Unit 4 Inflation and unemployment

4.6 Expected inflation shifts the Phillips curve

In his presidential address to the American Economic Association in December 1967, Milton Friedman provided an explanation for why people’s expectations about inflation could change and why that would shift the Phillips curve. He referred to the recent experience in the US. Since 1966, unemployment had been steady, averaging 3.7%, but inflation had increased from 3.0% to 4.2%. He said that the only way unemployment could be kept as low as 3% was by allowing inflation to keep increasing to higher levels: ‘There is always a temporary trade-off between inflation and unemployment; there is no permanent trade-off,’ he claimed.1

Supported by evidence from many countries from the late 1960s, he showed that if unemployment remains ‘too low’ the result will be not just higher inflation, but rising inflation as well. We will discuss what ‘too low’ means and how this is represented in the model by a shift in the Phillips curve.

expected inflation
The belief formed by wage-setters and price-setters about the level of inflation in the next period. See also: inflation.

Friedman claimed that at low unemployment, inflation keeps increasing so that the simple Phillips curve relationship like the one plotted by Bill Phillips is misleading. Why does inflation keep rising when unemployment is kept low? This is because of the way wage setters and price setters form their views about what will happen to inflation, which is called expected inflation.

We need to keep in mind that households care about wages and firms care about profits in real terms, and consider the following two points:

  • People are forward-looking: They take actions now in anticipation of things they expect to happen. To stress this, economists say that ‘expectations matter’.
  • People treat prices as messages: People treat changes in prices as messages about what will happen in the future, just as people treat a build-up of clouds as a prediction of rain.

The way that people expect inflation to behave will depend on how they make forward-looking decisions and how they interpret price messages.

Introducing expected inflation

We introduce the role of expected inflation (which we denote with the symbol \(\pi^E\)) by returning to the Phillips curve.

Suppose that the economy is in supply-side equilibrium at the intersection of the wage- and price-setting curves, with a real wage of 100 and unemployment at 6%. But everyone expects the inflation rate to be 3%. So there is no bargaining gap: each year both wages and prices will be raised by 3% and the real wage will remain at the intersection of the WS and PS curves.

In Figure 4.11, at the supply-side equilibrium with an unemployment rate of 6%, the inflation rate is 3% and not zero as in Figure 4.9. Once we introduce inflation expectations, the economy can be in supply-side equilibrium with rising prices—as long as they are rising at the rate expected.

If wage setters and price setters expect prices to rise by 3% per annum, and the level of aggregate demand is ‘normal’ and keeps unemployment at 6%, then the economy can remain at the supply-side equilibrium with inflation remaining constant at 3% per annum. Actual inflation is equal to expected inflation and the level of unemployment is constant at the equilibrium where the WS curve and PS curve intersect (point A).

inflation-stabilizing unemployment rate
The unemployment rate (at supply-side equilibrium) at which inflation is constant. Originally known as the ‘natural rate’ of unemployment. Also known as: structural unemployment rate, non-accelerating rate of unemployment (NAIRU). See also: equilibrium unemployment, structural unemployment.

At the supply-side equilibrium, where the WS and PS curves intersect, the equilibrium or structural unemployment rate is also the inflation-stabilizing unemployment rate.

Now consider a business cycle upswing. Aggregate demand rises, taking the economy to lower unemployment of 4% at point B. What will happen to inflation? Workers expect prices to rise by 3% and will require a nominal wage increase of 3% just to keep their real wage unchanged. But they require an additional 2% rise to give them an expected real wage rise on the wage-setting curve, so wages increase by 5%. With their costs rising by 5%, firms will increase prices by 5% to maintain their profit-maximizing markup. In the boom, inflation will be 5% with unemployment at 4%. This gives a Phillips curve like the one in Figure 4.9. The only difference is that inflation at supply-side equilibrium is 3% rather than zero.

: There are 2 diagrams. In diagram 1, the horizaontal diagram shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical, rightmost line is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted within the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. The business cycle boom is depicted by point B situated on the PS curve but below the WS curve in diagram 1. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve higher than point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%. In diagram 2, the vertical coordinate of point B replicated from diagram 1 represents the sum of the inflation expectation of 3% and the bargaining gap of 2%, totaling 5%.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-11

Figure 4.11 Bargaining gaps, expected inflation, and the Phillips curve.

