Question

Scenario (use to answer questions 5-6) You are appointed the Chairperson of the FOMC. Use the link below to run a monetary simulation. You are required to hit the inflation target. In order to receive credit, you have to reappointed by hitting both your inflation and unemployment targets. You can run the simulation as many times as necessary. When you are successful enter in the ending inflation and unemployment rates.

http://www.frbsf.org/education/activities/chairman/

What is your ending inflation rate?

A. Above 6.0%
B. Between 5.0% - 5.9%
C. Between 3.6% - 4.9%
D. Between 0.1-3.5%

Answer 1

D. Between 0.1-3.5%

In this economy, it is required of you to keep the unemployment rate at 5%, and inflation target is 2%.

There is a Phillip's Curve which captures an inverse relation between inflation and unemployment.
The equation of the Phillip's Curve is given as follows.

(1)

Here,
is the inflation at any period of time t.
is what people would expect the inflation to be at time t.
is called the catchall variable, that captures things like job security, unemployement benefits etc.
is the mark up variable, that captures the margin that the firm makes to when charging a price from the customers and paying a wage to the workers.

What is important to note is that the price setters of firms charge a price based on what they expect the price to be next time. Therefore, given last period's price level, a higher price level this period implies a higher rate of increase in the price level from last period to this period, that is, higher inflation. Similarly, a higher expected price level this period implies a higher expected inflation.
Therefore, an increase in expected inflation , leads to an increase in actual inflation .

But people's expectation is a shaped by the what they observed in the previous years. Therefore,

=

Here, caputres the effect of last year's inflation rate, , on this year's expected inflation rate,. A higher value of , the more last year's inflation leads workers and firms to revise their expectations of what inflation will be this year.

This equation tells that expectations of the inflation rate this year are formed solely on last years inflation rate.
But, in reality, as inflation becomes more persistent, workers and firms start changing the way they form expectations. They start assuming that if inflation had been high last year, inflation is likely to be high this year as well. The parameter , the effect of last year's inflation rate on this year's expected inflation rate, increases. So, becomes close to 1.

So equation 1 now becomes,

Now, the natural rate of inflation is when the expected rate of inflation is equal to the actual rate of inflation. Similarly, the natural rate of unemployment is the unemployement rate such that the actual price level is equal to the expected price level, or the actual inflation is equal to the expected inflation. or =. Note also that, here we are taking to be equal to 1 for the reason mentioned above.

Substituting = in the above equation and replacing with , where n stands for the natural rate.

We solve it and get, =

Finally after rearranging equation 1 with the values above, we get

The above equation above says that: The change in the inflation rate depends on the difference between the actual and the natural unemployment rates. When the actual unemployment rate is higher than the natural unemployment rate, the inflation rate decreases, and when the actual unemployment rate is lower than the natural unemployment rate, the inflation rate increases.

In the simulation given, we can control the inflation rate by changing the Fed funds rate. The more the interest rate, the monetary policy gets tighetend, implying the real money supply decrease, which implies that the inflation decreases. And according to the above equation, unemployment decreases.

What is important here is that first needs to be made close to 1, so that the expected inflation rate moves one to one with the inflation rate last year. Only then will the above equation work the best. So when running the simulation, keep the Fed fund rate stable, so the people gain trust in the Fed. Then with time adjust the Fed fund rate so as to the attain the target inflation and unemployment.

Remember: an increase in Fed rate Tightening of monetary policy lowering inflation rate increase in unemployment. And similarly vice-versa