Editing Phillips curve (section)

====Price====
Then, combined with the wage Phillips curve [equation 1] and the assumption made above about the trend behavior of money wages [equation 2], this price-inflation equation gives us a simple expectations-augmented price Phillips curve:

: '''gP''' = −'''f'''('''U''' − '''U*''') + '''λ'''·'''gP<sup>ex</sup>'''.

Some assume that we can simply add in '''gUMC''', the rate of growth of '''UMC''', in order to represent the role of supply shocks (of the sort that plagued the U.S. during the 1970s). This produces a standard short-term Phillips curve:

: '''gP''' = −'''f'''('''U''' − '''U*''')  + '''λ'''·'''gP<sup>ex</sup>''' + '''gUMC'''.

Economist [[Robert J. Gordon]] has called this the "Triangle Model" because it explains short-run inflationary behavior by three factors: demand inflation (due to low unemployment), supply-shock inflation ('''gUMC'''), and inflationary expectations or inertial inflation.

In the ''long run'', it is assumed, inflationary expectations catch up with and equal actual inflation so that '''gP''' = '''gP<sup>ex</sup>'''. This represents the long-term equilibrium of expectations adjustment. Part of this adjustment may involve the adaptation of expectations to the experience with actual inflation. Another might involve guesses made by people in the economy based on other evidence. (The latter idea gave us the notion of so-called [[rational expectations]].)

Expectational equilibrium gives us the long-term Phillips curve. First,  with '''λ''' less than unity:

:'''gP''' = [1/(1 − '''λ''')]·(−'''f'''('''U''' − '''U*''') + '''gUMC''').

This is nothing but a steeper version of the short-run Phillips curve above. Inflation rises as unemployment falls, while this connection is stronger. That is, a low unemployment rate (less than '''U*''') will be associated with a higher inflation rate in the long run than in the short run. This occurs because the actual higher-inflation situation seen in the short run feeds back to raise inflationary expectations, which in turn raises the inflation rate further. Similarly, at high unemployment rates (greater than '''U*''') lead to low inflation
rates. These in turn encourage lower inflationary expectations, so that inflation itself drops again.

This logic goes further if '''λ''' is equal to unity, i.e., if workers are able to protect their wages ''completely'' from expected inflation, even in the short run. Now, the Triangle Model equation becomes:

:- '''f'''('''U''' − '''U*''') = '''gUMC'''.

If we further assume (as seems reasonable) that there are no long-term supply shocks, this can be simplified to become:

: −'''f'''('''U''' − '''U*''') = 0 which implies that  '''U''' = '''U*'''.

All of the assumptions imply that in the long run, there is only one possible unemployment rate, '''U*''' at any one time. This uniqueness explains why some call this unemployment rate "natural".

To truly understand and criticize the uniqueness of '''U*''', a more sophisticated and realistic model is needed. For example, we might introduce the idea that workers in different sectors push for money wage increases that are similar to those in other sectors. Or we might make the model even more realistic. One important place to look is at the determination of the mark-up, '''M'''.