On a different forum for Civil Service aspirants, someone asked the following:
"According to my professor, it is the relationship between inflation and output. Same explanation is given in my text books (Robert J. Gordon/Charles Jones) and it fits reasonably well while explaining monetary policy and other macroeconomic phenomena. But, Gregory Mankiw(another popular book) defines it as the relationship between inflation and unemployment.
Since there is another rule called Okun's law which relates output to unemployment, is it right to define Phillips curve in Mankiw's way?"
My response as follows:
Notwithstanding the fact that your professor did not further elaborate how the output(GDP) correlates to relationship b/w Inflation and employment levels, on which Phillips curve is based, I think both the sources for your understanding about Phillips Curve are correct.
As we know Inflation and Unemployment level are two very fundamental indicators of economic performance. The relationship between these two basic indicators - Inflation and Unemployment in short run, when Aggregate Demand(AD) shifts left or right on Short Run Aggregate Supply(SRAS) curve is called Phillips Curve.
In other words, in short run economy faces a tradeoff between Inflation and Unemployment and this is the fundamental point which comes out in Phillips Curve.
Equilibrium condition is the AD curve on right(sold BLACK line on right) and assumes that the economy is producing at its full employment level. This when we draw back on Phillips curve, corresponds to point A.
Say due to some wave of optimism, lets assume real estate boom, firms(investment) and consumers(consumption) start spending and to sustain the momentum govt. also starts expending(govt. expenses), which leads to AD curve move up along SRAS(shown by BLUE dotted line).
Expansionary Monetary/Fiscal Policies --> Aggregate Demand↑--> Economy move up along SRAS curve --> Unemployment↓ --> Inflation↑
Now assume in a different scenario of controlling the real estate boom, govt. starts lowering its expenditure(consumption) and the central bank controls money supply(investment), the AD curve then moves down along SRAS (shown by RED dotted line).
Contractionary Monetary/Fiscal Policies --> Aggregate Demand↓ --> Economy move down along SRAS curve --> Unemployment↑ --> Inflation↓
So you see how output and unemployment both are related to Phillips curve.