The graph above shows the AD, LRAS, and SRAS functions for a country. The Fed is following an inflation targeting policy. Its target inflation rate is Π* = 5.00 percent and the potential GDP equals YP = 100,000. The Fed is quite successful in achieving its inflation target in the long run. Okun's alpha equals 2. Currently the economy is in the state of long-run equilibrium. The Fed decides to reduce the inflation target to 1 percent.

This policy will cause the inflation rate in the short run to decrease to X percent and the cyclical unemployment in the short run to increase to Y percent. What are the values of X and Y?

Question

The graph above shows the AD, LRAS, and SRAS functions for a country. The Fed is following an inflation targeting policy. Its target inflation rate is Π* = 5.00 percent and the potential GDP equals YP = 100,000. The Fed is quite successful in achieving its inflation target in the long run.  Okun's alpha equals 2. Currently the economy is in the state of long-run equilibrium. The Fed decides to reduce the inflation target to 1 percent.

This policy will cause the inflation rate in the short run to decrease to X percent and the cyclical unemployment in the short run to increase to Y percent. What are the values of X and Y?

BlackTom AI · Accepted Answer

The question describes a macroeconomics scenario with AD, LRAS, and SRAS and an inflation-targeting Fed. Initially, the economy is in long-run equilibrium at Π* = 5% and Y = YP = 100,000, with Okun’s alpha = 2. The Fed then lowers its inflation target to 1%. We are asked to find the short-run inflation rate X and short-run cyclical unemployment Y corresponding to the new policy.

Option 1: X = 3% and Y = 0%.
- This would imply only a 2 percentage point reduction in inflation from 5% to 3%, and no cyclical unemployment (unemployment equal to the natural rate). In standard inflation-targeting policy, a credible reduction in the inflation target typically requires a temporary output gap (unemployment rises) to move short-run inflation toward the new target. Zero cyclical unemployment suggests staying at full employment, which is inconsistent with tightening enough to move inflation from 5% toward 1%. Therefore this option seems unlikely.

Option 2: X = 4% and Y = 2%.
- Here the inflation rate falls from 5% to 4%, a 1 percentage point reduction, and unemployment rises by 2 percentage points. A small downward move in inflation with a modest rise in unemployment could occur if the policy is modest or the short-run aggregate supply is relatively inelastic. However, given a large shift in the target from 5% to 1%, a larger move in inflation would be more expected in the short run, unless offset by other factors. This combination is plausible but may not align with the stated target drop magnitude.

Option 3: X = 3% and Y = 3%.
- In this case, inflation falls by 2 percentage points (5% to 3%), and unemployment rises by 3 percentage points. This indicates a more pronounced short-run cost in terms of unemployment than Option 2. The magnitude could be plausible if the policy is fairly contractionary, but one would typically expect a larger inflation drop toward the new target (1%), unless there are offsetting expectations or policy lags. The unemployment increase is reasonable but the inflation drop may be undershooting the target reduction.

Option 4: X = 3% and Y = 2%.
- Here, inflation drops from 5% to 3% (a 2 percentage point decline), and cyclical unemployment rises by 2 percentage points. This profile corresponds to a moderate but meaningful tightening: inflation moves toward the lower target (though not all the way to 1%), and unemployment increases due to the demand contraction in the short run. This combination aligns with a credible contractionary policy causing a short-run inflation decline and a positive output gap (negative output) that generates higher unemployment. This option is consistent with the typical short-run trade-off in monetary tightening aimed at lowering inflation from 5% toward a lower target.

Option 5: None of the above.
- If none of the listed pairs fit the actual diagram’s implied magnitudes, this would be selected. However, given the standard analysis of a contractionary policy aimed at an inflation target reduction, there exists a plausible pair—Option 4—that matches the described direction and relative magnitudes of changes in inflation and unemployment in the short run.

In summary, each option reflects a different combination of short-run inflation and unemployment responses to a tightening of the inflation target. The correct choice should depict a downward movement in inflation (toward the new, lower target) and an upward movement in cyclical unemployment (due to reduced demand in the short run). Among the presented options, X = 3% and Y = 2% best captures that pattern, showing a meaningful but not extreme drop in inflation and a modest rise in unemployment, consistent with a contractionary policy aimed at a much lower inflation target while the economy adjusts in the short run.

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