution line than is B’s Lorenz curve. In addition, in Country B each quintile except the richest has a greater share of income in Country A.

### Question

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Incorrect! The quintiles for 2014 are, from poorest to richest: 3.1, 8.2, 14.3, 23.2, and 51.2, resulting in cumulative numbers of 3.1, 11.3, 25.6, 48.8, and 100. These cumulative numbers are in between the corresponding numbers for Country A and Country B. Plotting them on an additional Lorenz curve would yield a curve that was between the two curves.
Correct! The quintiles for 2014 are, from poorest to richest: 3.1, 8.2, 14.3, 23.2, and 51.2, resulting in cumulative numbers of 3.1, 11.3, 25.6, 48.8, and 100. These cumulative numbers are in between the corresponding numbers for Country A and Country B. Plotting them on an additional Lorenz curve would yield a curve that was between the two curves.