Dynamics versus statics
Let p be an arbitrary price.
Statics assumes a timeless dimension. With supply S[p] and demand D[p], equilibrium (in expectations) is given by S[p] = D[p] and it solves for the equilibrating price p·.
Dynamics concerns developments in time. The price movement p’ = dp/dt is related to excess demand D[p] - S[p], so that p’ = dp/dt = f[D[p] - S[p]. The solution of this differential equation gives the movement towards equilibrium. Dynamics causes different concepts of equilibrium: depending upon the specification of variables and function, the equilibrium can be market clearing (p°) or the fulfillment of expectations (p*). Economic agents generally have different speeds of reaction when expectations are not fulfilled. When there are surprises, there can be a ‘trade-off’ between prices and quantities.
Phillipscurve
For the labour market, dynamics implies a relationship between unemployment and the change in wages. This relationship is called the (wage-) Phillipscurve. Sometimes there is an additional assumption of a strong relationship between wages and product prices, [74] and then the (price-) Phillipscurve gives the relationship between unemployment and prices.
The existence of a Phillipscurve thus follows essentially from the concept of dynamics itself. For the labour market, the price is the wage w and excess demand is represented by unemployment u (thus negative excess demand; with vacancies neglected partly because of unreliable measurement), so that w’ = f[u]. Much debate in macro-economics about whether the Phillipscurve ‘exists’ or not, could have been cut short by noting that it is a standard market adjustment equation. The true debate is about the proper form and stability of its parameters.
In the simplest model we choose inflation, [75] and have, with u = 1 - LE /LS:
dLog[P] = f[u]
and this would add another restriction that closes the model. For example: