Consider the following economic model. Let P be the price of a single item on the market. Let Q be the quantity of the item available on the market. Both P and Q are functions of time. If one considers price and quantity as two interacting species, the following model might be proposed:

where a, b, c, and ƒ are positive constants. Justify and discuss the adequacy of the model.

a. If a = 1, b = 20,000, c = 1, and ƒ = 30, find the equilibrium points of this system. If possible, classify each equilibrium point with respect to its stability. If a point cannot be readily classified, give some explanation.

b. Perform a graphical stability analysis to determine what will happen to the levels of P and Q as time increases.

c. Give an economic interpretation of the curves that determine the equilibrium points.

Transcribed Image Text:

dP dt dQ dt aP b - P CQ(fP-Q),