3

Using Supply and Demand to Analyze

Markets
Introduction 3

Chapter Outline
3.1 Consumer and Producer Surplus: Who Benefits in a Market
3.2 Price Regulation
3.3 Quantity Regulations
3.4 Taxes
3.5 Subsidies
3.6 Conclusion
Introduction 3
In this chapter, we use the supply and demand
model to answer the following questions
• How do we measure the benefits that accrue to
producers and consumers in a market?
• How do government interventions (e.g., taxes)
affect markets and the benefits associated with
market exchange?
Consumer and Producer Surplus: Who
Benefits in a Market 3.1
Consumers benefit from market exchange, otherwise they
would not participate
• Consumer surplus: the difference between the amount
consumers would be willing to pay for a good or service
and the amount they actually pay (the market price)

In many cases, this difference is positive, and consumers

experience net benefits from market exchange
Consumer and Producer Surplus: Who
Benefits in a Market 3.1
Figure 3.1 Defining Consumer Surplus

Price ($/pound) Demand

choke price
$5.50 A Total consumer
5 surplus (CS )
Person A’s B
4.50
consumer C
surplus = $1.50 4 D
3.50 Market price
3 E
D
2 The consumer at point E will
not buy any apples because the
1 market price is too high

0 1 2 3 4 5 Quantity of
apples (pounds)
Consumer and Producer Surplus: Who
Benefits in a Market 3.1
Producers benefit from market exchange, otherwise they
would not participate
• Producer surplus: the difference between the price
producers actually receive (market price) for their goods
and the price at which they are willing to sell them.

Producer surplus is not the same as profit, as we will see in

later chapters
Consumer and Producer Surplus: Who
Benefits in a Market 3.1
Figure 3.2 Defining Producer Surplus

The producer at point Z will not

Price ($/pound) produce any apples because the
Total producer market price is too low
5
surplus (PS ) S
4
Z
3.50 Market price
Seller V ’s Y
producer 3
X
surplus = $1.50 2.50
2 W
V
1.50
1 Supply
choke price

0 1 2 3 4 5 Quantity of
apples (pounds)
 In-text
figure it out

The demand and supply curves for newspapers in a

Midwestern city are given by:
QD = 152 – 20P
QS = 188P – 4
where Q is measured in thousands of newspapers per day
and P is the price in dollars per newspaper.

Answer the following questions:

a. Find the equilibrium price and quantity
b. Calculate consumer and producer surplus at the
equilibrium
 In-text
figure it out

a. Remember, the equilibrium is characterized by QD = QS

152 – 20P = 188P – 4
Combining terms and solving for P yields
156 = 208P → P* = $0.75
To find the equilibrium quantity, plug the above price into either the
supply or demand equation,
QD = 152 – 20(0.75) = 137 newspapers or
QS = 188(0.75) – 4 = 137 newspapers

b. The easiest way to calculate consumer and producer surplus

is with a graph; to do this, we must determine two points for
each curve
1. Equilibrium price/quantity
2. Choke prices (where QD /QS are equal to zero)
 In-text
figure it out

We already know one point for each curve: P* = $0.75 ; Q* = 137

Demand choke price: QD = 0 = 152 – 20P → 20P = 152 → P= $7.6; Q =0
Supply choke price: QS = 0 = 188P – 4 → 188P = 4 → P = $0.02; Q=0
Price of
newspapers Consumer surplus is the area below
(dollars) demand but above the price (Area A)
7.6
1
CS  Area A  × base × height
2
1
  137, 000  (7.6  0.75)  $469, 225
2
Producer surplus is the area above
supply but below the price (Area B)
A 1
PS  Area B  × base × height
S 1
2
0.75  137, 000  (0.75  0.02)  $50, 005
B 2
0.02 D Surplus is generally measured in dollars
0 137,000 Quantity of
newspapers
 Consumer and Producer Surplus: Who
Benefits in a Market 3.1
What happens to consumer and producer surplus when there is a shift in
supply or demand?
Price of Imagine a pie shop opens up in the same town.
cupcakes What will happen to the demand for cupcakes?
(dollars)
Demand will shift left, resulting in a new
equilibrium of P2 andQ2
E
A S What happens to consumer surplus?
• Old consumer surplus: A + B + F
• New consumer surplus: B + C
B F
P1 G
What happens to producer surplus?
C
P2 • Old producer surplus: C + D + E + G
D • New producer surplus: D

C has transferred from producers to consumers

D2 D1
A + E + F + G has disappeared from this market
0 Q2 Q1 Quantity of
cupcakes
(thousands)
Consumer and Producer Surplus: Who
Benefits in a Market 3.1
Figure 3.5 Changes in Surplus from a Supply Shift
Price Regulation 3.2
Politicians often call for the direct regulation of prices on
products and services
• Price ceiling: a regulation that sets the maximum price that can
be legally paid for a good or service
‒ Binding only when set below the equilibrium price

• Price floor: a regulation that sets the minimum price that can be
legally paid for a good or service (often called a price support)
‒ Binding only when set above the equilibrium price

What are the effects of price ceilings/floors on markets?

Price Regulation 3.2
Some important terminology
Transfer: surplus that moves from producers to consumers, or vice
versa, as a result of a regulation
Deadweight loss (DWL): the reduction in total surplus that occurs
as a result of a market inefficiency
• Remember the cupcake example of changing demand due to a pie shop

Nonbinding price ceiling: a price ceiling set at a level above the

equilibrium market price
Nonbinding price floor: a price floor set at a level below the
equilibrium market price
Price Regulation 3.2
Figure 3.7 The Effects of a Binding Price Ceiling
Price
Consumer surplus before A+B+C
($/pizza)
Consumer surplus after A+B+D
$20 Producer surplus before D+E+F
Producer surplus after F
A z DWL = C + E Supply
14
B w
C
10
D E y Price Ceiling $8
8 x
F
5
Transfer
of PS Demand
to CS
0 6 10 12 20 Quantity of pizzas
(thousands)/month
Shortage
Price Regulation 3.2
3.8 Deadweight Loss and Elasticities
Price Regulation 3.2
Figure 3.9 The Effects of Binding a Price Floor
Price
($/per ton) Transfer
of CS to PS S

A x y Price floor
$1,000
B w Consumer surplus before A+B+C
C
500 Consumer surplus after A
D E Producer surplus before D+E+F
Producer surplus after B+D+F
z
F

0 10 20 30 Quantity of peanuts
(millions of tons)
Surplus
Quantity Regulations 3.3
Like price regulations, quantity regulations restrict the
amount of a good or service provided to a market
Quota: a regulation that sets the quantity of a good or
service provided
• Often used to limit imports of certain goods
‒ Why might a government pursue an import quota?
• Sometimes used to limit exports (e.g., China and rare earths)

What are the effects of quotas on markets?

Quantity Regulations 3.3
Figure 3.10 The Effects of a Quota
Price
Consumer surplus before A+B+C
($/tattoo)
S2 Consumer surplus after A
$125 Producer surplus before D+E+F
Producer surplus after B+D+F
A z
Pquota = 100
Transfer
of CS to PS
B
C
x S1
P = 50
D E
40
35
y D
F

0 500 1,500 Quantity of

(Quota) tattoos/year
Taxes 3.4
Taxes are very prevalent in societies
Examples:
1. Product markets (VAT; sales taxes)
2. Labor markets (income taxes; payroll taxes)
3. Capital markets (capital gains taxes)

How do taxes impact markets?