Labour market equilibrium: There are 2 diagrams. In diagram 1, the horizaontal diagram shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical, rightmost line is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted within the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-11a

Labour market equilibrium

At supply-side equilibrium (point A), inflation is 3%, as expected.

A boom: There are 2 diagrams. In diagram 1, the horizaontal diagram shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical, rightmost line is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted within the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. In diagram 1, the business cycle boom is depicted by point B situated on the PS curve but below the WS curve. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve higher than point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-11b

A boom

At lower unemployment, point B, the bargaining gap is 2%.

The new rate of inflation, 5%: There are 2 diagrams. In diagram 1, the horizaontal diagram shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical, rightmost line is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted within the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. In diagram 1, the business cycle boom is depicted by point B situated on the PS curve but below the WS curve. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve higher than point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%. In diagram 2, the vertical coordinate of point B represents the sum of the inflation expectation of 3% and the bargaining gap of 2%, totaling 5%.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-11c

The new rate of inflation, 5%

At B, inflation is equal to expected inflation plus the bargaining gap.

When expected inflation is not zero, we can summarize the causal chain to inflation like this:

The flowchart illustrates the causal chain to inflation with expectations. It begins with an expected inflation and a bargaining gap in the economy, which simultaneously result in wage increases. These increased wages then raises firms’ unit costs, subsequently causing prices to rise, ultimately contributing to the inflation rate.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-12

Figure 4.12 Causal chain with expected inflation.

To work out the inflation rate:

\[\begin{align*} \text{inflation (%)} &\equiv \text{increase in prices (%)} \\ &= \text{increase in costs per unit of output (%)} \\ &= \text{increase in wages (%)}(\text{if wages are the only costs}) \\ &= \text{expected inflation (%) + bargaining gap (%)} \\ \pi_t &= \pi_t^E + \text{gap}_t \end{align*}\]

But Friedman pointed out that with continued low unemployment, inflation would continue rising rather than remain at 5% at point B. To understand why, we ask what happens next. The equation for inflation gives a hint—what will happen to expected inflation?

Expected inflation and the shifting Phillips curve

With low unemployment continuing, workers will be disappointed with the outcome, since they did not achieve their expected real wage. Why not? Workers expected a 2% real wage increase at B from their nominal pay rise of 5% (to give the real wage on the wage-setting curve), but they did not get this because firms raised their prices by 5%, thereby wiping out the real wage increase.

Remember that in the model, we assume firms can choose to set their prices straight after the wage round and that wages are not ‘reset’ for another year. This means that the real wage workers get is on the PS (not the WS) curve.

But the story does not end there. We know it is impossible for both parties to be satisfied with the outcome at low unemployment, because their claims add up to more than the size of the pie. What happens next depends on what workers expect inflation to be over the coming year. Higher expected inflation will shift the Phillips curve up.

We will model expected inflation by assuming that workers expect inflation over the year ahead to be equal to inflation over the last year—in this case, 5%. At the next wage-setting round, the human resources department has to take into account the fact that their employees expect prices to rise by 5%. So, in order to achieve a real wage increase of 2%, the size of the bargaining gap, the HR department sets a nominal wage increase of 7%.

Expected inflation equal to last year’s inflation is a simple form of so-called adaptive expectations, where expectations adapt to previous experience. Another interpretation is that HR includes inflation over the past year in the wage settlement, to make up for the shortfall in the real wage that workers experienced because inflation turned out to be higher than expected.

In response, the marketing department will increase prices to compensate for the higher unit costs, and the rate of inflation continues to increase.

The table in Figure 4.13 summarizes the situation. We compare inflation over a three-year period with unemployment at two different levels: 6% and 4%.

Year Unemployment Expected inflation Bargaining gap Inflation
Equilibrium employment; stable inflation 1 6% 3% 0% 3%
2 6% 3% 0% 3%
3 6% 3% 0% 3%
Lower unemployment; rising inflation 1 4% 3% 2% 5%
2 4% 5% 2% 7%
3 4% 7% 2% 9%

Figure 4.13 Unstable Phillips curves: expected inflation and the bargaining gap.

The Expected inflation column of Figure 4.13 reflects forward-looking behaviour. Each year, expected inflation over the year ahead is equal to the previous year’s inflation. Then expected inflation together with the bargaining gap determines the actual inflation outcome, shown in the final column.

