Summary of the Phillips curves

In neo-classical synthesis, augmented Phillips curve is known as the short-run Phillips curve. It is presumed to be stable as long as expectations of future inflation don't change. To summarize, we have three Phillips curves: 

• Traditional Phillips curve. Π_W = f(U) and same downward sloping relationship applies to both the short and the long run.
• Short-run Phillips curve (SPC). Π_w = f(U) + Πe and curve is valid only in the short run (SPC = Short-run Phillips Curve).
• Long-run Phillips curve (LPC). Π_w = Π_M, U = U_N and there is not any relationship between Π_w and U (U_N is natural rate of unemployment).