• Some taxes are imposed to correct market failures (see Chapter 16)
• In general, taxes distort market outcomes
Example: In 2003, Boston’s Mayor Tom Menino proposed a
$0.50 tax on movie tickets
‒ How should this tax (which was ultimately not adopted by the
legislature) affect the market for movie tickets?
Taxes 3.4
Figure 3.11 The Effects of a Tax on Boston Movie Tickets
Price
($/ticket)
$10
Transfer from CS and PS
to government
S2 = S1 + tax
A
y
Pb = 8.30 C S1
B x
P1 = 8.00
D D
Ps = 7.80 z E Consumer surplus (CS) before A+B+C
F Consumer surplus (CS) after A
Producer surplus (PS) before D+E+F
Producer surplus (PS) after F
6.67 Government revenue B+D

0 Q2 = 3.4 Q1 = 4 Quantity of tickets

(100,000s)
Taxes 3.4
We can also describe the effect of a tax on consumer and producer
surplus with equations. Demand and supply for tickets are given by
Q D  20  2 P; Q S  3P  20
where prices are measured in dollars and quantity in hundreds of
thousands of tickets. Equilibrium occurs when QD = QS,
20  2 P  3P  20  5P  40
Before the tax, tickets are $8 and 400,000 tickets are sold in Boston
CS   Q E  PDChoke  P1 
1
Pre-tax consumer surplus
2
where the demand choke price is found by solving
Q D  0  20  2 PDChoke  PDChoke  $10
and consumer surplus is equal to CS   400,000 $10  $8  $400,000
1
2
Taxes 3.4
Pre-tax producer surplus
PS   Q E  P1  PSChoke 
1
2
where the supply choke price is found by solving,
Q S  0  3PSChoke  20  PSChoke  $6.67
Solving for producer surplus yields

PS   400,000 $8  $6.67  $266,667

1
2
And Total Surplus PS  CS  $666,667

What happens after the tax?

Taxes 3.4
Define the after-tax price as
Pb  PS  $0.50
The market price (the price buyers pay), Pb , is equal to the price the
producer receives, PS , plus the tax. To find the new equilibrium,
substitute this expression into the demand equation
Q D  Q S  20  2 Pb  3PS  20  20  2PS  0.50  3PS  20

Solving for PS : 20 − 1 + 20 = 5𝑃𝑠

The price sellers receive after the tax is PS  $7.80

The price the buyers pay in the market is Pb  PS  $0.50  $8.30

and quantity sold is (substitute buyer price into demand function)

Q2  20  28.30   340 ,000
Taxes 3.4
Post-tax consumer surplus
CS   340,000 $10  $8.30  $289,000
1
2
Post-tax producer surplus
PS   340,000 $7.80  $6.67  $192,100
1
2
How much revenue has been generated by the tax?
Revenue  0.50Q2  $0.50  340,000  $170,000

And the deadweight loss associated with this distortion is

 tax
 1
DWL   Q1  Q2  Pb  Ps    400,000  340,000 $0.50  $15,000
1
2 2
Taxes 3.4
Deadweight loss (DWL) is the loss in total surplus generated
any time a policy creates a market distortion
• DWL associated with taxes is often referred to as “excess burden”
• The size of DWL increases at an increasing rate with the difference
between the pre- and post-policy equilibrium quantities
‒ i.e. Big taxes create more DWL than little taxes

Consider the movie example, but with a $1.00 tax

Pb  PS  $1.00
Q D  Q S  20  2 Pb  3PS  20  20  2PS  1.00  3PS  20

Solving for PS , Pb , and Q2

20  2 PS  2  3PS  20  PS  $7.60; Pb  $8.60
Q2  20  28.60   2.8
Taxes 3.4
Post-tax consumer surplus CS   280,000 $10  $8.60  $196,000
1
2

Post-tax producer surplus PS   280,000 $7.60  $6.67  $130,200

1
2
How much revenue has been generated by the tax?
Revenue  1.00Q2  $1.00  280,000  $280,000
And the deadweight loss associated with this distortion is

 tax
 1
DWL   Q1  Q2  Pb  Ps    400,000  280,000 $1.00  $60,000
1
2 2
So, while the tax has doubled, deadweight loss has quadrupled
from $15,000 to $60,000, and tax revenues have only increased by
78.5% (from $170,000 to $280,000)
Taxes 3.4
Figure 3.12 The Effect of a Larger Tax on Boston Movie
Tickets
Taxes 3.4
Tax incidence is a term describing who actually bears the burden
of a tax
• In the supply and demand model, it does not matter who is required
to pay the tax (e.g., a sales tax vs. a production tax)
‒ Tax incidence will be the same in each case!

