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An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between price and supply. The economist has proposed the following model, where Pr, represents the price of the product at year n, and Qn represents the quantity. Find the equilibrium values for this system. Pn+1 = Pn – 0.1(Qn – 500) %3D Qn+1 = Qn + 0.2(Pn – 100)

An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between price and supply. The economist has proposed the following model, where Pr, represents the price of the product at year n, and Qn represents the quantity. Find the equilibrium values for this system. Pn+1 = Pn – 0.1(Qn – 500) %3D Qn+1 = Qn + 0.2(Pn – 100)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.CR: Chapter 1 Review
Problem 86CR
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An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between price and supply. The economist has proposed the following model, where Pn, represents the price of the product at year n, and Qn represents the quantity. Find the equilibrium values for this system. Pn+1 = Pn – 0.1(Qn – 500) %3D Qn+1 Qn + 0.2(Pn – 100) -
Transcribed Image Text:An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between price and supply. The economist has proposed the following model, where Pn, represents the price of the product at year n, and Qn represents the quantity. Find the equilibrium values for this system. Pn+1 = Pn – 0.1(Qn – 500) %3D Qn+1 Qn + 0.2(Pn – 100) -
Using the dynamical system above, test the initial populations in the following table and predict the long-term behavior. Is the system sensitive to changes in initial population? Why or why not? Price Quantity Case A 100 500 Case B 200 500 Case C 100 600 Case D 100 400
Transcribed Image Text:Using the dynamical system above, test the initial populations in the following table and predict the long-term behavior. Is the system sensitive to changes in initial population? Why or why not? Price Quantity Case A 100 500 Case B 200 500 Case C 100 600 Case D 100 400
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