4. Consider below the system of equations for the demand (QD) for and supply (Qs) of piano lessons (Note: we already assume below that Qp = Qs = Q in equilibrium; P denotes the price of lessons in dollars; e, f, h> 0 and g ≤ 0 are constants): (Q=e-fP Q=g+hP 4.1. Let x = (demand) (supply) (system 4. A). = [] (To emphasize: You are required to set up x in this manner.). Transform system 4. A above into the matrix equation Ax = b. 4.2. Using your Ax=b equation in item 4.1 and matrix inversion, find the equilibrium price P* and the equilibrium quantity of lessons sold Q" when e = 100, f = 2, h = 3, and g = 0. 4.3. Using your answer in item 4.2, find the equilibrium price faced by consumers and sellers (Please do not overthink this item.).
4. Consider below the system of equations for the demand (QD) for and supply (Qs) of piano lessons (Note: we already assume below that Qp = Qs = Q in equilibrium; P denotes the price of lessons in dollars; e, f, h> 0 and g ≤ 0 are constants): (Q=e-fP Q=g+hP 4.1. Let x = (demand) (supply) (system 4. A). = [] (To emphasize: You are required to set up x in this manner.). Transform system 4. A above into the matrix equation Ax = b. 4.2. Using your Ax=b equation in item 4.1 and matrix inversion, find the equilibrium price P* and the equilibrium quantity of lessons sold Q" when e = 100, f = 2, h = 3, and g = 0. 4.3. Using your answer in item 4.2, find the equilibrium price faced by consumers and sellers (Please do not overthink this item.).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
4.1, 4.2, 4.3
![4. Consider below the system of equations for the demand (QD) for and supply (Qs) of piano
lessons (Note: we already assume below that Qp = Qs = Q in equilibrium; P denotes the price
of lessons in dollars; e, f, h> 0 and g <0 are constants):
(Q=e-fP
1Q=g+hP
(system 4. A).
4.1. Let x = =[] (To emphasize: You are required to set up x in this manner.).
(demand)
(supply)
Transform system 4. A above into the matrix equation Ax = b.
4.2. Using your Ax=b equation in item 4.1 and matrix inversion, find the equilibrium
price P* and the equilibrium quantity of lessons sold Q when e = 100, f = 2, h = 3, and g = 0.
1.3. Using your answer in item 4.2, find the equilibrium price faced by consumers
and sellers (Please do not overthink this item.).
Now suppose the government imposes a quantity tax of $t per lesson on consumers. System
(4. A) above thus becomes:
4.4 Let x =
[Q=e-f(P+t)
1Q = 8 + hP
(demand)
(supply)
(system 4. B).
= []. Transform system 4. B into the matrix equation Ax = b.
Using your Ax = b equation in item 4.4 and matrix inversion, find the following values when
e = 100, f = 2,h= 3, g = 0, and t = 10:
4.5. the new equilibrium price (P") and the new equilibrium quantity sold (Q")
4.6. the new equilibrium price faced by the consumer (Hint/note: Recall that the tax
is imposed on consumers.)
4.7. the new equilibrium price faced by the seller](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ed9542f-d658-47ef-8561-8166da0af35e%2Ff69d20ac-6de0-4123-b133-0c092dd19924%2Fsz4alek_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Consider below the system of equations for the demand (QD) for and supply (Qs) of piano
lessons (Note: we already assume below that Qp = Qs = Q in equilibrium; P denotes the price
of lessons in dollars; e, f, h> 0 and g <0 are constants):
(Q=e-fP
1Q=g+hP
(system 4. A).
4.1. Let x = =[] (To emphasize: You are required to set up x in this manner.).
(demand)
(supply)
Transform system 4. A above into the matrix equation Ax = b.
4.2. Using your Ax=b equation in item 4.1 and matrix inversion, find the equilibrium
price P* and the equilibrium quantity of lessons sold Q when e = 100, f = 2, h = 3, and g = 0.
1.3. Using your answer in item 4.2, find the equilibrium price faced by consumers
and sellers (Please do not overthink this item.).
Now suppose the government imposes a quantity tax of $t per lesson on consumers. System
(4. A) above thus becomes:
4.4 Let x =
[Q=e-f(P+t)
1Q = 8 + hP
(demand)
(supply)
(system 4. B).
= []. Transform system 4. B into the matrix equation Ax = b.
Using your Ax = b equation in item 4.4 and matrix inversion, find the following values when
e = 100, f = 2,h= 3, g = 0, and t = 10:
4.5. the new equilibrium price (P") and the new equilibrium quantity sold (Q")
4.6. the new equilibrium price faced by the consumer (Hint/note: Recall that the tax
is imposed on consumers.)
4.7. the new equilibrium price faced by the seller
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