微观计算题库及答案

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