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ECOS2001 – Intermediate Microeconomics

创建日期：2024-05-23 14:41:39

所属分类：经济Economics

标签： ECOS2001

Intermediate Microeconomics

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ECOS2001 – Intermediate Microeconomics

Tutorial 1- Answer Key
Chapters 2-3
Question 1
The supply and demand for monthly gym memberships are given as QS = 10P − 300 and
QD = 600 − 10P, where P is the monthly price of a membership.
1. If the current price for memberships is $50 per month, is the market in equilibrium?
2. Would you expect the price to rise or fall?
3. If so, by how much?
Solution:
1. Compute the quantity demanded and quantity supplied at a price of $50.
10 300 10 50 300 200
600 10 600 10 50 100
S
D
Q P
Q P
= − =  − =
= − = −  =
Therefore, since QD < QS, the market is not in equilibrium.
2. There is a surplus, so we can expect the price to fall.
3. Solve for the market equilibrium price and quantity.
10 300 600 10
$45, 150
S DQ Q
P P
P Q
=
− = −
= =
Therefore, the price must fall by $5, and 50 more memberships are sold.
Now suppose the town opens a new community center with a pool and a weight room. As a
result, consumers demand 200 fewer gym memberships at every price.
4. Write down the new demand equation.
5. What do you expect to happen to the equilibrium price and quantity?
6. Compute the new equilibrium price and quantity.
Solution:
4. QD has fallen by 200. Therefore, QD = 600 − 10P − 200 = 400 − 10P.
5. Because demand has fallen, we should see a reduction in both the equilibrium
price and quantity.
6. 10 300 400 10
$35, 50
S DQ Q
P P
P Q
=
− = −
= =
As expected, the price has fallen (by $10), and the quantity of memberships sold has
fallen as well (by 100).
2
Question 2
This summer, you noticed the price of lobster in your supermarket rising, but at the same time,
much less lobster was sold. Using a supply and demand diagram, what can you infer about this
market?
Solution:
The only shift that leads to a higher equilibrium price and a lower quantity sold is a
decrease in supply. Therefore, the supply curve for lobster shifted in. The new price is P2,
and the new quantity is Q2. This represents a change (or shift) in supply and a change in
the quantity demanded.
Question 3
The demand for movie tickets in a small town is given as QD = 1000 − 50P.
1. Calculate the price elasticity of demand when the price of tickets is $5.
2. Calculate the price elasticity of demand when the price of tickets is $12.
3. At what price is the price elasticity of demand unit elastic?
4. What happens to the price elasticity of demand as you move down a linear demand
curve?
Solution:
The price elasticity of demand is given as
D Q P
P Q
E

