Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
See similar textbooks
icon
Related questions
Question

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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS