This question concerns Pikettys Second Fundamental Law of Capitalism: = s/g, or the ratio of capital to national income equals the saving rate out

This question concerns Piketty’s Second Fundamental Law of Capitalism: β = s/g, or the ratio of capital to national income equals the saving rate out of national income divided by the growth rate of national income.

1. Suppose the saving rate is s= .09 and the growth rate of national income is g=.03. If s and g do not change, what value will the ratio of capital divided by national income, β, approach as time passes?
2. Suppose the value of β right now is 2, with r=.04, s=.09 and g=.03. What is capital income in the first year?
3. Use the sheet “CapitalIncome” on the accompanying spreadsheet “Assignment 3 Piketty” to determine the rate of growth of capital income in the second year.
4. Use the sheet “CapitalIncome” on the accompanying spreadsheet “Assignment 3 Piketty” to determine how many years it will take for β to get within ten percent of the final value, assuming s, r and g do not change. Do this by using the spreadsheet to calcule β for each year until it is within ten percent of the final value.
5. In the year determined in part d., what is capital’s share of national income? What is the rate of growth of capital income?
6. If the rate of return on capital is .06 instead of .04, will the ratio of capital to income be greater, less or the same after 10 years? Will capital’s share (capital income divided by national income) be greater, less or the same after 10 years?
7. How do the assumptions of these calculations differ from neoclassical economics, with output determined by a production function and wages and the return on capital determined by their marginal products?