Consider a competitive market in which price adjusts to excess demand or supply and firms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp 0.5(qº – q°) dt Where qº = 30 – 2p is the demand function, qº = 2N is the supply function, p is price, N is %3D the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN 5 3— (р — 10) dt Derive a system of differential equation to represent this information. Solve the system.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider a competitive market in which price adjusts to excess demand or supply and firms
enter and exit the industry if profits or losses are being made. Price adjusts to excess
demand according to
dp
0.5(qº – q$)
dt
Where qº = 30 – 2p is the demand function, qº
= 2N is the supply function, p is price, N is
the number of firms in the industry and a is the speed of adjustment coefficient. The
number of firms adjust according to
dN
5
(p
10)
dt
Derive a system of differential equation to represent this information.
Solve the system.
Transcribed Image Text:Consider a competitive market in which price adjusts to excess demand or supply and firms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp 0.5(qº – q$) dt Where qº = 30 – 2p is the demand function, qº = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN 5 (p 10) dt Derive a system of differential equation to represent this information. Solve the system.
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