We can summarize the causal chain from the last period’s inflation rate to this period’s inflation rate like this:

The flowchart depicts the causal progression from last year’s inflation to the inflation experienced this year. Initially, last year’s inflation translates into the expected inflation for this year. Subsequently, the combination of expected inflation and bargaining gap causes the increases in wages, resulting in increased unit costs. This, in turn, leads to price increases, culminating in inflation for this year.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-14

Figure 4.14 Causal chain from last year’s inflation to this year’s inflation.

To work out the inflation rate, we now have an extra step using \(\pi_t^E = \pi_{t-1}\):

\[\begin{align*} \text{inflation (%)} &\equiv \text{increase in prices (%)} \\ &= \text{increase in costs per unit of output (%)} \\ &= \text{increase in wages (%)}\text{(if wages are the only costs)} \\ &= \text{expected inflation (%)} + \text{bargaining gap (%)} \\ &= \text{last period's inflation} + \text{bargaining gap (%)} \\ \pi_t &= \pi_{t-1} + \text{gap}_t \end{align*}\]

The table in Figure 4.13 shows how a boom, in which unemployment falls below the equilibrium level (6%) to 4%, results in rising inflation. Figure 4.15 illustrates the same situation using the Phillips curve and WS–PS diagrams. Work through the diagrams below and then read the explanation that follows.

Note that each Phillips curve is labelled by the expected inflation rate at equilibrium unemployment: only at the supply-side equilibrium, is actual inflation equal to expected inflation.

: There are 2 diagrams. In diagram 1, the horizontal axis shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical line at the end of the horizontal axis is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted on the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. In diagram 1, the business cycle boom is depicted by point B situated on the PS curve but below the WS curve. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve above point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%. In diagram 2, an additional Phillips curve is depicted, maintaining the same shape as the original curve. However, it is positioned above the initial one due to a higher expected inflation rate of 5%, compared to the initial curve with an expected inflation rate of 3%. Point C is depicted directly above point B, representing an equivalent employment level of 4% but with a higher vertical coordinate. The vertical coordinate of point C corresponds to a 7% inflation rate, derived from the sum of the 2% bargaining gap and the 5% expected inflation rate.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-15

Figure 4.15 Inflation expectations and Phillips curves.

Supply-side equilibrium at A: There are 2 diagrams. In diagram 1, the horizontal axis shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical line at the end of the horizontal axis is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted on the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-15a

Supply-side equilibrium at A

Initially expected inflation is 3%. The diagram shows the corresponding Phillips curve. Unemployment is at the equilibrium level, so inflation is 3% as expected.

A boom: first period at B: There are 2 diagrams. In diagram 1, the horizontal axis shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical line at the end of the horizontal axis is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted on the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. In diagram 1, the business cycle boom is depicted by point B situated on the PS curve but below the WS curve. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve above point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-15b

A boom: first period at B

At lower unemployment, the bargaining gap is 2%. Inflation is equal to expected inflation plus the bargaining gap. It rises to 5%.

A boom: next period at C: There are 2 diagrams. In diagram 1, the horizontal axis shows employment and the vertical axis shows real wage. Coordinates are (employment, real wage). The vertical line at the end of the horizontal axis is labeled labour force. Two horizontal lines are depicted: one indicating output per worker and the other labeled PS curve, with output per worker positioned above the PS line. Output per worker and real wage are λ and 100 respectively, labled at the vertical axis. An upward-sloping, convex curve labeled WS curve intersects with both horizontal lines. The point of intersection between the WS and PS curves, labeled as point A, represents the supply-side equilibrium. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. One upward-sloping, convex line is labeled Phillips Curve at an inflation expectation level 3%. Point A, replicated from diagram 1, is depicted on the Phillips Curve, where its vertical coordinate indicates the expected inflation rate of 3%, and its horizontal coordinate represents employment at the supply-side equilibrium where there is no bargaining gap, corresponding to a 6% inflation-stabilising unemployment rate. In diagram 1, the business cycle boom is depicted by point B situated on the PS curve but below the WS curve. The horizontal coordinate of point B indicates a higher employment level compared to point A. With B’s employment level, the real wage captured by the WS curve, indicated as 102, surpasses that of the PS curve, indicated as 100, resulting in a positive bargaining gap of 2%. In diagram 2, point B is replicated from diagram 1 and located on the Phillips Curve above point A. B’s vertical coordinates represent a higher inflation rate of 5%, while the horizontal coordinates represent an unemployment level falling short of equilibrium at 4%. In diagram 2, an additional Phillips curve is depicted, maintaining the same shape as the original curve. However, it is positioned above the initial one due to a higher expected inflation rate of 5%, compared to the initial curve with an expected inflation rate of 3%. Point C is depicted directly above point B, representing an equivalent employment level of 4% but with a higher vertical coordinate. The vertical coordinate of point C corresponds to a 7% inflation rate, derived from the sum of the 2% bargaining gap and the 5% expected inflation rate.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-15c

