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)

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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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