the function of supply can be linear or nonlinear

We develop price dynamics equations using a function of supply with key symmetrproperties. the function of supply can be linear or nonlinear. the typeof function determines the nature of the tail of the distribution based on therandomness in the supply and demand. for example, if supply and demand arenormally distributed, and the function is assumed to be linear, then thedensity of relative price change has behavior $x^{-2}$ for large $x$ (i.e.,large deviations). the exponent approaches $-1$ if the function of supply anddemand involves a large exponent. the falloff is exponential, i.e., $e^{-x}$,if the function of supply is logarithmic.