Question

Consider the economic model below, where P is the price of a single item on the market and Q is the quantity of the item available on the market. Both P and Q are functions of time that can be viewed as two interacting species, and a, b, c, and f are positive constants. dQ dP cQ(fP Q) dt aP dt If a 1, b 15,000, c 1, and f= 10, find the equilibrium points of this system and classify each equilibrium point with respect to stability if possible. What are the equilibrium points of the given system? (Type an ordered pair. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) Classify the equilibrium point(s) with respect to stability. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The equilibrium point(s) is/are unstable. O B. The equilibrium point(s) is/are stable. O C. The equilibrium point(s)is/are stable and the equilibrium point(s) is/are unstable. (Type an ordered pair. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Answer 1

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