Consider the Solow growth model with Cobb-Douglas production function Y = z[KαL1-α], where Y is total output, z is total productivity, K is the total capital input, and L is the total labor input.
a. Show that in the competitive equilibrium, α is the fraction of national income that goes to the remuneration of capital and 1 - α is the fraction that goes to the remuneration of labor.
b. Use the (average) labor share in national income from your own country for the period 1990 to 2000 to find the value of α.
c. Use your answer to part b to calculate the ‘‘Solow residual'' z using the aggregate output, capital, and labor (Y, K, and L) from your country for each year in the period 1990 to 2000. How has this measure of total productivity evolved over time in your country? Is there a productivity slowdown? Explain the possible reasons of this evolution (inventions, government regulations, price of energy, etc.).