Simultaneous Adjustment of Quantities and Prices: An Example of Hamiltonian Dynamics

In a well-known essay first published in 1953, Goodwin analyzed the dynamic adjustment of quantities and prices to long-run equilibrium values, in a set ofn ‘Walrasian’ markets. He treated the crossed adjustment of prices and quantities as a linear Hamiltonian vector field. In more recent work, Goodwin introduced non-linear perturbations in his multi-sectoral adjustment model. He assumed that real consumption depends non-linearly on relative prices. This paper shows the following: (1) Goodwin's behavioural hypotheses are compatible with the assumption that agents maximize; (2) if the dynamic process is Hamiltonian, then symplectic coordinate changes are essential tools of analysis; (3) if the real wage is rigid and returns to scale are not constant, then the Hamiltonian model can generate chaotic transients or, in extreme cases, pure chaotic motions.