Both the short- and long-run Philips curves show a relationship between inflation and unemployment.
In the short run, the Philips curve is downward-sloping. The Y-axis is inflation and the X-axis is unemployment. This shows that as unemployment increases, inflation decreases and vice versa.
We can also think about this from the aggregate demand and supply standpoint. When aggregate demand decreases, consumers spend less (therefore price level and inflation decrease). When consumers spend less money, businesses lay off employees and unemployment increases.
The long-run Philips curve is a vertical line. This shows that in the long run there is no trade-off between unemployment and inflation. In the aggregate demand and supply model, we know that the economy will always come back to equilibrium (long-run aggregate supply), and the same applies here: the economy will eventually always come back to the long-run Philips curve.
Now on the Philips curve graph, the long-run Philips curve is at the natural rate of unemployment. It is a vertical line at 4–6% unemployment. The only way the long-run Philips curve shifts left or right is if the natural rate of unemployment changes.
Sometimes this confuses students because they notice that the long-run Philips curve and the long-run aggregate supply curve are both at the natural rate of unemployment. However, when the economy experiences growth, the long-run aggregate supply curve shifts right, but the long-run Philips curve does not shift, because the natural rate of unemployment has not changed. Why does one move and not the other?
It comes down to what each graph measures. The Philips curve measures unemployment on the x-axis. Unemployment isn't changing, so the long-run Philips curve will not shift. The x-axis on the aggregate demand and supply model measures real GDP. When the economy grows, real GDP increases; therefore, the long-run aggregate supply curve will shift to the right. Even though we know that the long-run aggregate supply curve is at the natural rate of unemployment, the x-axis doesn't measure unemployment—it measures real GDP.
What about short-run aggregate supply and the short-run Philips curve? When short-run aggregate supply increases (shifts right), then the short-run Philips curve will shift left. Why? Let's think about what happens when short-run aggregate supply shifts right. The price level will decrease and unemployment will decrease. How can we show both of these changes on the Philips curve? If we move along the Philips curve, we can only increase inflation and decrease unemployment, but not both. We need both measures (inflation and unemployment) to decrease. The only way to do this is to shift the Philips curve to the left.
Think of short-run aggregate supply and short-run Philips curves as mirrors of one another. When one shifts to the right, the other shifts to the left.
Aggregate demand and the short-run Philips curves work a little bit differently. Let's start by increasing aggregate demand. When aggregate demand increases, price level increases and unemployment decreases. When we look at the Philips curve, we can see that by sliding a point on the Philips curve to the left, we can increase inflation and decrease unemployment.
So, when aggregate demand shifts right, the short-run Philips curve slides along the graph to the left and vice versa.