3. An economy produces with the production function Y = F (K , L) = AK 1/ 3132/ 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. Dene fl = 213/ 2. Show that the production function can be written as Q = E313 where = -Y ~ ~ AL and k = . What is the growth rate of A? . What is the growth rate of each of the following in steady state: K Y flL, Y 3: K if: E: i L: 'Y'i C (hint: use the approximation that if X grows at g,: and Y grows at g!y then XY grows at 955 + 93;) . At what rate do wages and the capital rental rate grow? (hint: wage=MPL and rental rate=MPK) . Find the steady state value of capital per effective worker . If the economy wants to maximize consumption, should it save more or less? Find the con- sumption maximizing saving rate. In 2014, L=1000 and A=9 (assume the economy starts in steady state with the original parameters given in the question). Find total output in 2014 and 2015 (hint: for 2015 use the growth rate you derived in part b for total output) . The growth rate of population falls to 0. What is the new steady state? Show the change on a graph with investment and depreciation on the y axis and capital on the x axis (i.e. the usual steady state graph). Also show the change over time of capital per effective worker, capital per worker, and 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). . Another country uses the same production function, has the same level of total capital, but only has 810 workers. If there is free mobility across countries (so wage rates are equalized), what can we say about the level of technology (A) in the other country (Which country has a higher level of technology? You do not need to solve for the actual level, but you can if it helps)