Intermediate Macroeconomic Theory/Phillips Curve/Phillips Curve

6.1 The Early Phillips Curve
A British economist named A. William Phillips was the first to describe this curve in 1958. Hence its name. He published findings that defined a relationship between unemployment and inflation based on data he'd collected in the U.K.



The curve in its early life basically said that unemployment and inflation are negatively related. When unemployment is low, inflation is high. When unemployment is high, inflation is low. This correlated directly to Phillips findings. Figure 6-1 shows this relationship. The unemployment rate is graphed on the horizontal axis and the inflation rate is graphed on the vertical axis. As you can see when the unemployment rate decreases from u0 to u', the inflation rate climbs. When the unemployment rate increases from u0 to u" the inflation rate drops.

What does this mean? Well essentially, when unemployment decreases more people are employed and output is higher than normal. Higher output and employment leads to an increase in the price level because firms have to pay their workers more. Workers have to pay more because unemployment is low and it is easier for workers to find other jobs and it is difficult for firms to hire new workers; there aren't many people unemployed, i.e. looking for work.

The same is true for high unemployment, only vice-versa. Firms can pay their workers less because there are plenty of unemployed people willing to take that worker's place. So the wage, a factor of price and therefore inflation, is lower.

Simple right? Not quite. As we will see in the next section, this Phillips Curve doesn't quite fit the facts perfectly. Remember this curve very accurately depicted the data available in the 1960s, but it actually fell apart and had to be revised thereafter.

Algebraically
Let's take a look at the math behind this Phillips Curve.

Consider the following formula:

$$ \pi_t = \mathrm{v} -\alpha\left( U_t \right ) $$

where:
 * $$ \pi_t $$ is inflation in year $$ t $$
 * $$ \mathrm{v}\ $$ is a variable denoting exogenous economic shocks
 * $$ \alpha\ $$ is a constant
 * $$ U_t $$ is the unemployment rate in year $$t$$

Note: For now we'll just keep $$ \mathrm{v}\ $$ constant in order to make our analysis simpler.


 * What this tells us is that when unemployment, $$U_t$$, goes up the whole right side of the equation, $$ \mathrm{v} -\alpha\left( U_t \right ) $$ decreases because $$-\alpha\left( U_t \right )$$ becomes bigger. That is, more can be subtracted from $$ \mathrm{v}\ $$ so the whole thing becomes much smaller.


 * Or, conversely, as $$ U_t $$ gets smaller, i.e. unemployment goes down, the whole right side of the equation, $$ \mathrm{v} -\alpha\left( U_t \right ) $$, increases because $$-\alpha\left( U_t \right )$$ becomes smaller. That is, less can be subtracted from $$ \mathrm{v}\ $$ so the whole thing becomes much larger.

This explains how inflation behaves:
 * when $$ U_t $$ is HIGH, $$ \pi_t $$ is low.
 * when $$ U_t $$ is LOW, $$ \pi_t $$ is high.