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To simplify the algebra, assume that both the grey and the yellow lines are equal to 100 in 1980 and that the grey line is equal to 300 and the yellow line to 200 in 2018. (This is roughly in line with what the graph shows.) Then use this stylized version of the graph to answer the questions below. Let at denote the share of total income going to the bottom 90 percent in year t, that is, at = Y,90 t Yt (a) Show that by definition 0 < at ≤ 0.9. (b) Suppose in year t there is no income inequality, find the associated value of at. (c) Find Y2018/Y1980 and provide a verbal interpretation of your answer. (d) Find Y2018/Y1980 and provide an interpretation. (e) Find Y2018/Y1980 in terms of Q1980. 4 (f) Assume that a1980 = 2/3, which means that the total income of the bottom 90 percent of the population amounted to 67 percent of total income. Then compute Y2018/Y1980 and interpret your finding. (g) Find a2018 in terms of a1980- 1 (h) Let 20 - Y90/90 denote real per capita income of the bottom 90 percent in year t, 10 = ¹0/10 denote real per capita income of the top 10 percent in year t and xt = Yt/100 denote real per capita income in year t. Continue to assume that 1980 2/3. Find x/x20 for t = 1980 and t=2018. Discuss how much more unequal the distribution of income has become over this time period in the United States. =

To simplify the algebra, assume that both the grey and the yellow lines are equal to 100 in 1980 and that the grey line is equal to 300 and the yellow line to 200 in 2018. (This is roughly in line with what the graph shows.) Then use this stylized version of the graph to answer the questions below. Let at denote the share of total income going to the bottom 90 percent in year t, that is, at = Y,90 t Yt (a) Show that by definition 0 < at ≤ 0.9. (b) Suppose in year t there is no income inequality, find the associated value of at. (c) Find Y2018/Y1980 and provide a verbal interpretation of your answer. (d) Find Y2018/Y1980 and provide an interpretation. (e) Find Y2018/Y1980 in terms of Q1980. 4 (f) Assume that a1980 = 2/3, which means that the total income of the bottom 90 percent of the population amounted to 67 percent of total income. Then compute Y2018/Y1980 and interpret your finding. (g) Find a2018 in terms of a1980- 1 (h) Let 20 - Y90/90 denote real per capita income of the bottom 90 percent in year t, 10 = ¹0/10 denote real per capita income of the top 10 percent in year t and xt = Yt/100 denote real per capita income in year t. Continue to assume that 1980 2/3. Find x/x20 for t = 1980 and t=2018. Discuss how much more unequal the distribution of income has become over this time period in the United States. =

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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2. (Rising Income Inequality in the United States.) The graph below appeared in a NYT article entitled "Why you should not believe those GDP Numbers," by David Leonhardt. We analyzed this graph in class. Before answering this question, make sure to go over that discussion by reading the notes for lecture 1 (Lecturel.pdf) or Chapter 1, Section 1, of SGU. The Trouble with G.D.P. Change in per capita G.D.P and average mcomes for the bottom 90 percent of eamers 300% GOP 200 Bottom 90% In the mid-20th century, G.D P and incomes for most Americans tracked each other closely If anything, mass incomes grew more quickly.. 100 but over the last 40 years incomes have fallen badly behind economid growth. 1947 1960 1970 1980 1990 2000 2010 2018 Adjusted for inflation. Incomes are post-tax and include government benefits By The New York Times | Sources: Federal Reserve and Thomas Piketty Emmanuel Saez and Gabriel Zucman Source: NYTimes, Dec. 16, 2019, Section A, Page 31 of the New York edition. Assume the economy consists of 100 individuals in 1947 and population is constant over time. Individual i has income y in yeart for i 1,..., 100 and t generality, that y; < y*. Let Y denote total real GDP in year t, which is given by 1947, 1948, .., 2018. Suppose, without loss of 100 Y = Let Y90 denote the total income going to the bottom 90 percent of the population, 90 and Y0 the total income going to the top 10 percent of the population, 100 91 We then have Y =Y," + Y°,
