Principles of Macroeconomics (MindTap Course List)
Principles of Macroeconomics (MindTap Course List)
7th Edition
ISBN: 9781285165912
Author: N. Gregory Mankiw
Publisher: Cengage Learning
Question
Chapter 8, Problem 10PA

Subpart (a):

To determine

Equilibrium price.

Subpart (a):

Expert Solution
Check Mark

Explanation of Solution

The equilibrium price and the quantity are determined at the interaction of the demand curve and the supply curve of the commodity in the market. When the demand and supply for the commodity are equal at a particular price point, the point will be the equilibrium price level and the equilibrium quantity in the economy.

We have given the supply equation and the demand equations and we can equate them in order to obtain the equilibrium price as follows:

Supply = Demand2P = 300P2P+P=3003P=300P=3003=100

Thus, the equilibrium price is $100. Now we can calculate the equilibrium quantity by substituting the equilibrium price in the equations as follows:

2P=300P2×100=300100200=200

Thus, the equilibrium quantity is 200 units.

Economics Concept Introduction

Concept introduction:

Equilibrium: It is the market equilibrium which is determined by equating the supply to the demand. At this equilibrium point, the supply will be equal to the demand and there will be no excess demand or excess supply in the economy. Thus, the economy will be at equilibrium.

Subpart (b):

To determine

Equilibrium price.

Subpart (b):

Expert Solution
Check Mark

Explanation of Solution

We have given the supply equation and the demand equation changes due to the tax on consumers and the new demand equation is QD=300(P+T) . The equilibrium price and the quantity can be calculated by equating the equations as follows:

Supply = Demand2P = 300(P+T)3P=300TP=300T3P=100T3

Thus, the price received by the producers is 100T3 . The consumers will pay a price which is equal to the price received by the producer plus the tax amount which will be equal to 100+2T3 . The quantity sold can be calculated by substituting the price in the equation as follows:

Q=300(P+T)=300(100+2T3)=2002T3

Thus, the quantity is now 2002T3 .

Economics Concept Introduction

Concept introduction:

Equilibrium: It is the market equilibrium which is determined by equating the supply to the demand. At this equilibrium point, the supply will be equal to the demand and there will be no excess demand or excess supply in the economy. Thus, the economy will be at equilibrium.

Subpart (c):

To determine

Total tax revenue.

Subpart (c):

Expert Solution
Check Mark

Explanation of Solution

We have given that the tax revenue equals to the tax rate multiplied with the quantity. The quantity is calculated in part b as 2002T3 and the tax revenue can be calculated as follows:

Tax revenue=T×Q=T×(2002T3)=200T2T23

This relation between the tax revenue can be illustrated as follows:

Principles of Macroeconomics (MindTap Course List), Chapter 8, Problem 10PA , additional homework tip  1

The graph depicts that the tax revenue will be zero at the tax levels of T = $0 and also at the tax rate of T = $300.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.

Tax revenue: Tax revenue refers to the total revenue earned by the government through imposing tax.

Subpart (d):

To determine

Deadweight loss.

Subpart (d):

Expert Solution
Check Mark

Explanation of Solution

We have given that deadweight loss is the area of the triangle between the demand and supply curves. The following diagram shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 × base × height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity ( 2T3 ).

Principles of Macroeconomics (MindTap Course List), Chapter 8, Problem 10PA , additional homework tip  2

The deadweight loss can be calculated as follows:

Deadweight loss=12×Size of tax×amount of decline in quantity=12×T×2T3=T23

Thus, the deadweight loss is equal to T23 . The relation is illustrated on the graph as follows:

Principles of Macroeconomics (MindTap Course List), Chapter 8, Problem 10PA , additional homework tip  3

In the above diagram horizontal axis measures quantity and vertical axis measures deadweight loss.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.

Deadweight loss: It is the reduction in the units where the marginal benefit to the consumer is higher than the marginal cost of production of the unit.

Subpart (e):

To determine

Determine the tax amount.

Subpart (e):

Expert Solution
Check Mark

Explanation of Solution

A tax of $200 will not turn out to be a good policy because the tax revenue decreases when the tax rate reaches to $300 where the tax revenue is zero. The tax revenue is at its maximum at the middle of the tax rate of $0 and $300 which is $150. Thus, in order to increase the tax revenue, the government should reduce the tax rate to $150 from $200 which will be the good alternative policy.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.

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Students have asked these similar questions
Suppose that a market is described by the following supply and demand equations: QS= 2P QD= 300 - P a. Solve for the equilibrium price and the equilibrium quantity. b. Suppose that a tax of T is placed on buyers, so the new demand equation is QD= 300 - (P + 1) Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? c. Tax revenue is Tx Q. Use your answer from part (b) to solve for tax revenue as a function of T.Graph this relationship for T between 0 and 300. d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is 1/2 x base x height, solve for deadweight loss as a function of T.Graph this relationship for T between 0 and 300. (Hint Looking sideways, the base of the deadweight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.) e. The government now…
The figure below shows a market of good X. Suppose that the government levied the tax of 30 on X. Regarding the after-tax equilibrium quantity, does it matter on which side (sellers or buyers) the tax was levied? What is the quantity and the price buyers pay and the price sellers receive in the after-tax equilibrium? Quantity: Price buyers pay: Price sellers receive:
Suppose that policymakers are considering placing a tax on either of two markets. In Market A, the tax will have a significant effect on the price consumers pay, but it will not affect equilibrium quantity very much. In Market B, the same tax will have only a small effect on the price consumers pay, but it will have a large effect on the equilibrium quantity. Other factors are held constant. In which market will the tax have a larger deadweight loss?     Market A     Market B     The deadweight loss will be the same in both markets.     There is not enough information to answer the question.
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  • Suppose that a market is described by the following supply and demand equations:Qs=2PQD=300-Pa.Solve for the equilibrium price and the equilibrium quantity.b.Solve that a tax of T is placed on buyers,so the new denad equation is QD=300-(P+T).Solve for the new equilibrium.What happens to the price receive by sellers,the price paid by buyers.and the quantity sold?c.Tax revenue is TxQ.Use your answer from part(b)to solve for tax revenue as a function of T.Graph this relationship for T between 0 and 300.d.The dead weight loss of a tax is the area of a triangle between supply and demand curves.Recalling that the area of the triangle is 1/2xbasexheight,solve for the dead weight loss as afunction of T.Graph this relationship for T between 0 and 300.e.The government now levies a tax of $200per unit on this good.Is this a good policy?Why or why not?Can you propose a better policy?
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