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1. Market research has revealed the following information about the market for chocolate bars: The demand schedule can be represented by the equation Q d= 1,600 – 300P , where Q d is the quantity demanded and P is the price.The supply schedule can be represented by the equation Q s= 1,400 + 700P , where Q s is the quantity supplied.
a. Calculate the equilibrium price and quantity in the market for chocolate bars.
b. Calculate the price elasticity of demand and supply in equilibrium level.
c. a . Equilibrium occurs where quantity demanded is equal to quantity supplie
d. d. Thus:
e. Q d = Q s
f. 1,600 –300P = 1,400 + 700P
g. 200 = 1,000P
h. P = $0.20
i. Q d= 1,600 –300(0.20) = 1,600 –60 = 1,540 j. Q s= 1,400 + 700(0.20) = 1,400 + 140 = 1,540.
k. The equilibrium price of a chocolate bar is $0.20 and the equilibrium quantity is 1,540 bars.
l. b . In equilibrium,
m. Q P dP dQ P /P Q /Q e •==
∆∆ n. e pd =-1/300*0.2/1540= -1/2310000
o. e ps =1/700*0.2/1540= 1/5390000
2.The supply and demand for broccoli (西兰花）are described by the following equations:
Supply: Q S = 4P – 80
Demand: Q D = 100 – 2P .
Q is in bushels, and P is in dollars per bushel.
a. Graph the supply curve and the demand curve. What is the equilibrium price and quantity?
b. Calculate consumer surplus, producer surplus,and total surplus at the equilibrium.
c. If a dictator who hated broccoli were to ban the vegetable, who would bear the larger burden—the buyers or sellers of broccoli?
a. In equilibrium, Q S =Q D
Therefore, 4P – 80 = 100 – 2P
Pe=30 , Qe = 40
b. CS = 40 * (50 - 30)/2 = 400
PS = 40* (30 - 20)/2 = 200
TS = CS + PS = 400 +200 = 600
c. If a dictator were to ban the vegetable, the total surplus, including CS and PS, will decrease to 0. The consumers will bear the larger burden because of more decrease in CS than PS.
3. 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 pricepaidby buyers, and the quantity sold?
c. Tax revenue is T × Q. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0and 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 triangleis 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.)
a. Setting quantity supplied equal to quantity demanded gives
2P = 300 –P Therefore, P = 100.
Plugging P = 100 back into either equation for quantity
demanded or supplied gives Q = 200.
b.Now P is the price received by sellers and
P +T is the price paid by buyers.
Equating quantity demanded to quantity supplied gives 2P = 300 - (P +T).
P = 100 - T/3.
This is the price received by sellers.
The buyers pay a price equal to the price received by sellers p
lus the tax:
P +T = 100 + 2T/3.
The quantity sold is now
Q = 2P = 200– 2T/3.
c. Since TR =T x Q and Q= 200 - 2T/3,
TR = 200T -2T2/3.
Tax revenue is zero at T =0 and at T=300.
d. As Figure 10 shows, the area of the tri
angle (laid on its side) that represents
the deadweight loss is 1/2 x base x height,
where the base is the change in the price, whic
h is the size of the tax (T) and the height is the am
ount of the decline in
quantity (2T/3).
So the deadweight loss equals 1/2x T x 2T/3= T
2/3.
This rises exponentially from 0 when
T =0 to 45,000 when T = 300
4. Suppose that your demand schedule for compact discs is as follows:
a. Use the midpoint method to calculate your price elasticity of
demand as the price of compact discs increases from $8 to $10 if(i) your income is $10,000 and (ii) your income is $12,000. b. Calculate your income elasticity of demand as your income increases from $10,000 to$12,000 if (i) the price is $12 and (ii) the price is $16.
(i)
If your income is $10,000, your price elasticity of demand as the price of c ompact discs rises from $8 to $10 is
]
2/)P P /[()P P (]2/)Q Q /[()Q Q (P /P Q /Q e 12121212+-+-==∆∆ 1分 e pd = [(40 – 32)/36]/[(10 –8)/9] =0.22/0.22 = 1 2分
(ii) If your income is $12,000, the elasticity is
e pd = [(50 – 45)/47.5]/[(10 –8)/9] = 0.11/0.22 = 0.5. 2分
b.
(i)
If the price is $12, your income elasticity of demand as your income increase s
from $10,000 to $12,000 is
]
2/)I I /[()I I (]2/)Q Q /[()Q Q (I /I Q /Q e 12121212+-+-==∆∆ 1分 e id = [(30 –24)/27]/[(12,000 –10,000)/11,000]
= 0.22/0.18 = 1.22. 2分 (ii)If the price is $16, your income elasticity of demand as your income incre ases
from $10,000 to $12,000 is e id =[(12 – 8)/10]/[(12,000 –10,000)/11,000]
= 0.40/0.18 = 2.2. 2分
5. Assume the United States is an importer of televisions and there are no trade restrictions. U.S.consumers buy 2 million televisions per year, of which 600,000 are produced domestically and 1,400,000 are imported.
a. Suppose that a technological advance among Japanese television manufacturers causes the world price of televisions to fall by $15.Draw a graph to show how this change affects the welfare of U.S. consumers and U.S.producers and how it affects total surplus inthe United States.
b. After the fall in price, consumers buy 2.5 million televisions, of which 400,000 areproduced domestically and 2.1 million areimported. Calculate the change in consumersurplus, producer surplus, and total surplusfrom the price reduction.
c. If the government responded by putting a$15 tariff on imported televisions, whatwould this do? Calculate the revenue thatwould be raised and the deadweight loss.
Would it be a good policy from the standpointof U.S. welfare?
ΔPS= - C
= - (0.6 + 0.4) *15/2 M
= - 7,500,000
ΔTS = ΔCS + ΔPS = D + E + F
= 26,250,000
c. If the government puts a$15 tariff on imported televisions,
the new price will increase to P1. Therefore,
Tariff Revenue = E
=(2 - 0.6) *15 M
= 21,000,000
Deadweight loss = D + F
=(0.6-0.4)*15/2 + (2.5-2）*15/2
=5,250,000
This policy would do harm to the U.S welfare due to the deadweight loss. However, the domestic producers and government would support this policy because their surplus increase with a tariff.。