A boom: next period at C

Next period, expected inflation is equal to last period’s inflation, 5%. So the Phillips curve has shifted up. With unemployment still below the equilibrium level, inflation is equal to expected inflation plus the bargaining gap. It rises to 7%.

wage–price spiral
This occurs if an initial increase in wages in the economy is followed by an increase in the price level, which is followed by an increase in wages and so on. It can also begin with an initial increase in the price level.

At point A, with unemployment of 6% and inflation of 3%, inflation remains stable, year after year. A boom reduces unemployment to 4%. When inflation expectations in the year are 3%, there is a movement along the Phillips curve to B and inflation is 5%. In the next year, at the same low unemployment, inflation is expected to be 5% and the Phillips curve shifts up from the one through point B to the one through point C. This is called the wage–price spiral. It explains why, at low unemployment, inflation rises, not just in the year that unemployment fell, but year after year.

Question 4.5 Choose the correct answer(s)

Figure 4.15 shows the supply-side WS–PS model and the Phillips curve model, incorporating inflation expectations.

Based on this information, read the following statements and choose the correct option(s).

  • There is a supply-side equilibrium at zero inflation and 6% unemployment rate.
  • With the fall in the unemployment rate to 4%, the Phillips curve shifts up immediately.
  • The bargaining gap returns to zero after firms have set their prices.
  • A rising inflation rate for a given unemployment rate is consistent with wage setters updating their expectations of inflation in a situation in which there is a positive bargaining gap.
  • In this diagram, the supply-side equilibrium occurs at an unemployment rate of 6% (where the WS and PS curves intersect). If expected inflation is 0%, then there will be a Phillips curve going through the horizontal axis (that is, with inflation of zero) at the unemployment rate of 6%. More generally, there will be an equilibrium at \(U = 6\%\) for any expected rate of inflation. In equilibrium, inflation will be equal to its expected level and the economy will remain there until there is a shock.
  • With unemployment at 4%, initially the wage rises along the Phillips curve through point A to point B. The shift in the curve occurs only at the next round of wage setting when the previous period’s inflation feeds into the next period’s expected inflation.
  • With the unemployment rate stable at 4%, the bargaining gap remains at 2%. This causes the inflation rate to rise further in subsequent wage rounds.
  • The Phillips curve continues to shift upwards as long as there is a positive bargaining gap, caused by the low unemployment rate.

Exercise 4.7 A negative aggregate demand shock with high unemployment

Copy Figure 4.15, making sure you leave plenty of space to the left of the 6% unemployment marker. Assume that from an initial position at A, there is a negative shock to private sector demand such as depressed private investment, which raises unemployment to 9%.

  1. Show the inflation, expected inflation, and the bargaining gap at the new level of unemployment on your diagram.
  2. What do you predict will happen to inflation over the following two years, assuming there is no further change in unemployment? 
  3. Draw the Phillips curves and write a brief explanation of your findings.

By plotting the path of inflation over time in Figure 4.16, we can determine the distinctive contributions of the bargaining gap and expected inflation to inflation. In this example, the bargaining gap opens up in year 1 because of the move to low unemployment. The assumption that unemployment remains below the inflation-stabilizing rate is reflected in the persistence of the bargaining gap. Inflation rises in every period because the previous period’s inflation feeds into expected inflation and therefore into wage and price inflation. Note that the real wage does not change, but remains on the price-setting curve.