Transcribed Image Text:2. (Rising Income Inequality in the United States.) The graph below appeared in a NYT article entitled "Why you should not believe those GDP Numbers," by David Leonhardt. We analyzed this graph in class. Before answering this question, make sure to go over that discussion by reading the notes for lecture 1 (Lecturel.pdf) or Chapter 1, Section 1, of SGU. The Trouble with G.D.P. Change in per capita G.D.P and average mcomes for the bottom 90 percent of eamers 300% GOP 200 Bottom 90% In the mid-20th century, G.D P and incomes for most Americans tracked each other closely If anything, mass incomes grew more quickly.. 100 but over the last 40 years incomes have fallen badly behind economid growth. 1947 1960 1970 1980 1990 2000 2010 2018 Adjusted for inflation. Incomes are post-tax and include government benefits By The New York Times | Sources: Federal Reserve and Thomas Piketty Emmanuel Saez and Gabriel Zucman Source: NYTimes, Dec. 16, 2019, Section A, Page 31 of the New York edition. Assume the economy consists of 100 individuals in 1947 and population is constant over time. Individual i has income y in yeart for i 1,..., 100 and t generality, that y; < y*. Let Y denote total real GDP in year t, which is given by 1947, 1948, .., 2018. Suppose, without loss of 100 Y = Let Y90 denote the total income going to the bottom 90 percent of the population, 90 and Y0 the total income going to the top 10 percent of the population, 100 91 We then have Y =Y," + Y°,
To simplify the algebra, assume that both the grey and the yellow lines are equal to 100 in 1980 and that the line is equal to 300 and the yellow line to 200 in 2018. (This is roughly in lie with what grey the graph shows.) Then use this stylized version of the graph to answer the questions below. Let a, denote the share of total income going to the bottom 90 percent in year t, that is, Y,90 at Y (a) Show that by definition 0 < a < 0.9. (b) Suppose in year t there is no income inequality, find the associated value of at. (c) Find Y8/Y0 and provide a verbal interpretation of your answer. 2018/ 1980 (d) Find Y2018/Y1980 and provide an interpretation. (e) Find Ys/Y80 in terms of a1980- 2018, (f) Assume that a1980 = 2/3, which means that the total income of the bottom 90 percent of the population amounted to 67 percent of total income. Then compute Y018/Y80 and interpret 2018/ 1980 your finding. (g) Find a2018 in terms of a1980- (h) Let x0 = Y90/90 denote real per capita income of the bottom 90 percent in year t, z Y"/10 denote real per capita income of the top 10 percent in year t and r, Y/100 denote real per capita income in year t. Continue to assume that a1980 = 2/3. Find r/r for t= 90 1980 and t= 2018. Discuss how much more unequal the distribution of income has become over this time %3D period in the United States. MacBook Air
Transcribed Image Text:To simplify the algebra, assume that both the grey and the yellow lines are equal to 100 in 1980 and that the line is equal to 300 and the yellow line to 200 in 2018. (This is roughly in lie with what grey the graph shows.) Then use this stylized version of the graph to answer the questions below. Let a, denote the share of total income going to the bottom 90 percent in year t, that is, Y,90 at Y (a) Show that by definition 0 < a < 0.9. (b) Suppose in year t there is no income inequality, find the associated value of at. (c) Find Y8/Y0 and provide a verbal interpretation of your answer. 2018/ 1980 (d) Find Y2018/Y1980 and provide an interpretation. (e) Find Ys/Y80 in terms of a1980- 2018, (f) Assume that a1980 = 2/3, which means that the total income of the bottom 90 percent of the population amounted to 67 percent of total income. Then compute Y018/Y80 and interpret 2018/ 1980 your finding. (g) Find a2018 in terms of a1980- (h) Let x0 = Y90/90 denote real per capita income of the bottom 90 percent in year t, z Y"/10 denote real per capita income of the top 10 percent in year t and r, Y/100 denote real per capita income in year t. Continue to assume that a1980 = 2/3. Find r/r for t= 90 1980 and t= 2018. Discuss how much more unequal the distribution of income has become over this time %3D period in the United States. MacBook Air
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