2. Consider the system dP P(1000/Q – P) dt OP Q(20P – Q), dt where P is the price of a single item on the market and Q is the quantity of the item available on the market. Find the equilibrium points of this system. (a) Classify each equilibrium point with respect to its stability, if possible. If a point cannot be readily classified, explain why. (b) Perform a graphical stability analysis to determine what will happen to the levels of P and Q as time increases.

2. Consider the system dP P(1000/Q – P) dt OP Q(20P – Q), dt where P is the price of a single item on the market and Q is the quantity of the item available on the market. Find the equilibrium points of this system. (a) Classify each equilibrium point with respect to its stability, if possible. If a point cannot be readily classified, explain why. (b) Perform a graphical stability analysis to determine what will happen to the levels of P and Q as time increases.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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