1. Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function, where K is capital, L is the labor force, and u is the natural rate of unemployment which in this case is 6%. The national saving rate is 20%, the labor force grows at rate 4%, and capital depreciates at rate 10%.
a. Express output per worker (y=Y/L) as a function of capital per worker and the natural rate of unemployment.
b. Write an equation that describes the steady state of this economy.
c. Suppose that some change in government policy reduces the natural rate of unemployment to 5%. Describe how this change affects output both immediately and over time. Is the steady state effect on output larger or smaller than the immediate effect?
2. Suppose and economy described by the Solow model has the following production function:
a. For this economy, what is f(k)?
b. Use your answer to part a to solve for the steady state value of y as a function of s, n, g, and δ.
c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 25% and a population growth rate of 2% per year. Xanadu has a saving rate of 10% and a population growth rate of 5% per year. In both countries, g=0.02 and δ=0.04. Find the steady state value of y for each country.