Consider the Cobb-Douglas production function with labor-augmenting technology used in class: Y = F(K, L) = K\"(EL)1_\" with 1 > a > 0 a) In a competitive equilibrium, labor is paid its marginal product (in real terms), so % = MPL. Show that the sixth of Kaldor's Great Ratios holds that is, show that \"The real wage grows at the same rate as output per worker in the steady state\". b) Suppose the labor share of income is g, national savings is 20 percent of GDP, 5 percent of capital breaks down each year, technology grows at 3 percent per year, and the population grows by 2 percent each year. Find 19*, y*, and c*, the steady-state values of k, y, and c. c) Using the parameterization from (b) and the 'growth trick', calculate the growth rate of capital per effective worker , capital per worker %, aggregate capital K and aggregate output Y at the steady state. d) Write down two conditions that hold at the Golden Rule steady state. e) Calculate k*GR, y*GR, and c*GR at the Golden Rule Steady steady state. Confirm that c*GR is larger than in part (b)