Now suppose the government imposes a quantity tax of $t per lesson on consumers. System (4. A) above thus becomes: JQ=e-f(P+t) 1Q = 8 + hP (demand) (supply) 4.4 Let x = = []. Transform system 4. B into the matrix equation Ax = b. (system 4. 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.)
Now suppose the government imposes a quantity tax of $t per lesson on consumers. System (4. A) above thus becomes: JQ=e-f(P+t) 1Q = 8 + hP (demand) (supply) 4.4 Let x = = []. Transform system 4. B into the matrix equation Ax = b. (system 4. 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.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
4.4, 4.5, 4.6
![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%2Fa0d9250e-7dd2-4247-934b-169cdc6227d1%2Fjfvc1pd_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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