Project 2 – Form C2 Created Summer 2017/Modified Spring 2019 Business Calculus Project In this project you are to present all your results in a “business report”. This report must be typed. The details of your calculus and algebra work that support your results are to be included at the end. This project is worth 100 points. A Global and Business Perspective on Income Inequality Consider yourself a Business analyst consulting for a global social policy research institute as well as for a regional business research institute. In this report you will present the trends of income inequality in America and compare these to trends in two other countries. Use this information and your research to discuss what social policies can be implemented to reduce income inequality in America. You will also discuss income inequality and the impact on businesses. The mathematics involved includes learning about the Lorenz function, and using calculus to determine the gini index. You will perform data analysis (1. Data Analysis), and global data collection (2. Global Data Collection). The mathematics is completed first in order have the information to write the report. The written report should begin with an introduction and the mathematics and graphs and images are embedded to support and illustrate the points made in the writing. Be creative and clear in your report, choose appropriate headings, and citations. Use additional graphs and/or images for visual impact and for emphasizing your points. Mathematics of Income Inequality Income distribution amongst families is an important economic and social issue that has been brought to the public’s attention over the past few years. The U.S Bureau of the Census has collected and analyzed data for income distribution amongst families. To quantify income distribution economists use Lorenz curves. Economists use the Gini coefficient to compare Lorenz curves over different years or different nations. Lorenz Curve The Lorenz curve is the graph of the Lorenz function that shows the proportion of national income earned by a given percentage of the population. For example according to the above Lorenz curve 20% of the population receives 5% of the total income for all families in this year. Absolute equality would be if 10% of the population received 10% of the total income. This is represented by the line as shown above. The greater the area between the Lorenz curve and the line the greater the income inequality. Gini Index The Gini Index allows more precise comparison of Lorenz curves. It is the proportion of the area taken up by the Lorenz curve (A) in relation to the overall area under the line of equality. In this project you will use Calculus to determine the Gini index for given Lorenz functions over a period of years. Subsequently you will discuss and synthesize the Gini indices and what this means for income distribution. Gini index = where is the Lorenz function y = x y = x 2 [x − f (x)] 0 1 ∫ dx f (x) Project 2 – Form C2 1. USA Data Collection [10 points] The following data, table 693 is from the US Census Bureau. It can be used to model a Lorenz function for a given year. As an example, let’s consider income distribution in 1970. According to the data here, the poorest 20% (lowest 5th) of the population receives 4.1% of total income for families. Table 693. Share of Aggregate Income Received by Each Fifth and Top 5 Percent of Households: 1970 to 2008 Source: U.S. Census Bureau, Income, Poverty and Health Insurance Coverage in the United States: 2008, Current Population Reports, P60-236RV, and Historical Tables—Tables H1 and H2, September 2009. (2015, Oct 31) retrieved from Census data. In order to model the data, we need to consider cumulative population and cumulative percentage of national income. Using the data from table 693 for 1970, the cumulative population and cumulative percentage of national income is calculated: Table 1 Cumulative Population (%) x Cumulative Income (%) y Data Points (x,y) 20% 4.1% (0.2,0.041) 40% (20% + 20%) 14.9% (4.1% + 10.8%) (0.4,0.149) 60% (40% + 20%) 32.3% (14.9% + 17.4%) (0.6,0.323) 80% (60% + 20%) 56.3% (32.3% + 24.5%) (0.8,0.568) 100% (80% + 20%) 100% (56.3% + 43.3%) (1,1) A power function is used to model the Lorenz function. Using regression and the data points above (in the last column in the table above), you should get the following equation: � = 0.92�!.!” • As described above, select a year between 1970 and 1990 (do not select 1970 or 1990), this year is referred to as Year A. Use table 693 for the data for Year A, calculate the cumulative population and cumulative percentage of national income, and create a table (like Table 1 for 1970). • As described above, select a year between 1990 and 2008, this year is referred to as Year B. Use table 693 for the data for Year B, calculate the cumulative population and cumulative percentage of national income, an
