1. In the equation for the Phillips curve,
p t = p et + (m +z) - a ut,
what does a stand for? What is the effect of an increase in a on the estimate of the natural rate of unemployment?
2. Draw a diagram which shows a scatter plot of inflation and unemployment which would result in an economy full of people with perfect foresight, i.e. full of people who never made a mistake in their inflationary expectations.
3. Suppose that the Phillips curve in an economy is given by the equation,
p t - p et = 0.18 - 3ut, where p et = q p t-1. Furthermore suppose that in period t-1, the unemployment rate is equal to the natural rate, and the inflation rate is 0 percent.
b. Suppose that beginning in period t, the authorities bring the unemployment rate down to 5% and keep it there indefinitely. Determine the inflation rate in periods, t, t+1, t+2, and t+3 when q =0. Next do the same exercise for q =1.0.
5. If the United States experienced three or fours years of low (under 1%) inflation, would it return to the original Phillips curve of the 1950s and 1960s. Why or why not?
6. During the 1980s and early 1990s the price of oil decreased. What has been the probable effect of this on the natural rate of unemployment?
7. Suppose that the economy can be described by the following three equations:
ut - ut-1 = -.4(gyt - 0.3) (Okun's Law)
p t - p t-1 = -(ut - .06) (Phillips Curve)
gyt = gmt - p t (Aggregate Demand)
b. Suppose that inflation is running at 10% each year and the economy is operating at the natural rate of unemployment. To keep unemployment at its natural rate, what must be:
(ii) the growth rate of the money supply?
8. Suppose that conditions are as in part b (of question 7), and then, in year t, the authorities use monetary policy to reduce the inflation rate to 5% and keep it there. What will happen to the unemployment rate and output growth in years t, t+1, and t+2? What money growth rate in years t, t+1, and t+2 will accomplish this goal?
9. Suppose that the economy is described by the equations in question 7. Assume initially that ut = ut-1 =.06, gmt = .10, and p t = .07, and that this year money growth is permanently reduced from 10% to 0%.
c. Determine the long run impact on unemployment and inflation.
10. What is the importance of "credibility" in inflation fighting? How can you determine whether or not policy makers have "credibility"?
11. The model of the economy we have used assumes that inflationary expectations are modeled by p e = q p t-1. Explain what the long-run Phillips curve looks like if
a. q =0,
b. q =1.0, and
c. q =1.5.
12. Under the assumption of "rational expectations" the only expectational errors made by agents in the economy are completely random, i.e. there is no way of predicting these expectational errors. Under this assumption, what is your best prediction of the unemployment rate when the economy is experiencing increasing inflation versus when the economy is experiencing disinflation?