On the complexity of simultaneous price-quantity adjustment processes

While the Walrasian price tâtonnement represents the traditional dynamic process in the general equilibrium context with and without production, Walras and other classics designed the process exclusively for pure exchange economies. In productive economies, the short-run output adjustment of existing firms and the entry/exit of firms should be modeled as well. So-called cross-dual processes which represent the classical approach to the dynamics of productive economies are discussed and extended. Complex motion can emerge in a discrete-time version of the original two-dimensional system when the aggregate demand function has a non-standard shape. A simultaneous process of price and short-run quantity adjustment with free entry and exit of competitive firms in a single market with a continuum of firms can generate closed orbits via a Hopf bifurcation when the slope of the demand function is positive at equilibrium. When the continuum economy is replaced by an economy with a finite number of firms, noisy limit cycles and complicated behavior can be observed.