: In the diagram, the horizontal axis shows years starting in year 0 and ending in year 6. The vertical axis shows inflation rate in percentages, ranging from 0 to 11%. The coordiantes are (Years, Inflation). The paths of 3 vairables, inflation, expected inflation which equals last year’s inflation, and bargaining gap, are to be plotted. At the start of year 0, the bargaining gap is depicted as a horizontal line at zero on the vertical axis. The inflation line, positioned above the bargaining gap, shows a 3% inflation rate. An arrow is depicted on the graph to illustrate its path of changes. At the start of year 1, the bargaining gap line exhibits a rise to 2%, captured by a vertical ascent from 0 to 2%, followed by a horizontal trajectory throughout the entirety of year 1. Simultaneously, the inflation line mirrors this increase of 2%, illustrated by an upward arrow and a vertical line extending from 3% to 5% at the commencement of year 1, followed by a horizontal alignment for the duration of the year. The expected inflation line starts at 3%, the inflation rate in year 0, and extends horizontally from the start of year 0 to the end of year 1. At the start of year 2, the bargaining gap remains at 2%, depicted by a horizontal line persisting at the 2% vertical coordinate throughout. Simultaneously, the expected inflation line rises to 5% that equals year 1’s inflation rate, depicted by a vertical ascent from 3% to 5% at the start of year 2, maintaining a consistent level for the remainder of the year. The inflation line displays a similar step-wise progression but is positioned above, with a 2% increase in the inflation rate. This is illustrated by an upward arrow and a vertical increase from 5% to 7% at the start of year 2, followed by a horzizontal path for the remainder of the period. For the following years, a consistent 2% bargaining gap is represented by the horizontal bargaining gap line from year 1 to year 6, maintaining 2% in its vertical coordinate. Meanwhile, both the inflation and expected inflation lines exhibit a steady, step-wise upward trajectory, increasing by 2% annually. The inflation line is persistently positioned above the expected inflation line, maintaining a 2% vertical gap, equaling the positive bargaining gap throughout the depicted years. The inflation rate depicted by the inflation line eventually reached 11% in year 5.
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Figure 4.16 Inflation, expected inflation, and the bargaining gap.

A zero bargaining gap: In the diagram, the horizontal axis shows years starting in year 0 and ending in year 6. The vertical axis shows inflation rate in percentages, ranging from 0 to 11%. The coordiantes are (Years, Inflation). The paths of 3 vairables, inflation, expected inflation which equals last year’s inflation, and bargaining gap, are to be plotted. At the start of year 0, the bargaining gap is depicted as a horizontal line at zero on the vertical axis. The inflation line, positioned above the bargaining gap, shows a 3% inflation rate. An arrow is depicted on the graph to illustrate its path of changes.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-16a

A zero bargaining gap

At the start of year 0, inflation is as expected: 3%.

Year 1: In the diagram, the horizontal axis shows years starting in year 0 and ending in year 6. The vertical axis shows inflation rate in percentages, ranging from 0 to 11%. The coordiantes are (Years, Inflation). The paths of 3 vairables, inflation, expected inflation which equals last year’s inflation, and bargaining gap, are to be plotted. At the start of year 0, the bargaining gap is depicted as a horizontal line at zero on the vertical axis. The inflation line, positioned above the bargaining gap, shows a 3% inflation rate. An arrow is depicted on the graph to illustrate its path of changes. At the start of year 1, the bargaining gap line exhibits a rise to 2%, captured by a vertical ascent from 0 to 2%, followed by a horizontal trajectory throughout the entirety of year 1. Simultaneously, the inflation line mirrors this increase of 2%, illustrated by an upward arrow and a vertical line extending from 3% to 5% at the commencement of year 1, followed by a horizontal alignment for the duration of the year. The expected inflation line starts at 3%, the inflation rate in year 0, and extends horizontally from the start of year 0 to the end of year 1.
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Year 1

At the start of year 1, following the opening up of the bargaining gap and after wages and prices have been adjusted, inflation is equal to the bargaining gap (2%) plus expected inflation (3%).

