1.Recall the Solow Model with population growth. Let aggregate production = ¹, s = .3,

= .07, and = .5. In class, we considered a case where n was constant. In this problem, we'll

consider a case where n depends on per-capita capital, k.

a.Why might the birth rate depend on k?

b.Suppose n(k) = .08 for k 6 and .03 for k > 6. Draw a diagram showing the investment curve (sy(k)) and the (n+)k line. How many steady states are there?

c.Solve for the steady state level(s) of k.

d.If the IMF gifted this country 1 unit of k, what would happen in the long run?

e.What if they gifted them 3 units?

2.Using FRED data, plot the unemployment rate and output growth in the US for the period 1960 to 2020 on the same graph.

a.Describe your graph

b.Now plot the CHANGES in the same variables on a graph with the changes in the unemployment rate on the x axis and the changes in output growth on the y axis.

c.Run simple regressions and see if the proposition of Okun's Law is valid for the period

1990 - 2020 as well as for the period 1960 to 2020.

d.Okun's Law is expressed often as follows:

(1)

Where = unemployment rate

(-1) is the unemployment rate in the preceding period gy is the growth rare of output.

Does this equation shed light on your findings from c above? Explain

e.In class we wrote Okun's law as follows: Percentage Change in Real GDP = 3% - 2 (change in Unemployment rate) approximately. Does this equation shed light on your findings from c above? Explain

f.Why is the 3% included?

3.Compare two countries, one rich and one poor. Using data from the World Bank, find the income per person in each country. Look for data on country characteristics that might help explain the difference in income: e.g. investment rates, population growth rates, educational attainment, and others. How might you figure out which of these factors is most responsible for the observed income difference? In your judgment, how useful is the Solow model as an analytic tool for understanding the difference between the two countries you compared?

4.Suppose that a technological advance enhances productivity and that the resulting lower costs are passed along to consumers in the form of lower prices. Use the aggregate demand- aggregate supply model to illustrate graphically the impact in the short run and the long run of this favorable supply shock. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; v. the short-run equilibrium values; and vi. the long-run equilibrium values. State in words what happens to prices and output in the short run and the long run.

5.In the 1970s there were two oil shocks in the US.

a.Model the resulting stagflation. Explain using diagrams and words.

b.What stabilization policies were out into effect and what was the outcome?

6.Assume that the long-run aggregate supply curve is vertical at Y = 3,000, while the short-run aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 3 M / P, and M = 1,000.

a.If the economy is initially in long-run equilibrium, what are the values of P and Y?

b.Now suppose a supply shock moves the short-run aggregate supply curve to P = 1.5. What are the new short-run P and Y?

c.If the aggregate demand curve and long-run aggregate supply curve are unchanged, what are the long-run equilibrium P and Y after the supply shock?

d.Suppose that after the supply shock the Fed wanted to hold output at its long-run level. What level of M would be required? If this level of M were maintained, what would be long-run equilibrium P and Y?