Summary
Derives the Phillips Curve from wage-setting and price-setting equations, linking inflation to unemployment. Recitation walkthrough covering the same material as The Phillips Curve and Inflation.
We will discuss labor markets, especially understanding price changes through wage setting. We’ll also discuss the Phillips Curve and derive the relationship between unemployment and inflation.
Intuitively, wages are set when what firms are willing to pay equals what workers want. To model this, we have two equations:
This is the workers’ wage-setting equation, which is a function of expected future prices and labor market conditions. When unemployment is low, workers have more bargaining power, pushing wages up. The catchall captures things like unemployment benefits and employment protections. The second equation:
is the firms’ price-setting equation, which comes from setting price as marginal cost times some markup . Here, wages are the marginal cost of a unit of labor (since we assume , i.e., one worker produces one unit of output).
From Wages to Prices
Since firms set prices based on market wage, we can substitute the wage-setting equation into the price-setting equation to get:
Note that when (expectations are correct), we recover the natural rate of unemployment: .
More generally, and labor market conditions drive price changes. This equation shows how wage-setting conditions produce a relationship between inflation and unemployment.
To derive the Phillips Curve, we give a functional form . Divide each side by last period’s prices:
Notice that and . Taking logs and using for small , we get the Phillips Curve:
Intuitively, firms need to raise wages when unemployment is low and labor market conditions are good. Higher wages lead to higher prices, which causes inflation. The parameter captures how sensitive inflation is to labor market slack.
In our model, moves one-for-one. If the Fed wants to target , inflation expectations need to be aligned with this. When this happens (), we say inflation is [[The IS-LM-PC Model#anchored-vs-de-anchored-expectations|anchored]]. With anchored expectations, the central bank can stabilize inflation without causing a recession, but de-anchored expectations (as in the 1970s) require painful unemployment to bring inflation back down.
We can also think of the natural rate of unemployment as what we get when expected inflation equals realized inflation:
Plugging this into the Phillips Curve gets
When the economy runs hot (), inflation exceeds expectations. When there’s slack (), inflation falls below expectations. This form of the Phillips Curve is what feeds into the The IS-LM-PC Model.