Tax incidence and elasticities

• Elasticities of supply and demand are the major determinants of
incidence
• In general, when demand is relatively more elastic, consumers will
experience less burden, and vice versa
‒ Rule: The more elastic curve (supply or demand) bares the
least burden (producer or consumer)
 Taxes 3.4
Figure 3.13 Tax Incidence

(a) Seller Taxed (b) Buyer Taxed

Price ($) Price ($)

S2
Tax = Pb – Ps
S1 S

Pb Pb
P1 P1
Ps Ps

D D1

D2
Tax = Pb – Ps
0 Q2 Q1 Quantity 0 Q2 Q1 Quantity
 A TAX ON GASOLINE

QD = 150 – 25Pb (Demand)

QS = 60 + 20Ps (Supply)
QD = QS (Supply must equal demand)
Pb – Ps = 1.00 (Government must receive $1.00/gallon)

150 − 25Pb = 60 + 20Ps

Pb = Ps + 1.00
150 − 25Pb = 60 + 20Ps
20Ps + 25Ps = 150 – 25 – 60
45Ps = 65, or Ps = 1.44
QD = 150 – (25)(2.44) = 150 – 61, or Q = 89 bg/yr

Annual revenue from the tax tQ = (1.00)(89) = $89 billion per year
Deadweight loss: (1/2) x ($1.00/gallon) x (11 billion gallons/year )= $5.5 billion
per year
 A TAX ON GASOLINE

FIGURE 9.20
IMPACT OF $1
GASOLINE TAX
The price of gasoline at the
pump increases from $2.00
per gallon to $2.44, and the
quantity sold falls from 100
to 89 bg/yr.
Annual revenue from the
tax is (1.00)(89) = $89
billion (areas A + D).
The two triangles show the
deadweight loss of $5.5
billion per year.
Taxes 3.4
Tax incidence and elasticities

A general formula(s) for incidence as a function of elasticities

ES ED
Share born by consumer  S Share born by producer 
E  ED ES  ED

• Notice, the share born by the consumer relies primarily on the

elasticity of the supplier/producer, and vice versa
Taxes 3.4
Figure 3.14 Tax Incidence and Elasticities

(a) Demand More Elastic, (b) Supply More Elastic,

Consumer Bares Less Burden Supplier Bares Less Burden
Subsidies 3.5
Subsidy: a payment by the government to a buyer or seller of a good or
service
• Subsidies are simply the opposite of a tax
Pb  subsidy  PS

Governments subsidize many products and production processes

Examples:
• Producer subsidies: ethanol production, research and development
• Consumer subsidies: education, public transportation
Subsidies 3.5
Figure 3.15 The Impact of a Producer Subsidy
Conclusion 3.6
This chapter examined the supply and demand model in more
detail, and analyzed how government policies affect markets
In the next few chapters, we examine the microeconomic
underpinnings of demand and supply

In Chapter 4, we introduce the concept of utility, which provides

context for understanding how consumers make consumption
decisions
 Additional
figure it out

The weekly supply and demand for cupcakes in a small town

are given as
QD = 124 – 18P
QS = 30P – 20
where P is the price, in dollars, and quantity is measured in
thousands of cupcakes per week

Answer the following questions:

a. Find the equilibrium price and quantity
b. Calculate consumer and producer surplus at the
equilibrium
 Additional
figure it out

a. Remember, the equilibrium is characterized by QS = QD

30P – 20 = 124 – 18P
Combining terms and solving for P yields
48P = 144 → P* = $3
To find the equilibrium quantity, plug the above price into either the
supply or demand equation,
QD = 124 – 18(3) = 70 cupcakes or
QS = 30(3) – 20 = 70 cupcakes
b. The easiest way to calculate consumer and producer surplus
is with a graph; to do this, we must determine two points for
each curve
1. Equilibrium price/quantity
2. Choke prices (where QD /QS are equal to zero)
 Additional
figure it out

