As we can see, all forces have become one-dimensional functions in this model. Then, using these equations, we obtain a very elegant system of two independent linear equations to determine market prices and quantities:

This system is so simple that you don't even have to solve it in the usual sense to get a very nice looking solution for market prices and quantities:

Thus, probabilistic market prices and quantities in a two-agent economy, when using factorized agent functions in the form of Gaussians, are determined by averaging the corresponding agent parameters, with the frequency parameters of the agents serving as weights in this averaging. The fundamental point here is that these two simple, and independent, algebraic formulas, which include only four buyer parameters (p^>D