  Proceeding from the concept of rational expectations, a new dynamic model of
supply and demand in a single market with one supplier, one buyer, and one kind
of commodity is developed. Unlike the cob-web dynamic theories with adaptive
expectations that are made up of deterministic difference equations, the new
model is cast in the form of stochastic differential equations. The
stochasticity is due to random disturbances ("input") to endogenous variables.
The disturbances are assumed to be stationary to the second order with zero
means and given covariance functions. Two particular versions of the model with
different endogenous variables are considered. The first version involves
supply, demand, and price. In the second version the stock of commodity is
added. Covariance functions and variances of the endogenous variables
("output") are obtained in terms of the spectral theory of stochastic
stationary processes. The impact of both deterministic parameters of the model
and the random input on the stochastic output is analyzed and new conditions of
chaotic instability are found. If these conditions are met, the endogenous
variables undergo unbounded chaotic oscillations. As a result, the market that
would be stable if undisturbed loses stability and collapses. This phenomenon
cannot be discovered even in principle in terms of any cobweb deterministic
model.
