1. Download LorenzData.xlsx. It contains data from 336 micro-borrowers in Thailand, on this year’s “Income” and next year’s “Expected Income”. Graph the Lorenz curve for both income and expected income, and turn in the graph. According to the Lorenz criterion, is there more inequality in income or expected income? (Ignore the small regions where the curves cross.) Why might this be? [HINT: Consider the income data. First, make sure to sort this column of data. Next, next to it create a column containing the cumulative sum of income – i.e. that has the sum of the first income in the first row, sum of the first two incomes in the second row, the sum of the first three incomes in the third row, etc. For cumulative sum, you can use something like a “=sum($A$2:A2)” command and then copy and paste to the next 335 rows, e.g., where the $signs make sure the first cell in the summation does not change with the copy and paste. Next, next to that create a cumulative fraction of income column, which is the cumulative sum divided by the total sum of income. (You can use the same $X$n command to fix the total sum of income and use cut and paste.) Put an extra 0 at the top of this column to make sure it will start at 0. Finally, make a column that contains the fraction of borrowers included up to that point. You can do this by starting at 0 (on the same row that has the 0 in the cumulative fraction of income column) and adding 1/336 every row. Now, repeat the process for expected income. Then, graph the Lorenz curves. You can do this (in Office 2007) by, for example, opening a second sheet and inserting a basic line chart (Insert, Line Chart, First Category). Then choose “Select Data”. You can then “Add” the columns on the previous sheet that you want to graph in the “Series” category (namely, income, expected income, and helpful also to graph fraction of the population, which gives a 45-degree line) and the column you would like to graph against (which is the fraction of the population) in the “Horizontal Axis” category. You can edit the graph by choosing the first option under “Chart Layouts” and clicking on the various text items and adjusting the labeling.] 2. a. Country A has an income distribution of (3,5,6,10) and country B has an income distribution of (1,2,4,5). Graph both Lorenz curves, labeling the key points, and say which is more unequal using the Lorenz criterion. b. Repeat part a. when B has a distribution of (2,4,5). 3. Graph and label the Lorenz curve for a country in which 1/4 of the population earns 3/4 of the income, 1/2 of the population earns 1/10 of the income, and 1/4 of the population earns 3/20 of the income. Assume that every individual within each class has the same income. 4. In Mexico in 1950, the richest 5% earned 40% of the income and the poorest 40% earned 14.3% of the income. In 1957, the richest 5% earned 37% of the income and the poorest 40% earned 11.3% of the income. In 1963, the richest 5% earned 28.8% of the income and the poorest 40% earned 10.1% of the income. Has inequality gone up or down between 1950 and 1957, between 1957 and 1963, and between 1950 and 1963, according to the Lorenz criterion? Justify answer graphically. 5. Calculate the gini coefficient and the coefficient of variation for each of the following distributions. [Hint: It will save significant time if you make use of the inequality principles (population, relative income, etc.) to simplify where possible.] a. Two people earn 3, one earns 6, and three earn 15. b. 2 million people earn 3, 1 million earn 6, and 3 million earn 15. c. 2 million people earn 3,000, 1 million earn 6,000, and 3 million earn 15,000. d. 250 million people earn 600, 1 billion people earn 300. e. The richest 20% earn 20% of the income. [Hint: it may help to draw the Lorenz curve.] 6. Consider an economy of 5 people and 2 sectors, modern and traditional. The annual income for a worker in the modern sector is $20k and in the traditional sector is $10k. Suppose that each year, the economy grows by moving one person from the traditional to the modern sector. That is, in year one the distribution is ($10k, $10k, $10k, $10k, $10k), in year two it is ($10k, $10k, $10k, $10k, $20k), in year three it is ($10k, $10k, $10k, $20k, $20k), and so on, until in year six it reaches ($20k, $20k, $20k, $20k, $20k). a. Plot the gini coefficient on the vertical axis against average income on the horizontal axis for this economy. You should calculate a gini coefficient for each average income level $10k, $12k, $14k, ... $20k. Based on the gini, is inequality varying with growth as predicted by the Kuznets hypothesis? How do you see this? b. Graph the Lorenz curves corresponding to each income level. According to the Lorenz criterion, what has happened to inequality as growth occurred? Say as much as possible that can be said unambiguously. 7a. Assume that skilled wages are twice that of unskilled wages, and that half of the population fits into each category, skilled and unskilled. Graph the Lorenz curve and calculate the gini coefficient. b. Assume that skilled wages become 3x that of unskilled wages, as demand for skilled workers increases due to new technology. The population breakdown into skilled and unskilled remains the same. Graph the new Lorenz curve and calculate the new gini coefficient. c. Assume now that there is a supply response to the higher skill premium, in that the fraction of skilled workers goes up from one half to two thirds of the population. Also, given the increased supply of skilled workers and decreased supply of unskilled workers, the ratio of skilled wages to unskilled wages drops to 2.5. Graph the new Lorenz curve and calculate the new gini coefficient. d. What has happened to inequality according to the Lorenz criterion? According to the gini coefficient? Are all comparisons unambiguous? 