2. (20 points) Consider a Solow economy with technological progress and a positive population growth. Production function is Cobb-Douglas with constant returns to scale in capital and labor, the capital share of income is 30%; the depreciation rate and the population growth rate are each 2% per year; the savings rate equals 60%. The economy is on a balanced growth path (BGP) with the growth rate of output per worker equal 2%. (a) (10 points) Find the ratio of aggregate capital to aggregate output, K/Y , on a BGP. Find the corresponding real interest rate on a BGP. (b) (10 points) At some arbitrary time t0, the savings rate in this economy is reduced permanently to a new constant level (to be determined by you), with the outcome that the economy converges to the golden rule steady state in the very distant future. What are the new savings rate, and capital-output ratio and the real interest rate when the economy is back on its BGP?

2. (20 points) Consider a Solow economy with technological progress and a positive population growth. Production function is CobbDouglas with constant returns to scale in capital and labor, the capital share of income is 30%; the depreciation rate and the population growth rate are each 2% per year; the savings rate equals 60%. The economy is on a balanced growth path (BGP) with the growth rate of output per worker equal 2%. (a) (10 points) Find the ratio of aggregate capital to aggregate output, K/Y, on a BGP. Find the correSponding real interest rate on a BGP. (b) (10 points) At some arbitrary time to, the savings rate in this economy is reduced permanently to a new constant level (to be determined by you), with the outcome that the economy converges to the golden rule steady state in the very distant future. What are the new savings rate, and capital-output ratio and the real interest rate when the economy is back on its BGP