Intermediate Macroeconomics Assignment
1. Assume that a country's aggregate production function is Y = K0.25 L0.75. Assume also that the saving rate is 40 percent (s=0.4) and that 10 percent of capital depreciates per year ( δ = 0.1).
(a) What are capital per worker, output per worker, and consumption per worker in the steady state?
(b) What would happen if the economy started with a capital per worker higher than the steady state level? Illustrate your answer with a graph.
(c) Define the Golden Rule level of capital. Find the Golden Rule level of capital per worker, output per worker, consumption per worker, and investment per worker, and compare it with your result in (a). Explain. What would the government have to do with the saving rate if it wanted the economy to achieve the Golden Rule level of capital.
(d) Illustrate graphically what would happen with output per worker, consumption per worker, and investment per worker during the transition from a higher level of steady-state capital per worker to the Golden Rule level of capital per worker. Explain with a graph.
2. Suppose that two countries are exactly alike in every respect except that the populations growns in Country A at 3% each year (nA = 0.03) while the population in Country B grows 1% each year (nB = 0.01).
(a) In which country will the capital stock per worker be larger? Illustrate graphically.
(b) In which country will the Golden rule level of capital per worker be higher? Illustrate graphically.
(c) Which country will have the faster growth of output per worker in steady state?
3. Suppose that the short-run aggregate-supply has a positive slope. Suppose also that the economy starts at a long-run equilibrium.
The principal tool used by the Federal Reserve Bank to change the money supply is open-market operations. Use the aggregate demand-aggregate supply model to illustrate graphically the impact in the short run and the long run of a Federal Reserve decision to reduce open-market purchases, effectively reducing the money supply in our economy. Be sure to label the axes, the curves, the initial equilibrium values, the direction the curve shift and when they do shift, the short-run equilibrium values, and the long-run equilibrium values as the economy adjusts to its long run final equilibrium. State in words what happens to prices and output in the short run and long run.
4. Suppose that the economy starts at a long-run equilibrium and that the short-run aggregate supply curve has a positive slope. Now suppose that a negative demand shock hits the US.
(a) No Policy Intervention: Using the model of aggregate demand and aggregate supply developed in Chapter 10, illustrate graphically the impact in the short run and in the long run of this negative demand shock. Be sure to label the axes, the curves, the initial equilibrium values, the direction the curves shift, the short-run equilibrium values, and the long-run equilibrium values. Explain what happens to prices and output in short run and the long run.
(b) Policy Intervention: Suppose that you are an economist working for the Treasury Department (thus, you can only use fiscal policy tools) when this negative demand shock is observed. Using the model of aggregate demand and aggregate supply developed in Chapter 10, illustrate graphically your policy recommendation to accommodate this adverse demand shock, assuming that your top priority is maintaining full employment in the economy. Be sure to label the axes, the curves, the initial equilibrium values, the direction the curves shift, the short-run equilibrium values, and the long-run equilibrium values. Explain what happens to prices and output in short run and the long run.