A question was recently asked: If the Phillips curve is _____ in the long run, there is no trade-off between inflation and unemployment in the long run. In order to answer this question we will have to understand two things, how to graph relationships between two variables, and what the Phillip's curve looks like. The Phillip's curve attempts to show the theoretical relationship between the inflation rate, and the unemployment rate in an economy. The two have a significant relationship if we change one of the variables, say inflation, and we see that this causes a change in unemployment. Lets test this idea on the graph to the left to see if we can come up with any sort of relationship given those two curves.
You can see in the graph below, that when we lower the inflation rate, we increase the unemployment rate. So with these two examples (both showing negative relationships), there IS a tradeoff between inflation and unemployment.
PPFs for a discussion of curve shapes). The only way to draw a line on this Phillip's Curve graph that shows no tradeoff between inflation and unemployment is to draw a line that is vertical or horizontal. If you look at the graph below, you can see that as we change either inflation (if the line is vertical), or unemployment (if the line is horizontal), we see no change in the other variable.