8. Imagine a country divided into four equally sized classes, poor, lower middle, upper middle, and upper. Within each class, incomes are the same. Imagine incomes of the poor class increase by 20%, of the lower middle class increase by 30%, of the upper middle class increase by 27%, and of the upper class increase by 23%. Assume the average increase in income is 24.5%. Further, assume the class orderings are unchanged, and that population size has not change. Has inequality increased, decreased, or changed in an unrestricted way, according to the Lorenz criterion? Justify your answer fully. [Hint: beware of solving this question using an example distribution. For example, if you use (100,200,300,400) and then apply the changes, you realize the mean went up by 25.3%, not 24.5% as stated in the question. This exercise can be solved just by using the definition of the Lorenz curve; it helps to focus on the bottom and top income segments.] Income 11450 276840 88060 82600 62780 335070 124900 43450 28050 77000 172790 60661 32435 49900 33600 13000 63400 7200 34100 24700 124363 20785 49070 29990 23900 49400 18399.5 519430 26200 38000 22700 58800 46350 30660 45100 137700 10000 6000 35800 37000 40300 194170 122824.5 33990 76900 15660 9465 31500 12050 71442 60390 Expected_Income 10000 180000 70000 60000 50000 225000 100000 30000 23510 60000 100000 50000 30000 40000 30000 10000 50000 6000 30000 20000 100000 19000 40000 25050 20000 40000 15000 300000 20000 30000 20000 50000 40000 26000 37000 100000 8000 5000 30000 30000 30000 120000 90000 30000 60000 10000 8000 27520 10000 55800 50000 55628 49000 108900 87775 51550 108500 198500 49200 5300 13160 139610 130660 195450 48595 29427 313725 2500 15000 10800 27520 85200 23510 320100 16960 17960 19650 34000 23800 16000 43400 70812 18500 23800 21500 20250 420250 48790 91737 6680 72040 22608 60500 18800 71600 186607.5 99133 40980 28415 109750 103328 53800 21680 45000 40000 80000 70000 40000 80000 120000 40000 5000 10000 100000 100000 120000 40000 25000 200000 3000 10000 8000 23000 66133 20000 220000 15000 15000 16000 30000 20000 12000 30000 55000 15000 20000 20000 18000 300000 40000 70000 6000 59200 20000 50000 16000 56000 120000 71442 30000 25000 80000 80000 43000 20000 16900 21700 124215 7600 545800 14965 21990 77700 11450 79732 31600 136500 81480 123200 16590 660480 11050 42740 17950 33925 10800 71800 17800 27010 160900 81300 54630 163865 29650 54480 39720 3625 59650 186025 99726 8400 57300 27850 2424.5 127652 33350 15000 199400 63329.5 48120 43500 94467.5 287990 121000 536600 71320 16100 14965 20000 90000 6165 400000 10000 20000 60000 10000 60000 27600 100000 60000 90000 14600 500000 10000 30000 15000 30000 8400 58000 15000 20000 100000 60000 44600 100000 25000 44000 30000 4000 50000 120000 72000 8000 50000 23000 2000 100000 30000 10000 130000 50000 40000 31500 70000 200000 90000 350000 55000 12000 10000 5500 18700 67348 31800 124300 35945 204200 51000 6600 26900 11000 63505 114125 205150 38004 254060 56000 49000 179810 52715 68450 55822 17700 15200 50600 60855 31670 196310 77000 58752.5 53350 52400 37800 30440 22700 84500 15000 5000 16200 84480 83180 35830 59006 70439.5 178700 109922.5 9100 9000 30500 45990 21800 8000 5000 15840 52000 29900 95000 30000 150000 40000 5360 20000 9000 50000 80000 150000 30000 160000 47000 40000 120000 42000 54925 45000 15000 10000 40000 50000 28000 120000 60000 50000 42332 40000 30000 25900 20000 65000 10000 5000 12000 62000 60000 30000 50000 55000 110000 80000 8000 8000 26000 39000 20000 32100 661540 569702.5 28540 22115 27200 138600 45580 10462.5 341700 20210 1200 64200 87000 31000 49925 42700 58000 33360 77735 12820 15840 20600 156820 8000 177050 61460 212400 18650 44000 51000 229858 30000 50540 25050 78200 50290 174316 88185 29900 19900 60000 26900 44830 20500 113025 11670 15350 28700 55735 64596 20400 30000 900000 400000 25000 20000 20500 100000 38000 8000 250000 18000 1500 50000 70000 26860 40000 30000 50000 30000 60000 10000 10000 18700 100000 7640 110000 50000 150000 15000 34000 40000 150000 25800 40000 20000 60000 40000 104000 70000 25000 17000 50000 20000 35000 18500 80000 10000 10000 25000 45000 50000 18500 32600 75617 64650 15000 33500 79900 237645 1750 12906 68500 171300 343100 40200 51600 21200 10640 27200 70512 13250 5400 44600 157700 100950 80500 34230 56700 51510 10360 95060 133000 11000 37000 20000 223160 367630 4300 18500 282450 179500 36350 28100 115617 20100 13000 282893 183849.5 82040 104060 85807 47515 54925 26300 30000 60000 50000 10000 30000 60000 156820 2000 10000 55000 100000 282000 30000 40000 20000 8000 20100 55000 10000 5000 35000 100000 76600 60000 30000 48000 40000 8000 70000 100000 8500 30000 17500 150000 300000 4000 15000 200000 120000 30000 24000 80000 18000 10000 200000 120000 60000 80000 69000 40000 45000 20000 41160 87800 47450 18140 116020 3291 35150 26860 17500 23640 66180 11937.5 120628.5 59200 71640 18700 27145 20950 120275 16500 64900 115000 281435 17500 23480 30000 70000 40000 15000 84000 3000 30000 20000 15000 20000 50000 10000 86885 50000 57000 15000 20000 19950 85000 14000 50000 80000 182500 15000 20000