Question

2. A central bank has decided to adopt inflation targeting and is now debating whether to target 5 percent inflation or zero inflation. The economy is described 3 by the following Phillips curve: u = 6 − 0.5(π − E π), where u and π are the unemployment rate and inflation rate measured in percentage points. The social cost of unemployment and inflation is described by the following loss function: L = u + 0.025π 2 The central bank would like to minimize this loss. a. If the central bank commits to targeting 5 percent inflation, what is expected inflation? If the central bank follows through, what is the unemployment rate? What is the loss from inflation and unemployment? (9 points) b. If the central bank commits to targeting zero inflation, what is expected inflation? If the central bank follows through, what is the unemployment rate? What is the loss from inflation and unemployment? (9 points) c. Based on your previous answers, which inflation target would you recommend and why? (9 points) d. Suppose that the central bank chooses to target zero inflation, and expected inflation is zero. The central bank then surprises people with 5 percent inflation. What is unemployment in this period of unexpected inflation? What is the loss from inflation and unemployment? (9 points) e. What problem does your answer in part (d) illustrate?

Answer 1

Ans) From the question above, it is given that

u=5-0.5(π-π^ee)

L=u+0.05π²

Now lets assume that the general public is having pure faith in the monetory authority. Which states that the public is having a believes that the decisions taken by the central bank are followed through and basis its expectations.

Thus when central bank have commit to 5% inflation, then the public will rely on it and the expected inflation.

Now π^e=5%

Substituting π^e=π=5% in the above equation

We get u=5-0.5(5-5)

u=5%

Thus the central bank follows through and so

π=5%

We can also compute the loss L, by plunging u and π in the other equation

We get L=5+0.05(5²)

L= 5+5(25) =5+1.25

L=6.125

Now moving forward assume the full faith of the general public on the central bank is:

π^e=0%

Thus if the central bank follows through, π=π^ee=0%, and we required to compute the unemployment rate form the equations used above:

u=5-0.5(0-0)

u=5%

Finally, compute the loss L from above equation :

L=5+0.05(0²)

L=5

Now,

It has been explicitly given that the central back looks minimise the loss L,

When we compare the two above cases,

it is clear that L is minor is case of π=0%,

Hence, it is recommend an inflation target of 0%. This conclusion is intuitively very attractive. This is because an inflation target, while having the same negative consequences as the target, will at least lead to lower prices.

In this case, expected inflation - πe = 0%

Real inflation, π = 57.

Plugging the two previous values ​​in,

we obtain u = 5-0.5 (5-0)

u=5-2.5

u=2.5

Plugging π in the equation of L

L=2.5+0.05(5²)

L=2.5+(0.05) (25)

L=3.75