Show your step-by-step derivation of the Phillips curve equation. Explain how inflation expectations, firms' market power, and unemployment rate may influence inflation rate. Discuss how the Phillips curve equation you've derived can be related to the original Phillips curve, modified Phillips curve, and expectations-augmented Phillips with different values of the parameter . Explain the comments by Milton Friedman and Edmund Phelps in the late 1960s regarding the trade-off implied by the Phillips curve equation.

(Macroeconomics, Fifth Canadian Edition)