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Aside: It is known mathematical fact that our Government runs on imaginary money everyday!

From his description, we have the following.

"We need to write the equations for supply and demand in terms of price (P), the rate of change of the price (P’), and the rate of change of the rate of change of the price (P’). The values given to w, u, and v depends on the peoples expectations about how prices are changing. If people think that prices are rising then the coefficient in front of the first derivative of price will be positive and if there is a belief that prices are falling then this coefficient will be negative. The magnitude and since of the v value reflects how fast people believe that prices are rising or falling. These values can be estimated using statistics and econometric methods, but the following solution is for the general case where these variable are arbitrary real numbers not equal to zero."

As mathematicians, what we like to do is to analyze our solutions using the general approach and to describe what the phases portraits will look like for these general cases. For this, we have several cases to consider. You can choose the variable representation to mean whatever you'd like and maybe in actuality you wouldn't get all those cases based on how you are representing reality (whatever that means).

If you are actually asking what the phase portraits will look like for the three cases, we can certainly draw them and then try and see if we can add actual meaning based on how the model and variables were chosen.