Suppose that an economy has the Phillips curve pi = pi_1 -0.5(u-u_n) and that th

Question

Suppose that an economy has the Phillips curve pi = pi_1 -0.5(u-u_n) and that the natural rate of unemployment is given by an average of the past two years' unemployment: u_n =0.5(u_-1, +u_-2) a) Why might the natural rate of unemployment depend on recent unemployment (as is assumed in the above equation)? b) Suppose that the Bank of Canada follows a policy to reduce permanently the inflation rate by 1 percentage point. What effect will that policy have on the unemployment rate over time? c) What is the sacrifice ratio in this economy? Explain. d) What do these equations imply about the short-run and long-run tradeoffs between inflation and unemployment?

Explanation / Answer

A). Non Accelerated Inflation Rate of Unemployment (NAIRU) consists of

Frictional Unemployment : may increase because after relatively higher unemployment rate times there might be some changes required to adopt labor-market infrastructure (unemployment agencies, government. services, etc.) to market forces distribution (e.g. switch from high supply of labor-force to low supply, and from low demand for labor to high demand).

Structural Unemployment: may be higher because over time of higher unemployment many workers may partially lose their skills, professionalism or competence level, thus after high unemployment their productivity is lower until they will get it back by learning (or sometimes by learning-by-doing)

Unemployment is often accompanied with deflation but high employment with inflation, thus it is relatively more profitable to be unemployed and receive unemployment benefits which are calculated taking into account higher nominal incomes.

B) Bank of Canada follows the policy to reduce the permanently the inflation rate by one 1% pont.

¹ = ° - (U¹-NAIRU¹)/2

NAIRU¹ = ( U (n-1) + U(n-2) ) /2

NAIRU¹ = (U¹ + U°) /2

¹ = ° - (U¹- (U¹ + U°)/2 )/2 =

= ° - U¹/2 + (U¹ + U°)/4

Inflation reduction by 1% means: ¹ = ° - 1

Thus first period it should be:

(U¹ + U°)/4 - U¹/2 = -1

(U¹ + U°)/2 - U¹ = -2

(U¹ + U°)/2 +2 = U¹

U¹ and U° are fixed by previous periods, thus the only variable which can be affected is U¹, so U¹ should be set using different fiscal tools equal to: U¹= 2 + NAIRU¹

So cost of reducing inflation by 1% first period is average of previous periods plus 2% of cyclical unemployment.

Next periods equation ¹ = ° should hold (because inflation reduction is permanent), so

¹ = ° - U¹/2 + (U¹ + U°)/4

¹ = °

0 = - U¹/2 + (U¹ + U°)/4

U¹/2 = (U¹ + U°)/4

U¹ = (U¹ + U°)/2

U¹ = NAIRU¹

Thus further (over time) system reaches new steady-state with zero cyclical unemployment rate (NAIRU¹- U¹=0).

Final Conclusion: Bank of Canada Permanent reduction of inflation rate by one percentage point will cost two percentage points of higher unemployment first period and further zero cyclical unemployment.

C) You should specify Okun's law details for calculation, or if this relationship is linear at very small interval, then NAIRU is assumed as potential GDP. All we currently know is what one first inflation point will cost 2 percentage points of unemployment. Thus if we know by how much these 2% of unemployment cause fall in output then we can easily calculate sacrifice ratio (so provide info which method to apply).

D) In this case NAIRU depends from previous periods, thus after one year it will fall to half, and then after some years will reach new steady state. Another outcome in reality is hard to achieve in long-run - zero cyclical unemployment.

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