Acrobat File Edit View Window Help BOLD? Q g Thu Feb 1 11:51 AM Chapter 6 - Revenue Recogniti Problem Set 3.pdf X Notes3.pdf + Create @ 4 : All tools Edit Convert E-Sign Find text or tools Q | H 2. An economy produces with the production function Y = F(K, L) = AK1/312/3. Population grows at 2% per year and A grows at 2% per year. The depreciation rate is 5% and the saving rate is 40%. The economy is in steady state. a. Define A = A3/2. Show that the production function can be written as y = kl/3 where y = = AT and K = . What is the growth rate of A? ... b. What is the growth rate of each of the following in steady state: k, y, k, y, K, Y c. At what rate do wages and the capital rental rate grow? (hint: wage=MPL and rental rate=MPK) d. Find the steady state value of capital per effective worker e. If the economy wants to maximize consumption per effective worker, should it save more or less? Find the consumption maximizing saving rate. f. In 2014, L=1000 and A=9. Find total output in 2014 and 2015 (hint: for 2015 use the growth rate you derived in part b for total output) g. The growth rate of population falls to 0. What is the new steady state? Show the change N on a graph with investment and depreciation on the y axis and capital on the x axis (i.e. the N usual steady state graph). Also show the change over time of capital per effective worker, (log) capital per worker, and (log) aggregate capital. In your graph, be sure to capture the > old steady state, transition, and new steady state (hint: the slope of the line should be equal to the growth rate at each point). zoom O R PS 4 424 O