1. Since the natural rate of unemployment is 0.06, e 2(u 0.06), so u 0.06 0.5(e ),
or u 0.06 0.5(e ).
2 0.02 0.04, or 4%.
Year 2: u 0.06 0.5(0.04 0.04) 0.06. The unemployment rate equals the natural rate, since
inflation equals expected inflation. Since unemployment is at its natural rate, output is at its
full-employment level.
1 0.08 0.10 0.07 0.01 0.02
2 0.04 0.08 0.08 0.02 0.04
3 0.04 0.06 0.07 0.01 0.02
4 0.04 0.04 0.06 0.0 0.0
The total output shortfall is 0.02 0.04 0.02 0.0 0.08 8-percentage points of output lost.
2. (a) Equating aggregate demand to short-run aggregate supply gives: 300 10(M/P) 500 P Pe, or 300
(10 1000/P) 500 P 50, or 10,000/P 150 P. Multiplying both sides of the equation by P
and rearranging gives P2 150P 10,000 0, which can be factored as (P 50)
(P 200) 0. This has the nonnegative solution P 50. Since Pe is also 50, the expected price level
equals the actual price level, so output is at its full-employment level of 500 and the unemployment rate
500)/500 0.02. With a natural unemployment rate of 0.06, Okun’s Law gives 0.02 2(u 0.06).
This can be solved to get u 0.05.
In the long run, Pe adjusts to equal P, output adjusts to its full-employment level of 500, and
unemployment adjusts to the natural rate of 0.06. To find P, use the aggregate demand curve
3. (a) 0.10 2(u 0.06) 0.22 2u. This is shown as the Phillips curve labeled PCa in Figure 12.6. If the
Fed keeps inflation at 0.10, then u 0.06, the natural rate of unemployment.