Assume that inflation depends on two things: the level of aggregate demand, indicated by the inverse of unemployment (1/U), and the expected rate of inflation (π ^e_t). Assume that the rate of inflation (π_t) is given by the equation:

                   π_t = (48/U – 6) + π^e_t

Assume initially (year 0) that the actual and expected rate of inflation is zero.

(a)  What is the current (natural) rate of unemployment?

(b) Now assume in year 1 that the government wishes to reduce unemployment to 4 per cent and continues to expand aggregate demand by as much as is necessary to achieve this. Fill in the rows for years 0 to 4 in the following table. It is assumed for simplicity that the expected rate of inflation in a given year (π^e_t) is equal to the actual rate of inflation in the previous year (π_t–1).

(c) Now assume in year 5 that the government, worried about rising inflation, reduces aggregate demand sufficiently to reduce inflation by 3 per cent in that year. What must the rate of unemployment be raised to in that year?

(d) Assuming that unemployment stays at this high level, continue the table for years 5 to 7.