To answer the next three questions, download the spreadsheet called GROWTH-Model-2020. The spreadsheet contains the values from a simple growth model. Please reconstruct the underlying formulas from this model and then use them to answer the questions below.

Set up the spreadsheet so that you can change the values for s and for the growth rate of the labor force in cells C1 and C2. Remember to use exponential growth rates and natural logs (ln). The three key relationships you need to fill in the formulas are the production function and the rules for calculating capital and labor next year from values of capital, labor, and output (GDP) this year. The production function is the one from the note: "Diminishing Returns": F(K,L)=K^(1/3)*L^(2/3). (Note: K^x means K raised to the power x) . The rule for labor, L, in given year is that it is equal to exp(g) times labor in the previous year, where g is the growth rate of the labor force, and exp is the exponential function described in "On Overview of Macroeconomics." The capital stock this year is equal to the capital stock yesterday plus s times output yesterday. You also need to be able to calculate the marginal product of an input and the growth rate of any variable.

5. Suppose you increase the savings rate from 20% to 40%. This increases the growth rate of output between years 1 and 2 by how much per year?

6. Between years 99 and 100, the increase in the savings rate from 20% to 40% causes the growth rate of output to be higher by how much per year?

7. Go back to a savings rate of 20%. Now suppose you increase growth rate of the labor force from 1.5% per year to 3 percent per year. This will cause an increase of how much in the rate of growth of output between years 99 and 100?