Separate a short-run tradeoff from changing expectations

Separate a short-run tradeoff from changing expectations

Question and record

Can policymakers hold unemployment below its assumed natural rate forever in this model?

A fictional expectations-augmented relation is inflation π = expected inflation πe − (u−5), with rates in percentage points and unemployment u. Initially expected inflation is 2. There is no supply shock in the baseline.

The quantities and graphs are teaching assumptions, not observed policy outcomes.

Mechanism and worked calculation

A short-run Phillips relationship can describe a conditional inverse association between inflation and unemployment. Expected inflation and supply conditions shift the relationship. The long-run natural-rate model does not offer a permanent unemployment reduction from continually anticipated inflation. The natural rate is estimated and can change; it is not zero unemployment or a moral optimum.

At u=4 and πe=2, inflation is 3. With expectations 4 and the same unemployment, inflation becomes 5. At u=5, inflation equals expectations. A +3 supply shock raises the first result to 6 without reducing unemployment.

Challenge the interpretation

In a second year, expectations rise to 4 after sustained inflation. A separate supply shock adds 3 points to inflation at any unemployment rate. These numerical coefficients are teaching assumptions, not a fitted Phillips curve.

Your evidence task

Plot both short-run lines for unemployment 3–7% and draw the u=5 benchmark. Label a movement along a line separately from an expectations or supply shift.

Revise your answer to “Can policymakers hold unemployment below its assumed natural rate forever in this model?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Vocabulary

Expected inflation: The inflation rate people anticipate when making decisions; it need not equal realized inflation.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Independent extension

Independently extend the investigation “Separate a short-run tradeoff from changing expectations” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.

Change one condition before explaining the curve

Predict whether a control moves the selected point along a curve, shifts the short-run curve, or changes the natural-rate benchmark. These are fictional comparisons, not policy forecasts. Selecting unemployment does not show that a policymaker can choose it freely.

Expected inflation2%4% Assumed natural unemployment rate4%5%6% Supply disturbance-1 percentage points0 percentage points3 percentage points Unemployment to inspect3%4%5%6%7%8%

Inflation = expected inflation − (unemployment − natural rate) + supply disturbance. Here: 2 − (5 − 5) + (0) = 2%. The coefficient of one is a teaching assumption. Subtracting two rates gives a percentage-point gap.

Solid sloping line: original curve (expectations 2%, natural rate 5%, no disturbance). Dashed sloping line: selected curve. Dotted vertical: original benchmark 5%. Dash-dot vertical: selected benchmark 5%. Circle: inspected point. Square: selected curve at the natural rate. Identical curves or markers overlap. Curves are shown only for unemployment 3–8%; axes remain fixed, including negative inflation.

Unemployment 5%, inflation 2%; unemployment minus natural rate 0 percentage points. At the natural rate, the selected curve gives inflation 2%.

The selected point is at the natural rate and inflation equals expectations: a long-run equilibrium under these assumptions.

Same unemployment values, original and selected regimes

Unemployment (%)	Original inflation (%)	Selected inflation (%)
3	4	4
4	3	3
5	2	2
6	1	1
7	0	0
8	-1	-1

Restore Phillips comparison

Controls are temporary and do not award completion. Record a prediction, the conditions changed, two coordinates and your explanation in the notebook.

Movement, expectations and a temporary disturbance

Start at the default point. Predict the result of inspecting unemployment 4% while keeping all other controls fixed. Next change expected inflation to 4%. Finally restore expectations to 2% and add a disturbance of three points. Explain why the last two changes can raise inflation at the same unemployment without being the same economic mechanism.

Check the three comparisons

The original point is (unemployment 5%, inflation 2%). Moving to unemployment 4% on the original curve gives inflation 3%. Changing expectations to 4% instead shifts the curve up two points: at unemployment 4%, inflation is 5%. With expectations restored to 2%, a three-point disturbance yields inflation 6% there. The coordinate alone does not identify which conditions changed. The disturbance is an added cost/supply term, not a change in the natural rate.

At the natural rate with that disturbance, inflation is 5% although expectations are 2%. Calling this intersection a stationary long-run equilibrium would ignore the mismatch. Remove the temporary disturbance before applying the no-shock long-run benchmark.

