Question

Problem I. Suppose that, instead of expectations being rational, expectations are adaptive. That is, each period the private sector expects that the inflation rate will be what it was the previous period. That is,, where i-1 is the actual inflation rate last period. Under these circumstances, determine what the actual inflation rate and the level of output will be, given i-1. How will the inflation rate and output evolve over time? What will the inflation rate and the level of output be in the long run? Explain your results.

Answer 1

The Friedman-Lucas money surprise model is given by the following simplified relationship:

$i=i^{e}+a(Y-Y^{t})$...........(1)

Where,i=inflation rate, i^e= private sector's amticipated inflation rate, a= constant, Y= aggregate output, Y^t= trend output. Eq(1) also represents the Philips curve relationship diagram drawn below :

#4 a(Y-Y*) 0 Yr Real Aggregate Output

The Philips Curve Relationship in the Friedman-Lucas Money Surprise Model

When i=i^e, then aggregate output is equal to its trend vaue. The assumption that i=i^e is a version of the rational expectations hypothesis, which states that economic agents are not surprised by the current inflation rate. That is economic agents can easily anticipate the inflation rate since they efficiently use all information available to them. Fed's goal is to maximise public welfare. Therefore Fed has an indirect control over the economic variables like inflation and aggregate output. Fed considers a certain inflation rate (i^*) to be optimal. If the inflation in the economy is more than the optimal(i>i^*), the Fed is happier if inflation falls and output increases. But if the inflation in economy is less than the optimal (i<i^*), then more inflation is preferred.The Fed always prefers more aggregate output to less. Given the expected inflation (i^e),the Fed is tempted to choose inflation rate (i>i^e) in order to push aggregate output above its trend level.

The Fed's preference over output and inflation can be seen with the help of differences curve. The slope of the indifference curves represents the amount of change in inflation rate the Fed is willing to tolerate for a given change in aggregate output.

If the expectations were adaptive rather than being rational then,in each period public expects that the inflation rate will be what it was in the previous period(i_-1) , that is people expect i^e=i_-1. Suppose the economy starts at the point (Y^T,I) and the inflation rate is(I) less than the optimal. In this case the actual inflation rate and the level of output can be determined as follows:

PC1 PCi 1 Real Output yrt

The equilibrium in economy when expectations are adaptive

If the Fed increases the inflation rate to i₁, the output rises to Y¹ along the Phillips curve PC₁.In the next periode people expect the inflation to be i_1.So the philips curve shifts tp PC₂.The new Phillips curve passes through the point(Y^T,i₁). Now the central bank adopts inflation rate i₂ in order to exploit PC₂. Outout falls to Y². The procss continues till the steady rate i^* is obtained with output equal to Y^T.

Now suppose the economy starts at (Y^T,i₁) and the inflation(I) is more than the optimal. In this case the actual Inflation Rate and the level of output can be determined as follows:

PC PC2 12 Real Output

The equilibrium in the economy when expectations are adaptive

The economy starts at point Y^T,i₁.If the Fed reduces the iflation rate to i₂, then the aggregate output reduces to Y₁ along th ephillips curve PC₁.In the next period people expect inflation to be i₂, so the phillips curve shifts to PC₂ where the point (Y^T,i₂) lies. Now if the central bank adopts inflation rate i₃ in order to exploit PC₂,it maintains the output at Y_1.The process continues till the inflation rate is equal to i^*, where the output equals to Y^T.

In the long run the inflation rate will be i* and the aggregate output will be at Y^T.