Year 2: In the diagram, the horizontal axis shows years starting in year 0 and ending in year 6. The vertical axis shows inflation rate in percentages, ranging from 0 to 11%. The coordiantes are (Years, Inflation). The paths of 3 vairables, inflation, expected inflation which equals last year’s inflation, and bargaining gap, are to be plotted. At the start of year 0, the bargaining gap is depicted as a horizontal line at zero on the vertical axis. The inflation line, positioned above the bargaining gap, shows a 3% inflation rate. An arrow is depicted on the graph to illustrate its path of changes. At the start of year 1, the bargaining gap line exhibits a rise to 2%, captured by a vertical ascent from 0 to 2%, followed by a horizontal trajectory throughout the entirety of year 1. Simultaneously, the inflation line mirrors this increase of 2%, illustrated by an upward arrow and a vertical line extending from 3% to 5% at the commencement of year 1, followed by a horizontal alignment for the duration of the year. The expected inflation line starts at 3%, the inflation rate in year 0, and extends horizontally from the start of year 0 to the end of year 1. At the start of year 2, the bargaining gap remains at 2%, depicted by a horizontal line persisting at the 2% vertical coordinate throughout. Simultaneously, the expected inflation line rises to 5% that equals year 1’s inflation rate, depicted by a vertical ascent from 3% to 5% at the start of year 2, maintaining a consistent level for the remainder of the year. The inflation line displays a similar step-wise progression but is positioned above, with a 2% increase in the inflation rate. This is illustrated by an upward arrow and a vertical increase from 5% to 7% at the start of year 2, followed by a horzizontal path for the remainder of the period.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-16c

Year 2

At the start of year 2, with no change in the bargaining gap, inflation goes up to 7%, equal to the bargaining gap plus expected inflation.

… and each year afterwards: In the diagram, the horizontal axis shows years starting in year 0 and ending in year 6. The vertical axis shows inflation rate in percentages, ranging from 0 to 11%. The coordiantes are (Years, Inflation). The paths of 3 vairables, inflation, expected inflation which equals last year’s inflation, and bargaining gap, are to be plotted. At the start of year 0, the bargaining gap is depicted as a horizontal line at zero on the vertical axis. The inflation line, positioned above the bargaining gap, shows a 3% inflation rate. An arrow is depicted on the graph to illustrate its path of changes. At the start of year 1, the bargaining gap line exhibits a rise to 2%, captured by a vertical ascent from 0 to 2%, followed by a horizontal trajectory throughout the entirety of year 1. Simultaneously, the inflation line mirrors this increase of 2%, illustrated by an upward arrow and a vertical line extending from 3% to 5% at the commencement of year 1, followed by a horizontal alignment for the duration of the year. The expected inflation line starts at 3%, the inflation rate in year 0, and extends horizontally from the start of year 0 to the end of year 1. At the start of year 2, the bargaining gap remains at 2%, depicted by a horizontal line persisting at the 2% vertical coordinate throughout. Simultaneously, the expected inflation line rises to 5% that equals year 1’s inflation rate, depicted by a vertical ascent from 3% to 5% at the start of year 2, maintaining a consistent level for the remainder of the year. The inflation line displays a similar step-wise progression but is positioned above, with a 2% increase in the inflation rate. This is illustrated by an upward arrow and a vertical increase from 5% to 7% at the start of year 2, followed by a horzizontal path for the remainder of the period. For the following years, a consistent 2% bargaining gap is represented by the horizontal bargaining gap line from year 1 to year 6, maintaining 2% in its vertical coordinate. Meanwhile, both the inflation and expected inflation lines exhibit a steady, step-wise upward trajectory, increasing by 2% annually. The inflation line is persistently positioned above the expected inflation line, maintaining a 2% vertical gap, equaling the positive bargaining gap throughout the depicted years. The inflation rate depicted by the inflation line eventually reached 11% in year 5.
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https://www.core-econ.org/macroeconomics/04-inflation-and-employment-06-expected-inflation-shifts-phillips-curve.html#figure-4-16d

… and each year afterwards

As long as the bargaining gap remains unchanged, inflation rises each year.

To summarize, inflation will continue to rise period by period if the bargaining gap persists and the expected rate of inflation rises, shifting the Phillips curve up. We can model expected inflation over the year ahead by assuming it is equal to inflation over the past year.

Exercise 4.8 Inflation, expected inflation, and the bargaining gap

Use the same axes as in Figure 4.16 to plot inflation, expected inflation, and the bargaining gap in a single diagram. Assume that the price level is constant in year 0. The economy is hit by a recession at the beginning of period 1 and unemployment remains at a constant high level until the beginning of period 6.

  1. Plot the path of the bargaining gap.
  2. Plot the path of inflation and expected inflation.
  3. Give a brief explanation of why the bargaining gap might have disappeared and state any other assumptions you are making. Summarize your findings.
  1. Milton Friedman. 1968. ‘The Role of Monetary Policy’. The American Economic Review 58 (1): pp. 1–17.