Test a proposed permanent tradeoff

Use a separate annual sequence with no supply disturbance and natural unemployment 5%. Suppose expectations for each new year equal the preceding year’s inflation. Initially expectations are 2%. A proposal assumes unemployment can be held at 4% for three years. Calculate the three inflation rates before opening the check. This is a conditional thought experiment; no instrument-to-unemployment rule is supplied.

Check the expectations sequence

Inflation is 3% in year one. Next year’s expectations become 3%, so inflation is 4%; year three expectations are 4%, so inflation is 5%. The proposed unemployment gap requires repeatedly higher inflation under this adjustment rule, rather than a permanent choice between two fixed rates. If unemployment instead returns to 5% in year two, inflation is 3%, equal to that year’s expectations. Other expectation rules would give different transition paths; this arithmetic does not estimate adjustment speed in a real economy.

Change the benchmark, not just the observed unemployment rate

Restore the panel. Hold observed unemployment at 4%, expected inflation at 2% and the disturbance at zero. Compare natural rates 5% and 4%. A hypothetical improvement in matching may reduce structural unemployment, but the new natural rate here is stipulated, not estimated from the fall in observed unemployment.

Check the changed natural rate

With natural rate 5%, the unemployment gap is −1 point and inflation is 3%. With natural rate 4%, the gap is zero and inflation is 2%. Both the vertical benchmark and the short-run curve change in this particular formula. A cyclical movement from unemployment 5% to 4% with the natural rate fixed would instead move along the original curve. An observed unemployment decline alone cannot distinguish these explanations.

Connect the diagrams without confusing levels and rates

A price level is an index at a date; inflation is its percentage change over a period. If a price index moves from 100 to 103 and then stays at 103, inflation is 3% in the first period and 0% in the next. An AD/SRAS diagram showing a higher price level does not by itself specify continuing inflation. A bridge to a Phillips diagram must state the period, expectations and how output relates to unemployment.

For a separate fictional bridge, assume output gap in percent equals −2 times the unemployment gap in percentage points. This is an imposed coefficient, not an estimated law. With natural unemployment 5%, calculate the output gaps at unemployment 4% and 6%, then pair each with the no-shock, expectations-2% Phillips point. Do not reuse a real-output level of 80 as an 80% output gap.

Check the output-gap bridge

Unemployment 4% implies a +2% output gap and inflation 3%. Unemployment 6% implies a −2% output gap and inflation 1%. These are different points under the stated fixed expectations. An adverse supply disturbance can raise inflation at the same unemployment or accompany falling output; it cannot be represented simply by moving along the old no-shock curve. Real-world comparisons require evidence about expectations, capacity and supply conditions.

Unfamiliar case: repair the explanation

A new case has expected inflation 1%, natural unemployment 6%, observed unemployment 7% and no disturbance. A memo reports inflation 0%, then claims that raising expectations to 3% lowers the natural rate to 4%. Draw the original curve using unemployment 5%, 6% and 7%; mark the long-run benchmark. Calculate the new inflation rate at unemployment 7% if only expectations change. Explain which part of the memo lacks support. These values intentionally extend beyond the panel’s presets: construct the graph or provide labeled coordinates yourself.

Check the unfamiliar curve and claim

Original coordinates (unemployment, inflation) are (5,2), (6,1) and (7,0), with a vertical benchmark at unemployment 6%. Changing expectations alone to 3% raises each inflation value by two points; at unemployment 7%, inflation becomes 2%. Nothing in the record changes the natural rate. A defensible explanation preserves the distinction between a different expectation and a different labor-market benchmark. Retain your initial graph before comparing this feedback; seeing the worked answer does not certify independent understanding.

Draw two diagrams for the same dated scenario

Use four alternative year-one outcomes, all measured from a year-zero price index of100. They are parallel comparisons, not four consecutive years. Potential real output is100 teaching units and natural unemployment is5%. Define the percentage output gap as g=100×(Y−100)/100, so in this special normalization g has the same numerical value as Y−100. For another potential-output value this shortcut would fail.

Assume unemployment u=5−g/2, where u is in percent and g in percent of potential. Expected inflation is2%. Annual inflation is π=2−(u−5)+s, where s is a temporary supply disturbance in percentage points. With the previous price index100, the year-one price index is P=100×(1+π/100). Combining the equations gives SRAS: P=102+0.5(Y−100)+s. Every coefficient is a supplied teaching assumption, not an empirical estimate.

Write down the output/unemployment and inflation/price conversions before solving. Draw an AD/SRAS panel with Y horizontally and P vertically, and a Phillips panel with u horizontally and π vertically. The vertical benchmarks are Y=100 and u=5, respectively.