We already know one point for each curve: P* = $3.00 ; Q* = 70

Demand choke price: QD = 0 = 124 – 18P → P = $6.89; Q = 0
Supply choke price: QS = 0 = 30P – 20 → P = $0.67; Q = 0

Price of
cupcakes Consumer surplus is the area below
(dollars) demand but above the price (Area A)
6.9 1
CS  Area A   base × height
1 2
  70,000  (6.89  3)  $136,150
S 2

A Producer surplus is the area above

supply but below the price (Area B)
3
1
PS  Area B   base × height
B 2
1
  70,000  (3  0.67)  $81,550
2
0.67 D Surplus is generally measured in dollars
Quantity of
0 70,00
cupcakes
0
 In-text
figure it out

The supply and demand for tires in a local tire market are given as
QD = 3,200 – 25P
QS = 15P – 800
Where Q is the number of tires sold weekly and P is the price, in
dollars, per tire. The equilibrium price is $100 per tire, and 700 tires
are sold each week
Suppose an improvement in technology of tire production makes
them cheaper to produce; specifically, suppose the quantity supplied
rises by 200 at every price
Answer the following questions:
a. What is the new supply curve?
b. What are the new equilibrium price and quantity?
c. What happens to consumer and producer surplus?
 In-text
figure it out

a. Quantity supplied rises by 200, so we simply add it to the

equation for QS:
𝑄2𝑆 = 15𝑃 − 800 + 200 = 𝟏𝟓𝑷 − 𝟔𝟎𝟎

b. The new equilibrium occurs where 𝑸𝑫 = 𝑸𝑺𝟐

3,200 − 25𝑃 = 15𝑃 − 600
3,800 = 40𝑃
𝑷∗ = $𝟗𝟓

Plugging this into either the demand or supply equation:

Demand: 𝑄 ∗ = 3,200 − 25 95 = 𝟖𝟐𝟓 𝐭𝐢𝐫𝐞𝐬
Supply: 𝑄∗ = 15 95 − 600 = 𝟖𝟐𝟓 𝐭𝐢𝐫𝐞𝐬

The new equilibrium price is $95 and the new equilibrium

quantity is 825 tires per week
 In-text
figure it out

c. We need to calculate the consumer and producer surplus

both before and after the shift then compare the two
Before the Supply Shift:
i. Equilibrium: 𝑷𝑬 = 100; 𝑸𝑬 = 700
ii. Demand Choke Price: 𝑸𝑫 = 0
‒ 𝑄𝐷 = 0 = 3,200 − 25𝑃  𝑷𝑫 𝐜𝐡𝐨𝐤𝐞 = $128
iii. Supply Choke Price: 𝑸𝑺𝟏 =0
‒ 𝑄1𝑆 = 0 = 15P − 800  𝑷𝑺𝐜𝐡𝐨𝐤𝐞 =$53.33
𝟏
Consumer Surplus: 𝑪𝑺 = × 𝑸𝑬 × 𝑷𝑫
𝐜𝐡𝐨𝐤𝐞 − 𝑷
𝑬
𝟐
1
𝐶𝑆 = × 700 × 128 − 100
2
𝑪𝑺𝐢𝐧𝐢𝐭𝐢𝐚𝐥 = $𝟗, 𝟖𝟎𝟎.00
𝟏
Producer Surplus: 𝑷𝑺 = × 𝑸𝑬 × 𝑷𝑬 − 𝑷𝑺𝐜𝐡𝐨𝐤𝐞
𝟐
1
𝑃𝑆 = × 700 × 100 − 53.33
2
𝑷𝑺𝐢𝐧𝐢𝐭𝐢𝐚𝐥 = $𝟏𝟔, 𝟑𝟑𝟒. 𝟓𝟎
 In-text
figure it out
c. We need to calculate the consumer and producer surplus
both before and after the shift then compare the two
After the Supply Shift:
i. Equilibrium: 𝑷𝑬 = 95; 𝑸𝑬 = 825 (found in b)
ii. Demand Choke Price: 𝑸𝑫 = 0; 𝑷𝑫 𝐜𝐡𝐨𝐤𝐞 = $128
‒ Unchanged because the demand curve has not shifted
iii. Supply Choke Price: 𝑸𝑺𝟐 =0
‒ 𝑄2𝑆 = 0 = 15𝑃 − 600  𝑷𝑺𝐜𝐡𝐨𝐤𝐞 = $40
𝟏
Consumer Surplus: 𝑪𝑺 = × 𝑸𝑬 × 𝑷𝑫
𝐜𝐡𝐨𝐤𝐞 − 𝑷
𝑬
𝟐
1
𝐶𝑆 = × 825 × 128 − 95
2
𝑪𝑺𝐧𝐞𝐰 = $𝟏𝟔, 𝟔𝟏𝟐. 𝟓𝟎
𝟏
Producer Surplus: 𝑷𝑺 = × 𝑸𝑬 × 𝑷𝑬 − 𝑷𝑺𝐜𝐡𝐨𝐤𝐞
𝟐
1
𝑃𝑆 = × 825 × 95 − 40
2
𝑷𝑺𝐧𝐞𝐰 = $𝟐𝟐, 𝟔𝟖𝟕. 𝟓𝟎
 In-text
figure it out

