Question 3 (10 points) Now consider the notechnology CobbDouglas production function used in class Y = F(K, L) = K\"L(1\") with 1 > a > 0 a) Find the intensive form of the production function y = f(k), where y E Y/L and k E K/L, and describe its shape. b) Find the marginal product of labor (MPL E 31;). Find 335131. and 3.151th and use them to describe in words how K and L affect M PL. Provide some intuition for how K and L affect M PL. c) Find the marginal product of capital (MPK E 33;). Find agK and ang, and use them to describe in words how K and L affect MPK. Provide some intuition for how K and L affect M PK . d) In a competitive equilibrium, workers are paid their marginal productivity, so the real wage W/P = M PL. Prove that 10: is the labor share of GDP. (The labor share is real income paid to workers, KL, as a share of total income.) e) In a competitive equilibrium, capital is paid its marginal productivity, so the real capital rental rate R/P = MPK. Prove that a is the capital share of GDP. (The capital share is real income paid to capital, 3K, as a share of total income.) f) Suppose a = 1/3. If in a given year population growth is 3% and the capital stock grows at 6%, use the 'growth trick' to show that output grows at 4% and output per worker grows at 1%. Question 4 (10 points) Consider the notech Solow Growth Model discussed in class. a) Describe in words the intuition for the st.st. equilibrium condition: 3k\" = (:5 + n)k b) Suppose the labor share of income is 3, national savings is 20 percent of GDP, 8 percent of capital breaks down each year, and the population grows by 2 percent each year. Find k*, y*, and 0*, the steady-state values of k, y, and c. c) Suppose the savings rate increases. What do you expect to happen to y*? Explain why. d) Suppose the population growth rate increases. What do you expect to happen to '9'\"? Explain why