The following table provides selected points on the Lorenz curve for the 2018 US wealth distribution, downloaded from the World Inequality Database:

• L(0)=0
• L(0.9)=0.2932
• L(0.99)=0.6510
• L(0.999)=0.8207
• L(0.9999)=0.9055
• L(0.99999)=0.9531
• L(1)=1
• 1/ Compute the fraction of wealth controlled by

(a) the top 10% of the entire population

(b) the top 10% of the top 10%

(c) the top 10% of the top 1% (d) the top 10% of the top 0.1%

(e) the top 10% of the top 0.01%

2/ Based on your answers to (1), is the wealth distribution in the United States well-approximated by a Pareto distribution? If so, which part of the distribution is approximately Pareto?

3/ Assuming that the US wealth distribution is indeed Pareto, at least for the top 0.01%, use your answer from 1.e to estimate the PLE.

4/Recall that the best source of wealth data in the U.S. is the Survey of Consumer Finances (SCF). A shortcoming of the SCF is that (for privacy reasons) it does not include people on the Forbes 400 list of wealthiest people. Using the PLE from (3), estimate the fraction of wealth controlled by the 400 wealthiest families in 2018. In 2018, there were approximately 127.9 million households in the US.