1. In his book Capital in the 21st Century, Thomas Piketty estimates that the annual continuously compounded growth rate of the median income of Capitalists, r, will be 4% for the 40 years from 2010 to 2050. He also estimates that the annual continuously compounded growth rate of Workers' wages, g, over this period will be 3%. Suppose that in 2010 the median income for Workers is $80,000 and the median income for Capitalists is $120,000.
2. equation for the median income of Capitalists in 2050, C(2050), as a function of their income in 2010, C(2010) = $120,000 and the average annual continuously compounded growth rate of the return to capital, r = 4%. Calculate the dollar value of the median income for capitalists in 2050.
3. The ratio of Capitalists' income to Workers' income in 2010, R(2010), was 1.5 (R(2010) = $120,000/$80,000). equation for this ratio in 2050, R(2050), as a function of r, g, and the 40 years between 2010 and 2050 (Note: e should appear only once in this equation.) Using the values of r and g given above, calculate R(2050).