c. Comparing the initial and the new values:

Before the Supply Shift:
i. Consumer Surplus: 𝐶𝑆initial = $9,800
ii. Producer Surplus: 𝑃𝑆initial = $16,334.50

After the Supply Shift:

i. Consumer Surplus: 𝐶𝑆new = $16,612.50
ii. Producer Surplus: 𝑃𝑆new = $22,687.50

Change in Consumer Surplus = 𝐶𝑆new − 𝐶𝑆initial

= $16,612.50 − $9,800
• Consumer surplus has increased by $3,812.50

Change in Producer Surplus = 𝑃𝑆new − 𝑃𝑆initial

= $22,687.50 − $16,334.50
• Producer surplus has increased by $6,353
 Additional
figure it out

The weekly supply and demand for tires in a small town are given as
QS = 15P – 400; QD = 2,800 – 25P
where P is the price, in dollars, and quantity 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

Answer the following questions:

a. What is the new supply curve?
b. What are the new equilibrium price and quantity?
c. What happens to consumer and producer surplus?
 Additional
figure it out

a. Quantity supplied rises by 200, so we simply add it to the

equation for QS:
𝑄2𝑆 = 15𝑃 − 400 + 200 = 𝟏𝟓𝑷 − 𝟐𝟎𝟎

b. The new equilibrium occurs where 𝑸𝑫 = 𝑸𝑺𝟐

2,800 − 25𝑃 = 15𝑃 − 200
3,000 = 40𝑃
𝑷∗ = $𝟕𝟓
Plugging this into either the demand or supply equation:
Demand: 𝑄 ∗ = 2,800 − 25 75 = 𝟗𝟐𝟓 𝐭𝐢𝐫𝐞𝐬
Supply: 𝑄∗ = 15 75 − 200 = 𝟗𝟐𝟓 𝐭𝐢𝐫𝐞𝐬