Alternative year-one case	AD equation	Supply disturbance s	Expected inflation
Baseline	P=202−Y	0	2%
Higher demand	P=205−Y	0	2%
Lower demand	P=199−Y	0	2%
Temporary adverse supply	P=202−Y	3	2%

Demand changes move along the stated short-run relationship

Solve the first three AD/SRAS intersections. For each, calculate g, unemployment and inflation. Place the same cases on the Phillips panel, preserving the case labels across diagrams. Explain which curves stay fixed and why a three-unit AD intercept change need not produce a three-unit output change.

Check the linked demand diagrams

Baseline SRAS is P=52+0.5Y. Equating it with202−Y gives Y=100 and P=102. The output gap is zero, unemployment5%, and inflation(102−100)/100×100=2%.

Higher demand solves205−Y=52+0.5Y: Y=102,P=103. The output gap is+2%, unemployment4%, and inflation3%. Lower demand gives Y=98,P=101, gap−2%, unemployment6%, and inflation1%. The same no-shock Phillips line contains the three coordinates(u,π)=(5,2),(4,3),(6,1). Expected inflation, natural unemployment and the disturbance stay fixed, so these are movements along that line.

AD shifts while SRAS stays fixed. The three-unit intercept change is shared between a two-unit output change and a one-point price-index change under the supplied slopes. It is not a general spending multiplier. The Phillips panel’s movement has the opposite horizontal direction because higher output corresponds to lower unemployment in the imposed bridge.

Supply changes shift both short-run relationships

Keep baseline AD and solve the adverse-supply row. Compare it with baseline in both panels. Explain why keeping the original Phillips line would misclassify the result, and whether this temporary disturbance changes either vertical benchmark.

Check the linked supply diagrams

The disturbance raises SRAS to P=55+0.5Y. With202−Y, the intersection is Y=98,P=104. The gap is−2%, unemployment6%, and inflation4%. At unemployment6%, the old no-shock Phillips line would predict1%; the disturbance shifts it upward by three points to4%. This combines lower output with higher inflation relative to baseline.

AD remains fixed in this comparison. Potential output remains100 and natural unemployment5% because the record stipulates a temporary cost/supply term, not a loss of productive capacity. A lasting capacity loss would require changing those assumptions and justifying the connection; it cannot be inferred from the observed output decline alone.

Audit a point that does not fit

An analyst assigns a year-one observation of unemployment4% and inflation5% to the baseline Phillips curve, with expectations2% and disturbance0. Check the point against the equation. Give two separate regime changes that could fit the observation while keeping the natural rate5%. Explain what additional evidence could distinguish those explanations.

Check the point and alternative regimes

The baseline equation predicts2−(4−5)=3%, not5%. One possible alternative is expected inflation4% with no disturbance:4−(4−5)=5%. Another is expected inflation2% with disturbance2:2−(4−5)+2=5%. The observed pair alone cannot distinguish them.

Expectations surveys or market-based measures, with their limitations, would address the expectations hypothesis. Input-cost, supply-disruption and wage/price-setting evidence could address a supply mechanism. Neither is established by selecting a control that makes a toy equation fit. If an alternative regime is adopted, the linked SRAS equation must also change; do not leave the first panel on baseline assumptions while silently changing the second.

Do not carry a price index into an inflation axis

In the higher-demand alternative, year-one P=103. Suppose a separate year-two record says P remains103. Compute year-two inflation and explain why the point from year one cannot simply be reused. Is year-two unemployment determined by that price record alone?

Check the next-period boundary

Year-two inflation is(103−103)/103×100=0%, even though the price level remains above year zero. The year-one inflation rate was3%. Neither the year-two expectations nor its disturbance or output record is supplied, so unemployment cannot be inferred from the unchanged price index alone without additional assumptions.

A new-year AD/SRAS link must use103 as the preceding price index and specify new expectations and shocks. Reusing P=100+π or the old SRAS equation would incorrectly retain the year-zero normalization. A higher price-level point is not a permanent inflation rate.

Retain your paired diagrams, a table of Y/P/g/u/π and the point-consistency repair. AP practice should label each movement or shift and the held-fixed conditions. College extension should compare an attributable dated dataset and explain why an estimated output/unemployment relationship need not equal this imposed coefficient. Public feedback supports guided practice; independent transfer requires a new record and review.