Solutions to Problem Set 3

a. Since the output ratio equals 100 and the inflation rate equals 2 percent, that combination is on the long-run Phillips curve. Therefore, the expected inflation rate is 2 percent. The following points are on the short-run Phillips curve, given that actual real GDP grows by 2 percent for every 1 percent increase in the inflation rate above its expected level: (95, -0.5); (97, 0.5); (100, 2); (101, 2.5); and (103, 3.5)

b. Since the inflation rate equals the growth rate of nominal GDP at points on the long-run Phillips curve when natural real GDP is constant, the growth rate of nominal GDP equals 2 percent. Recall: x = y + p. y = 0 so x = p = 2 percent.

c. The SP curve shifts up by 3 percentage points, the amount of the adverse supply shock. Therefore, the following points are on the new SP curve: (95, 2.5); (97, 3.5); (100,5); (101, 5.5); and (103, 6.5)

d. Since that actual real GDP grows by 2 percent for every 1 percent increase in the inflation rate above its expected level, the slope of the SP curve is ½ = 0.5.

The new inflation rate p is given by the following equation (10) on p. 278 in the text:

P = 2/3[p^e_-1 + 0.5(y_-1 + x-hat) + z]

where z is impact on the inflation rate of the supply shock, and x-hat is the growth rate of nominal GDP.

Substituting, using actual values, we get:

P = 2/3[2 +0.5(0 + 2) + 3] = 4 percent

Under a neutral policy (keeping the nominal GDP growth constant) the increase in p must be exactly offset by the decrease in real GDP. Since the increase in p is 2 percent (4 – 2), the decrease in real GDP must be 2 percent, implying an output ratio of 98. The new nominal GDP growth rate is x = -2 + 4 = 2 percent

e. Under an accommodating policy, we want to keep real GDP at its natural rate implying an output ratio of 100. Since x= p + y, dx = dp + dy. We want dy = 0 so dx = dp = 3 percent. The new inflation rate is p + dp = 2 + 3 = 5 percent= the new nominal GDP growth rate.

f. Under an extinguishing policy, we want to keep the inflation rate at the same level of 2 percent. This requires dp = -3 to offset the increase in inflation rate due to the adverse supply shock. dp = -3 means that dx = 2 times -3 = -6. The output ratio must decrease by 6 percent and be equal now to 94. The new nominal GDP growth rate is x = 2 – 6 = -4 percent