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.

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:

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).