Question

Consider an economy described by the following equations:

QD = 30M - 2P

QS = (1-t)P -5

QD = QS

where QD is quantity demanded, QS is quantity supplied, M is the income of consumers, and t is the tax rate (with 0 < t < 1). Consider the vector of endogenous variables X = [ QD P QS ] T .

1)Write the model in matrix form.

2) Does the model have a unique solution? Explain.

3) Solve the model by matrix inversion. (You have to show the work done to calculate the inverse! “Magical” inverse matrices will not be accepted.)

4) Find the equilibrium value of P by using Cramer's rule. Check whether you obtain the same solution as the one from question 3.

5) Suppose you want to find out the tax rate, income and price in an equilibrium with QD = QS = 7. How would you change your answer to question 1?

Answer #1

Subject to do only 4 parts.

Hint for 5th:-- just now the X vector will change

Now the X = [ t M P ]^{T}

Now do same as the below.

1. Consider a demand curve of the form QD = 40 - 2P, where QD is
the quantity demanded and P is the price of the good. The supply
curve takes the form of QS = -4 + 2P, where QS is the quantity
supplied, and P is the price of the good. Be sure to put P on the
vertical axis and Q on the horizontal axis. a. What is the
equilibrium price and quantity? Draw out the supply...

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If the government imposes a price ceiling of $70, does a
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QS = 2P
QD = 400 - 3P
Solve for the equilibrium price and the equilibrium
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Suppose that a tax of T is placed on buyers, so the new demand
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QD = 400 – 3(P+T)
Solve for the new equilibrium. What happens to the price
received by sellers, the price paid by buyers, and the quantity
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Tax revenue is T x Q. Use...

Consider the following market. Demand is given by qd = 150 – 2P,
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you are given the following information:
Qs = 100 +
3P
Qd = 400 -
2P
From this information compute equilibrium price and quantity.
Now suppose that a tax is placed on buyers so that
Qd = 400 - 2(P +
T).
If T = 15, solve for the new equilibrium price and quantity.
(Note: P is the price received by sellers and P + T is the price
paid by buyers.) Compare these answers for...

Suppose that a market is described by the following supply and
demand equations:
QS = 2P
QD = 400 - 3P
Suppose that a tax of T is placed on buyers, so the new demand
equation is
QD = 400 – 3(P+T)
Solve for the new equilibrium. What happens to the price
received by sellers, the price paid by buyers, and the quantity
sold?
Tax revenue is T x Q. Use your answer from part (b) to solve for
tax...

Qd = 240 - 5P
Qs = P
(a) Where Qd is the quantity demanded, Qs is the quantity
supplied and P is the Price. Find:
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(2) the Equilibrium quantity before the tax
(3) buyers reservation price
(4) sellers reservation price
(5) consumer's surplus before tax
(6) producer's surplus before tax
(b) Suppose that the government decides to impose a tax of $12
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c) At the equilibrium price and quantity, what is the price
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Suppose Qd=40-P and Qs= -2+2P. If Price equals 20, quantity
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Question 16 options:
22
18
40
10
20
Question 17 (1 point)
Suppose Qd=40-P and Qs= -2+2P. What is the equilibrium price in
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Question 17 options:
14
2
13
20
12.66
Question 18 (1 point)
Suppose Qd=40-P and Qs= -2+2P. What is the consumer surplus at
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39
676
169
338
14
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