In the market for Fante Kenley, the supply and demand functions respectively are Q° = 0.25P+10 and Q° =-0.5P+100 When there is excess demand, price adjusts according to the equation 2-0.5(Q° -Q°) a) Find the long run equilibrium price, P* (that is, the price at which there is no excess demand or supply). b) Formulate and solve he first order differential equation giving Pas a function of time, 1. Is this market dynamically stable or unstable? c) If the initial price is P= 50, how close will the price be to its long run equilibrium value, when t= 10?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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In the market for Fante Kenley, the supply and demand functions respectively are
Q° = 0.25P+ 10 and Q° =-0.5P+100
When there is excess demand, price adjusts according to the equation
-0.5(Q" -0)
dt
a) Find the long run equilibrium price, P* (that is, the price at which there is no excess
demand or supply).
b) Formulate and solve he first order differential equation giving Pas a function of time, t. Is
this market dynamically stable or unstable?
c) If the initial price is P = 50, how close will the price be to its long run equilibrium value,
when t= 10?
Transcribed Image Text:In the market for Fante Kenley, the supply and demand functions respectively are Q° = 0.25P+ 10 and Q° =-0.5P+100 When there is excess demand, price adjusts according to the equation -0.5(Q" -0) dt a) Find the long run equilibrium price, P* (that is, the price at which there is no excess demand or supply). b) Formulate and solve he first order differential equation giving Pas a function of time, t. Is this market dynamically stable or unstable? c) If the initial price is P = 50, how close will the price be to its long run equilibrium value, when t= 10?
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