If the Bank of Canada's monetary policy rule is r = 0.02 +
,the aggregate demand function for the economy is ADI = 5,000 + 0.8Y - 20,000r,current inflation equals 5% (0.05),and potential output (Y*)equals 20,000,then short-run equilibrium output equals __________,and inflation will eventually equal ________% when the economy returns to potential.
A) 17,000;3
B) 17,000;5
C) 18,000;5
D) 18,000;3
E) 19,000;4

Question

If the Bank of Canada's monetary policy rule is r = 0.02 + 
,the aggregate demand function for the economy is ADI = 5,000 + 0.8Y - 20,000r,current inflation equals 5% (0.05),and potential output (Y*)equals 20,000,then short-run equilibrium output equals __________,and inflation will eventually equal ________% when the economy returns to potential.
A) 17,000;3 
B) 17,000;5 
C) 18,000;5 
D) 18,000;3 
E) 19,000;4

Quizplus · Accepted Answer

To find the short-run equilibrium output, we need to set aggregate demand equal to aggregate supply:

ADI = Y

Substituting in the aggregate demand function and the monetary policy rule:

5,000 + 0.8Y - 20,000r = Y

5,000 + 0.8Y - 20,000(0.02 + 11(0.05)) = Y

Simplifying:

5,000 + 0.8Y - 2,420 = Y

2,580 = 0.2Y

Y = 12,900

So the short-run equilibrium output is $12,900.

To find the eventual inflation rate, we need to use the Phillips curve:

π = πe - 0.5(u - u*)

where πe is expected inflation, u is the unemployment rate, and u* is the natural rate of unemployment.

We know that u = u* because we are at potential output, so:

π = πe

We also know that the Bank of Canada targets an inflation rate of 2%, so we can use this as the expected inflation rate:

π = 0.02

Substituting in the actual and potential output values:

u = (Y/Y*) - 1

u = (12,900/20,000) - 1

u = -0.355

So the eventual inflation rate is:

π = 0.02 - 0.5(-0.355 - 0)

π = 0.02 + 0.178

π = 0.198 or 19.8%

Rounding up to the nearest integer, the answer is 20%. However, none of the answer choices match this, so the closest option is D, with an inflation rate of 3%.

If the Bank of Canada's Monetary Policy Rule Is R