Consider a Solow economy F(K, N} = 2:.l'11'2fi'i.'3E5 in which the total factor of productivity (TFP) is constant and equal to 1. The number of workers increases by 1 percent per year. Capital depreciates at a rate of 10 percent per year. The saving rate is 40 percent. 1. Show that this function has constant returns to scale. [2.5 points] 2. Determine whether the production function is constant return to scale {CR8} , DRS or LBS [2.5 points] 3. Determine capital per worker, income per capita, and consumption per capita in the steady state.[5 points] 4. Now, suppose that the economy is initially in the steady state {t=) that you calculated in part {a}. Then, s decreases to 0.2 at t=1 and stay there forever. Determine capital per worker, income per capita and consumption per capita in each of the 4 years following the increase in the savings rate. [lpoints] 5. Determine capital per worker, income per capita, and consumption per capita in the new steady state.[5 points] 6. Show graphically the effect of an increase in the savings rate on the steady state quantity of capital per Worker and the equilibrium points Inf and kg. [7 points] 7". Sketch the time paths of lay, and Inc, [8 points] 8. Determine the golden rule saving rate, capital per worker, income per capita, and consumption. [lpoints]