3140fps4sol - Economics 314-1 Problem Set 4 Suggested...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 314-1 Fall 2010 Problem Set 4 Suggested Solutions Questions 1: 1. The economy has the Phillips curve: π = π -1 – 0.4(u – 0.05). a. The natural rate of unemployment is the rate at which the inflation rate does not deviate from the expected inflation rate. Here, the expected inflation rate is just last period’s actual inflation rate. Setting the inflation rate equal to last period’s inflation rate, that is, π = π -1 , we find that u = 0.05. Thus, the natural rate of unemployment is 5 percent. b. In the short run (that is, in a single period) the expected inflation rate is fixed at the level of inflation in the previous period, π -1 . Hence, the short-run relationship between inflation and unemployment is just the graph of the Phillips curve: it has a slope of -0.4, and it passes through the point where π = π -1 and u = 0.05. In the long-run, expected inflation equals actual inflation, and so π = π -1 , and output and unemployment equal their natural rates. The long-run Phillips curve thus is vertical at an unemployment rate of 5 percent. The curves are graphed below. π LRPC 0.4 π 1 SRPC 0.05 u
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
c. To reduce inflation, the Phillips curve tells us that unemployment must be above it natural rate of 5 percent for some period of time. We can write the Phillips curve in the form π - π -1 = 0.4(u – 0.05). Since we want inflation to fall by 2 percentage points, we want π π -1 = -0.02. Plugging this into the left-hand side of the above equations, we find -0.02 = -0.4(u – 0.05). We now solve the above equation for u: u = 0.10. Hence, we need 5 percentage points of cyclical unemployment above the natural rate of 5 percent. Okun’s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 5 percentage points corresponds to a fall in output of 10 percentage points. The sacrifice ratio is the percentage of a year’s GDP that must be foregone to reduce inflation by 1 percentage point. Dividing the 10 percentage-point decrease in GDP by the 2 percentage-point decrease in inflation, we find that the sacrifice ration is 10/2 = 5. d. One scenario is to have very high unemployment for a short period of time. For example, we could have 10 percent unemployment for a single year. Alternatively, we could have a small amount of cyclical unemployment spread out over a long period of time. For example, we could have 6 percent unemployment for 5 years. Both of these plans would bring the inflation rate down from 4 percent to2 percent, although at different speeds.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern