Unit 4 Inflation and unemployment

4.5 Modelling the relationship between inflation and unemployment

In the previous section, we saw that when the rate of unemployment is lower, the wage-setting and price-setting model predicts higher wage and price inflation, similar to Phillips’ empirical observations. We will now derive the Phillips curve relationship between inflation and unemployment graphically from the WS–PS model. Remember the assumptions in the WS–PS model:

  • The only input used in production is labour.
  • The real wage, \(w\), that workers care about is their nominal wage, \(W\), relative to the economy-wide level of prices, and is defined as:
\[w = \frac{W}{P}\]
  • HR departments of firms set nominal wages (for example, in dollars, pounds, or euros) once a year sufficiently high to get the required effort from workers taking the unemployment rate as given.
  • Immediately after wages are set, marketing departments set prices.

To understand how inflation comes about in a business cycle upswing, we begin with the economy at the supply-side equilibrium and with constant prices and wages: inflation is zero. To simplify the calculations, we use an index for the real wage: it is equal to 100 in the initial equilibrium. Then, a rise in aggregate demand reduces unemployment.

bargaining gap
The difference between the real wage that firms wish to offer in order to recruit/retain workers and provide them with incentives to work, and the real wage that allows firms the markup that maximizes profits given the degree of competition.
  • Since unemployment is low, the HR department needs to set higher wages to recruit and retain workers. Wages rise by, say, 2%.
  • Higher wages mean higher costs for firms: Firms’ costs rise by 2%.
  • To cover the higher wage costs, the marketing department will raise prices by the same percentage. This is because competitive conditions have not changed, so the profit share is constant. Prices rise by 2%.
  • Since wages and prices both increased by 2%, there is no change in the real wage: \(\frac{W}{P}\) is at its initial level equal to the wage on the PS curve.
  • There is a gap between the real wage workers get (\(w^{\text{PS}}\) on the PS curve) and what they had expected (\(w^{\text{WS}}\) on the WS curve). This is called the bargaining gap, or ‘gap’ for short. In this example, the bargaining gap is 2%, which is calculated like this:
\[\text{bargaining gap} \equiv \frac{w^{\text{WS}} − w^{\text{PS}}}{w^{\text{PS}}} = \frac{102-100}{100} = 2\]
  • The economy has experienced wage and price inflation of 2%.

What happens next? We assume that aggregate demand remains unchanged. Unemployment is therefore still below the supply-side equilibrium. At the next annual round of wage setting, HR departments are in the same position as the previous year: with continuing low unemployment, workers are disappointed with their real wage (unchanged at its initial level). HR must raise nominal wages. When costs go up, the marketing departments immediately raise prices once more.

With our assumptions about the nature and timing of the wage- and price-setting process, the level of inflation is exactly equal to the bargaining gap in each year. Work through Figure 4.9 to understand how the Phillips curve relationship between the unemployment rate and the inflation rate is derived graphically.

Bargaining gaps, inflation, and the Phillips curve.: There are 2 diagrams. In diagram 1, the horizontal diagram 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. The PS curve intersects with the upward-sloping, convex curve labeled WS curve. This intersection is marked by point A, representing the supply-side equilibrium. The horizontal coordinate of point A represents employment at supply-side equilibrium, where there’s no bargaining gap. The horizontal distance from Point A to the vertical labour force line captures the corresponding unemployment level of 7%, labelled as structual unemployment. Point B located on the PS curve but below the WS curve indicates a higher employment level with a positive bargaining gap of 2%. Point C located on the PS curve but above the WS curve indicates a lower employment level with a negative bargaining gap of −1%. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate, ranging from −2% to 8%. One upward-sloping, convex line is labeled Phillips curve at an inflation expectation level 3%. Points A, B, and C are replicated from diagram 1,  all of which are lying on the Phillips curve. The vertical coordinate of A indicates an inflation rate of 3%, while B indicates a higher inflation rate of 5% equaling to the sum of the 2% bargaining gap and 3% expected inflation, and C indicates a lower inflation rate of 2% equaling to the sum of the −1% bargaining gap and 3% expected inflation.
Fullscreen
https://www.core-econ.org/macroeconomics/04-inflation-and-employment-05-modelling-relationship-inflation-unemployment.html#figure-4-9

Bargaining gaps, inflation, and the Phillips curve.

Figure 4.9 Bargaining gaps, inflation, and the Phillips curve.

The bargaining gap: 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 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 where the bargaining gap is zero. At Point B, positioned on the PS curve but below the WS curve, the employment level is higher than equilibrium at A and corresponds to a real wage of 102 on the WS curve, whereas it is 100 on the PS curve, resulting in a positive bargaining gap of 2%. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. Coordinates are (employment, inflation rate). The points A and B are replicated from diagram 1 with their original employment levels. Positioned to the northeast of point A, point B reflects a higher employment level, surpassing the equilibrium displayed at A. Additionally, B’s vertical coordinate represents a 2% inflation rate, equivalent to the bargaining gap, which exceeds the equilibrium level represented by point A, where the vertical coordinate is zero, indicating zero inflation rate.
Fullscreen
https://www.core-econ.org/macroeconomics/04-inflation-and-employment-05-modelling-relationship-inflation-unemployment.html#figure-4-9a

The bargaining gap

The bottom panel plots the bargaining gap associated with different levels of employment. At point A, the economy is in labour market equilibrium so the bargaining gap is 0%. At point B, the real wage demanded by workers is 102 while the price-setting real wage is 100, so the bargaining gap is 2%.

The Phillips curve: 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 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 where the bargaining gap is zero. At Point B, positioned on the PS curve but below the WS curve, the employment level is higher than equilibrium at A and corresponds to a real wage of 102 on the WS curve, whereas it is 100 on the PS curve, resulting in a positive bargaining gap of 2%. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. Coordinates are (employment, inflation rate). The points A and B are replicated from diagram 1 with their original employment levels. Positioned to the northeast of point A, point B reflects a higher employment level, surpassing the equilibrium displayed at A. Additionally, B’s vertical coordinate represents a 2% inflation rate, equivalent to the bargaining gap, which exceeds the equilibrium level represented by point A, where the vertical coordinate is zero, indicating zero inflation rate. In diagram 2, an upward-sloping, convex curve is depicted to represent the Phillips curve. Both points A and B lie on this curve, with A representing its intersection with the horizontal axis.
Fullscreen
https://www.core-econ.org/macroeconomics/04-inflation-and-employment-05-modelling-relationship-inflation-unemployment.html#figure-4-9b

The Phillips curve

At point B, the bargaining gap of 2% causes wages and prices to rise by 2%. Since the inflation rate is equal to the bargaining gap, point A (bargaining gap of 0%) and point B (bargaining gap of 2%) are both points on the Phillips curve. Inflation is zero at A, and 2% at B.

Deflation: 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 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 where the bargaining gap is zero. At Point B, positioned on the PS curve but below the WS curve, the employment level is higher than equilibrium at A and corresponds to a real wage of 102 on the WS curve, whereas it is 100 on the PS curve, resulting in a positive bargaining gap of 2%. In diagram 2, the horizontal axis displays employment and the vertical axis displays inflation rate. Coordinates are (employment, inflation rate). The points A and B are replicated from diagram 1 with their original employment levels. Positioned to the northeast of point A, point B reflects a higher employment level, surpassing the equilibrium displayed at A. Additionally, B’s vertical coordinate represents a 2% inflation rate, equivalent to the bargaining gap, which exceeds the equilibrium level represented by point A, where the vertical coordinate is zero, indicating zero inflation rate. In diagram 2, an upward-sloping, convex curve is depicted to represent the Phillips curve. Both points A and B lie on this curve, with A representing its intersection with the horizontal axis. In diagram 1, an additional point C is situated on the PS curve and above the WS curve. At Point C, the employment level is lower than equilibrium at A and corresponds to a real wage of 99 on the WS curve but 100 on the PS curve, resulting in a negative bargaining gap of -1%. In diagram 2, point C, replicated from Diagram 1, is positioned southwest of point A on the Phillips curve. Its horizontal coordinate represents a lower employment level compared to point A that signifies employment at supply-side equilibrium. The vertical coordinate of point C is negative, indicating deflation of -1%, contrasting with point A that represents zero inflation rate with no bargaining gap.
Fullscreen
https://www.core-econ.org/macroeconomics/04-inflation-and-employment-05-modelling-relationship-inflation-unemployment.html#figure-4-9c

Deflation

At point C, the bargaining gap in the top panel is negative (−1%), so there is deflation (bottom panel).

