1.-Growth. Suppose the production function for a country is:
$Y = AK^{0.3}L^{0.7}$
a) Convert the production function to per-worker level where output per-worker, y, is a function of capital per-worker, k.
b) Suppose the savings rate is s, and that capital depreciates at rate $\delta$. Using the steady state condition that investment = depreciation, solve for the steady state capital per worker, k.
c) Now suppose that there are two countries, Aloha and Bimini. Assume that 5% of the capital depreciates each year. Assume that each year Aloha saves 10% of their output and Bimini saves 20 percent of their output. Using your answer in part b compute for each country the steady state levels of k, y, c, and i. Compute the ratio of income per worker of Bimini to Aloha's.
2.-Money. In the country of Galapagos, the velocity of money is constant. Real GDP grows by 5% per year, the money stock grows by 14% per year, and the nominal interest rate is 14% per year. What is the real interest rate? Hint: Use the quantity theory of money and the Fisher equation. Show all your work
