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Principles of Microeconomics

7th Edition
N. Gregory Mankiw
ISBN: 9781305156050

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BuyFindarrow_forward

Principles of Microeconomics

7th Edition
N. Gregory Mankiw
ISBN: 9781305156050
Textbook Problem

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 + T)

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 T × 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 × base × 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 levies a tax of $200 per unit on this good. Is this a good policy? Why or why not? Can you propose a better policy?

Subpart (a):

To determine
Equilibrium price.

Explanation

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

Subpart (b):

To determine
Equilibrium price.

Subpart (c):

To determine
Total tax revenue.

Subpart (d):

To determine
Deadweight loss.

Subpart (e):

To determine
Determine the tax amount.

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