The final slide shows that if there is a recession instead of a boom, there is a negative bargaining gap, and the price level falls year after year. This is deflation. The model predicts that we will observe lower unemployment with higher inflation or higher unemployment with lower inflation as in Phillips’ original empirical scatter plot (Figure 4.8).

In our model, where the assumptions lead to a constant (horizontal) price-setting real wage and an inflation rate equal to the bargaining gap, the Phillips curve is exactly the same shape as the WS curve.

The bargaining gap and the Phillips curve

We can summarize the causal chain from the bargaining gap to inflation like this:

This flowchart outlines the causal chain leading from a bargaining gap to inflation. Initially, a bargaining gap results in an increase in wages. This, in turn, causes an increase in unit costs. The rise in unit costs then leads to higher prices, culminating in inflation.
Fullscreen
https://www.core-econ.org/macroeconomics/04-inflation-and-employment-05-modelling-relationship-inflation-unemployment.html#figure-4-10

Figure 4.10 Deriving the Phillips curve from the causal chain from higher aggregate demand to lower unemployment and higher inflation.

So, to work out the inflation rate, we use the following:

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

where \(\text{gap}_t\) is the bargaining gap defined above and \(\pi_t\) is inflation in year t. The subscript ‘t’ refers to the year or period ‘t’. The symbol ‘≡’ on the first line indicates that inflation is equal to the percentage increase in prices by definition. The equalities at the following steps are predictions of the model.

To summarize, we model inflation as a process in which the timing of nominal wage and price setting means that firms set real wages. When unemployment is lower so that \(\text{WS} > \text{PS}\), workers want, and get, higher nominal wages because their alternative options in the labour market have improved, but firms immediately raise prices so that real wages are unchanged (on the PS). This results in the Phillips curve: inflation is driven by the bargaining gap between the real wage workers want (on the WS) and the wage that they actually get (on the PS).

Exercise 4.5 The bargaining gap in a recession

Suppose the economy is initially at supply-side equilibrium with stable prices (inflation is zero). At the beginning of year 1, investment falls and the economy moves into recession with high unemployment.

  1. Explain why a negative bargaining gap arises.
  2. Assume the negative bargaining gap is 1%. Draw a diagram with years on the horizontal axis and the price level on the vertical axis. Starting from a price index of 100, sketch the path of the price level for the 5 years that follow, assuming the bargaining gap remains at −1%.
  3. Who are the winners and losers in this economy?

Exercise 4.6 Positive and negative shocks

Draw a WS–PS diagram where the economy is at supply-side equilibrium with stable prices. Now consider:

  • a positive shock to aggregate demand that reduces the unemployment rate by 2 percentage points
  • a negative shock that increases it by 2 percentage points.
  1. What happens to the bargaining gap in each case?
  2. What would you expect to happen to the price level in each case? Explain your answers.

Question 4.4 Choose the correct answer(s)

Figure 4.9 shows the relationship between the WS–PS diagram and the Phillips curve. Based on this information, read the following statements and choose the correct option(s).

  • If the real wage was on the WS when employment is at point C, the markup is too high.
  • If the real wage was on the WS when employment is at point C, the profit share is too low.
  • If employment is at C and there is a negative shock to aggregate demand, the economy will definitely experience deflation.
  • If employment is at C and there is a positive shock to aggregate demand, the economy will definitely experience inflation.
  • Point C is above the wage-setting curve, which means that the real wage is lower than is consistent with a firm’s profit-maximizing markup. If the real wage is too low, it means the markup is too high.
  • Competitive conditions in the economy imply a profit share shown by point A, so a profit share shown by point C is too high.
  • The bargaining gap becomes more negative, which means the economy is still experiencing deflation.
  • It depends on whether the positive shock moves employment to a level higher than that at point A or not.