Equilibrium quantity of investment


I. Short Response:

For each of the following statements write a brief answer. Make sure your answers are well organized, neatly written, and explicit. Do not exceed the space provided under the question: these are short responses.

Question 1. The population growth rate in the US is currently approximately 2% per year.  Assume that this rises to 4% per year due to decreased border security and higher birth rates.  Write out the condition which defines the Golden Rule level of capital per effective worker.  If the rate of technological change in the US economy and the capital depreciation rate are constant, what will happen to the level of capital per effective worker after this change in the population growth rate if the social planner wishes to keep the economy at k*gold?

Question 2. For this question use a Solow Growth Model with no technological change and no population change. An economy is initially in steady state at a level of capital per worker below the Golden Rule level of capital per worker.  What must a social planner do to the savings rate to reach k*gold?  Compare the current steady state values of consumption per worker, investment per worker, and output per worker to those at the Golden Rule steady state.

Question 3. Use a long-run model of a small open economy to graph and analyze the effects of increased United States government spending on Jamaica’s real exchange rate and trade balance as well as on Jamaica’s level of national savings and investment. Assume that everything else that might affect the world loanable funds market is unchanged except for this increased level of government spending in the United States. Furthermore, assume that there is no change in monetary policy in either country.

Using graphs illustrate the effect of this change in US policy on Jamaica’s real exchange rate and trade balance as well as on Jamaica’s level of national savings and investment. Be sure to label your graph: including the axes, appropriate curves, initial equilibrium values, shifts if they occur, and new long-run equilibrium values. What happens to Jamaica’s level of net exports, real exchange rate, equilibrium interest rate, and the equilibrium quantity of investment?

Question 4. Define structural unemployment.  What are three causes of structural unemployment? What would happen to the level of structural unemployment if the minimum wage were increased?

Question 5. Define the natural rate of unemployment.  What is the natural rate of unemployment if the job separation rate (s) is 3% and the job finding rate (f) is 22%? What will happen to the natural rate of unemployment if state governments create job placement centers all across the country?

II. Problems:

Answer the following problems in the space provided. Make sure you show all your work and that you write the general form of any formula you use before you enter explicit numbers into the formula, as you may receive partial credit for shown work with an incorrect answer.  Your work must be neat, legible, and organized in order to get full credit.

1. A closed economy has an aggregate production function given by Y = 5K1/2(EL)1/2 where Y is real GDP, K is capital, L is labor, and E is a labor augmenting technology.  Assume that E is initially at 10 and that there is no government sector.

a) Rewrite this production function in terms of output per effective worker and capital per effective worker.

b) Suppose there are 10 labor hours and 100 units of capital in this economy. What is the current level of capital per effective worker?

c) Given the information in part (b) and the initial information, what is the current level of output,Y, in this economy?

d) Assume that 18% of capital depreciates in any given year. If the population is growing at 12% per year and labor-augmenting technology is improving at 20% per year, what savings rate is necessary to sustain the current ratio of capital per effective worker in steady state?

e) Using your answer in d), find the steady state values of consumption per effective worker and investment per effective worker.

f) What will the level of real GDP be in this economy next year?

g) What will the capital/labor ratio be in this economy next year?

h) Find the Golden Rule level of capital per effective worker.

2. Use an aggregate demand and aggregate supply model of the economy to answer the following questions.

a. Define aggregate demand.

b. Define aggregate supply.

c. What happens to the US aggregate demand curve if the Federal Reserve Bank purchases treasury bonds in an open market operation?

d. Describe what happens in the short run and in the long-run to the equilibrium level of output and equilibrium price level if the hurricane season destroys most crops and reduces the food supply.

e. Suppose the economic forecast is for a boom caused by a decrease in production prices.  Policymakers, once the boom occurs, enact a stabilization policy that will keep the level of output constant at the full employment level. Describe the stabilization policy and how the policy enables the economy to return to the full employment level of output. Draw a graph that illustrates the initial long run equilibrium, the short run effect of the change in production prices, and the final long run equilibrium after the policy intervention. In your graph depict the SRAS, LRAS, and AD curves. In your graph make sure to label each curve, any shifts in the curves, the initial long run equilibrium level of output and aggregate price level, the short run equilibrium levels of output and aggregate price level due to the boom, and the long run equilibrium output and aggregate price level after the effective policy intervention.

IV. Essay:

General Directions for Essay: You are to write an essay on the following topic.  This should be a unified, thoughtful essay. The essay will be graded on content, expression, clarity, organization, and overall quality (including legibility).

1. Great Britain and the Falkland Islands are a large open economy and a small open economy, respectively. During a recent diplomatic meeting, Great Britain agreed to assist the Falkland Islands by implementing one of two policies:

a) Great Britain would offer a tax credit to any of their own citizens who invest in the Falkland Islands economy. British citizens who opted to invest in the Falkland Islands economy would pay lower taxes to Great Britain. Great Britain government officials estimate that this policy will effectively reduce their tax collections by a significant amount. In implementing this policy, Great Britain does not alter its money supply.

b) Great Britain would decrease its own money supply, while maintaining its existent fiscal policy at the current level.

For your analysis, assume that Great Britain’s government spending is unchanged and that private savings in the Falkland Islands does not depend on the real interest rate (i.e., Private savings in the Falkland Islands is constant no matter what the level of the real interest rate). Also assume that the Falkland Islands make no changes in fiscal or monetary policy.

For both policies a) and b), describe the effect these policies would have on the real interest rate, nominal interest rate, and nominal exchange rate in the Falkland Islands.  Which policy would result in a higher rate of long term growth for the Falkland Islands economy?

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