= 

.
For this demand curve,
Q
P


is constant and equal to −50.
1. When P = $5, QD = 750. Therefore,
5
50 0.3333.
750
DE = −  = −
Since |E| <1, then the demand is inelastic.
2. When P = $12, QD = 400. Therefore,
12
50 1.5.
400
DE = −  = −
Since |E| > 1, then the demand is elastic.
3. Demand is unit elastic when ED = −1. Therefore, we substitute −1 for ED and then
solve for P:
( )
1 50
1,000 50
1,000 50 50
1,000 50 50
100 1,000
$10
P
P
P P
P P
P
P
− = − 
−
− = −
− =
=
=
−
Demand will be unit elastic at a price of $10.
4. As you move down a linear demand curve, demand becomes less elastic (more
inelastic).
3
Question 4
The weekly supply and demand for cupcakes in a small town are given as QS = 30P − 20, and
QD = 124 − 18P, where P is the price of a cupcake and Q is measured in thousands per week.
a. Find the equilibrium price and quantity.
b. Calculate the consumer and producer surplus at the equilibrium price.
Solution:
a. Equilibrium is characterized by QS = QD.
30P − 20 = 124 − 18P
48P = 144
P = $3
Q = 70
b. The simplest way to calculate consumer and producer surplus is to use a
diagram. It is also necessary to find both the demand choke price and the supply
choke price.
Demand choke price is the price at which QD = 0:
0 = 124 − 18P
18P = 124
P = $6.89
Supply choke price is the price at which QS = 0:
0 = 30P − 20
30P = 20
P = $0.67
We can now draw our diagram:
Area of consumer surplus = 0.5  base  height = 0.5  70  3.89 = $136.15.
Area of producer surplus = 0.5  base  height = 0.5  70  2.33 = $81.55.
4
Question 5
The weekly supply and demand for tires in a small town are given as QS = 15P − 400, and
QD = 2,800 − 25P, where P is the price and Q is the number of tires sold weekly. The
equilibrium price is $80 per tire, and 800 tires are sold each week.
Suppose an improvement in technology makes tires cheaper to produce; specifically, suppose
the quantity supplied rises by 200 at every price.
1. What is the new supply curve?
2. What are the new equilibrium price and quantity?
3. What happens to consumer and producer surplus?
Solution:
1. The new supply curve is 2 15 400 200 15 200
SQ P P= − + = − .
2. The new equilibrium occurs where 2 .
S DQ Q=
15P − 200 = 2,800 − 25P
40P = 3,000
Pnew = $75
Qnew = 925
3. To find consumer surplus, we need to find the demand choke price:
2,800 − 25P = 0
25P = 2,800
P = $112
Therefore, the original consumer surplus is
CSinitial = 0.5  base  height = 0.5  Qinitial  (PDChoke − Pinitial)
CSinitial = 0.5  800  (112 − 80) = $12,800.
The new consumer surplus is
CSnew = 0.5  base  height = 0.5  Qnew  (PDChoke − Pnew)
CSnew = 0.5  925  (112 − 75) = $17,112.50
To find producer surplus, we need to find the supply choke price:
15P − 200 = 0
15P = 200
P = 13.33
Therefore, the original producer surplus is
PSinitial = 0.5  base  height = 0.5  Qinitlial  (Pinitial − PSChoke)
PSinitial = 0.5  800  (80 − 26.67) = $21,332
The new producer surplus is
PSnew = 0.5  base  height = 0.5  Qnew  (Pnew − PSChoke)
PSnew = 0.5  925  (75 − 13.33) = $28,522.38
Consumer surplus has risen by $4,312.50 and producer surplus has risen by $7,190.38
5
Question 6
The supply and demand for soda in a market are represented by QS= 50P − 60 and
QD = 12 − 8P, where P is the price per bottle and Q is in millions of bottles per year. The
current equilibrium price is $1.24, and 2.07 million bottles are sold per year.
1. Calculate the price elasticity of demand and the price elasticity of supply at the
current equilibrium.
2. Calculate the share of a tax that will be borne by consumers and the share borne by
producers.
3. If a tax of 10 cents per bottle is levied, what price will buyers now pay for a bottle?
What price will sellers receive?
Solution:
1.
1.24
8 4.79
2.07
1.24
50 29.95
2.07
D
S
Q P
E
P Q
Q P
E
P Q

=  =−  =−


=  =  =

While both are elastic, supply is much more elastic than demand. Therefore, we would
expect that buyers will bear a larger proportion of the tax.
2.
29.95 29.95
Share borne by the consumer 0.86
29.95 4.79 34.74
4.79 4.79
Share borne by the consumer 0.14
29.95 4.79 34.74
S
S D
D
S D
E
E E
E
E E
= = = =
++
= = = =
++
Buyers will bear 86% of the tax, while sellers will bear 14% of the tax.
3. To solve for Pb and Ps, we need to note that Pb − Ps = $0.10. Thus, Pb = Ps + 0.10.
QD = QS
12 − 8Pb = 50Ps − 60
12 − 8(Ps + 0.10) = 50Ps − 60
12 − 8Ps − 0.80 = 50Ps − 60
11.2 − 8Ps = 50Ps − 60
58Ps = 71.2
Ps = 1.23
Pb = Ps + 0.10 = 1.23 + 0.10 = 1.33
Of the 10-cent tax, buyers pay 9 cents (rounded because their share is 86%), and sellers
pay 1 cent.
6
Question 7
For years the government has subsidized higher education through grants; consider the supply
and demand for college credit hours at a local private liberal arts college:
QS = 1,000P − 2,500 and QD = 8,000 − 500P,
where P is the price (in hundreds of dollars), and Q is the number of credit hours per
semester. The current equilibrium price is $700, and 4,500 credit hours are taken per
semester.
Suppose the government decides to subsidize credit hours at a rate of $200 per hour.
1. What will happen to the price paid by students, the price received by the college,
and the number of credit hours completed?
2. What is the cost of the subsidy to the government?
Solution:
1.
Ps − Pb = 200, so Ps = Pb + 2
QS = QD
1,000Ps − 2,500 = 8,000 − 500Pb
1,000(Pb + 2) − 2,500 = 8,000 − 500Pb
1,000Pb + 2,000 − 2,500 = 8,000 − 500Pb
1,000Pb − 500 = 8,000 − 500Pb
1,500Pb = 8,500
Pb = 566.67
Ps = 766.67
Q = 5,166.65
2. Cost = (subsidy)  (quantity sold) = $200  5,166.65 = $1,033,330.

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