Quarterly of Applied Mathematics

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Nonlinear price evolution

Author(s): G. Caginalp
Journal: Quart. Appl. Math. 63 (2005), 715-720.
MSC (2000): Primary 91B24, 37W40; Secondary 91B08, 91B26
Posted: September 27, 2005
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Abstract: The neoclassical price adjustment equation stipulates that prices move toward equilibrium at a rate that is proportional to the excess demand, i.e., the difference between the demand and supply divided by the demand (at that price). However, the demand and supply are generally nonlinear functions of price. We show that the information on this nonlinear variation of demand and supply leads to a more accurate description of price evolution toward equilibrium. With this additional information the optimal forecast for the price of the good or asset is given by a nonlinear equation. This yields an advantage to traders utilizing all of the available information on supply and demand functions, rather than simply the value at the current price.

References:

1.: Watson, D. and Getz, M., Price Theory and Its Uses, University Press of America, Lanham, MD, (1981).
2.: Plott, C., http://www.hss.caltech.edu/~cplott/, (2004).
3.: Caginalp, G. and Balenovich, D., Asset flow and momentum: deterministic and stochastic equations, Phil. Trans. Proc. Royal Soc. A, 357, 2119-2133 (1999). MR 1712407 (2000e:91067)