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Problem 6 (Sec 12.2) 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 we consider price and quantity as two interacting species, the following model might be proposed: dP dt dQ dt = aP = LP ( 1/2 - P) cQ(fP-Q) where a, b, c, and f are positive constants. Justify and discuss the adequacy of the model. (a) If a 1, b = 20000, c = 1, and f = 30, find the equilibrium points of this system. 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 (phase space 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.

Problem 6 (Sec 12.2) 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 we consider price and quantity as two interacting species, the following model might be proposed: dP dt dQ dt = aP = LP ( 1/2 - P) cQ(fP-Q) where a, b, c, and f are positive constants. Justify and discuss the adequacy of the model. (a) If a 1, b = 20000, c = 1, and f = 30, find the equilibrium points of this system. 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 (phase space 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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help answer a, b and c please thank you. Handwritten asnwer

Problem 6 (Sec 12.2) 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 we consider price and quantity as two interacting species, the following model might be proposed: dP dt dQ dt = aP = LP ( 1/2 - P) cQ(fP-Q) where a, b, c, and f are positive constants. Justify and discuss the adequacy of the model. (a) If a 1, b = 20000, c = 1, and f = 30, find the equilibrium points of this system. 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 (phase space 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:Problem 6 (Sec 12.2) 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 we consider price and quantity as two interacting species, the following model might be proposed: dP dt dQ dt = aP = LP ( 1/2 - P) cQ(fP-Q) where a, b, c, and f are positive constants. Justify and discuss the adequacy of the model. (a) If a 1, b = 20000, c = 1, and f = 30, find the equilibrium points of this system. 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 (phase space 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.
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