The new equilibrium price is $75 and the new equilibrium

quantity is 925 tires per week
 Additional
figure it out

c. We need to calculate the consumer and producer surplus

both before and after the shift then compare the two
Before the Supply Shift:
i. Equilibrium: 𝑷𝑬 = $80; 𝑸𝑬 = 800
ii. Demand Choke Price: 𝑸𝑫 = 0
‒ 𝑄𝐷 = 0 = 2,800 − 25𝑃  𝑷𝑫 𝐜𝐡𝐨𝐤𝐞 = $112
iii. Supply Choke Price: 𝑸𝑺𝟏 =0
‒ 𝑄1𝑆 = 0 = 15𝑃 − 400  𝑷𝑺𝐜𝐡𝐨𝐤𝐞 = $26.67
𝟏
Consumer Surplus: 𝑪𝑺 = × 𝑸𝑬 × 𝑷𝑫
𝐜𝐡𝐨𝐤𝐞 − 𝑷
𝑬
𝟐
1
𝐶𝑆 = × 800 × 112 − 80
2
𝑪𝑺𝐢𝐧𝐢𝐭𝐢𝐚𝐥 = $𝟏𝟐, 𝟖𝟎𝟎
𝟏
Producer Surplus: 𝐏𝑺 = × 𝑸𝑬 × 𝑷𝑬 − 𝑷𝑺𝐜𝐡𝐨𝐤𝐞
𝟐
1
𝑃𝑆 = × 800 × 80 − 26.67
2
𝑷𝑺𝐢𝐧𝐢𝐭𝐢𝐚𝐥 = $𝟐𝟏, 𝟑𝟑𝟐
 Additional
figure it out

c. We need to calculate the consumer and producer surplus

both before and after the shift then compare the two
After the Supply Shift:
i. Equilibrium: 𝑷𝑬 = $75; 𝑸𝑬 = 925 (found in b)
ii. Demand Choke Price: 𝑸𝑫 = 0; 𝑷𝑫𝐜𝐡𝐨𝐤𝐞 = $112
‒ Unchanged because the demand curve has not shifted
iii. Supply Choke Price: 𝑸𝑺𝟐 = 0
‒ 𝑄2𝑆 = 0 = 15𝑃 − 200  𝑷𝑺𝐜𝐡𝐨𝐤𝐞 = $13.33
𝟏
Consumer Surplus: 𝑪𝑺 = × 𝑸𝑬 × 𝑷𝑫
𝐜𝐡𝐨𝐤𝐞 − 𝑷
𝑬
𝟐
1
𝐶𝑆 = × 925 × 112 − 75
2
𝑪𝑺𝐧𝐞𝐰 = $𝟏𝟕, 𝟏𝟏𝟐. 𝟓𝟎
𝟏
Producer Surplus: 𝑷𝑺 = × 𝑸𝑬 × 𝑷𝑬 − 𝑷𝑺𝐜𝐡𝐨𝐤𝐞
𝟐
1
𝑃𝑆 = × 925 × 75 − 13.33
2
𝑷𝑺𝐧𝐞𝐰 = $𝟐𝟖, 𝟓𝟐𝟐. 𝟑𝟖
 Additional
figure it out

c. Comparing the initial and the new values:

Before the Supply Shift:
i. Consumer Surplus: 𝐶𝑆initial = $12,800
ii. Producer Surplus: 𝑃𝑆initial = $21,332

After the Supply Shift:

i. Consumer Surplus: 𝐶𝑆new = $17,112.5
ii. Producer Surplus: 𝑃𝑆new = $28,522.38

Change in Consumer Surplus = 𝐶𝑆new − 𝐶𝑆initial

= $17,112.50 − $12,800
• Consumer surplus has increased by $4,312.50

Change in Producer Surplus = 𝑃𝑆new − 𝑃𝑆initial

= $28,522.38 − $21,332
• Producer surplus has increased by $7,190.38
 In-text
figure it out

The demand and supply for cola in a market is represented by

QD = 15 – 10P
QS = 40P – 50
Where Q is in millions of bottles per year and P is dollars per bottle,
The current equilibrium price is $1.30, and 2 million bottles are sold
per year

Answer the following questions:

a. Calculate the price elasticity of demand and the price elasticity
of supply at the current equilibrium
b. Calculate the share of a tax that will be borne by consumers and
the share borne by producers
c. If a tax of $0.15 per bottle is created, what do buyers now pay
for a bottle? What will sellers receive?
 In-text
figure it out

a. The elasticity of demand and supply are

Q D P 1 P 1 .3
E 
D
 D  D  E D  10   6.5
P Q slope Q 2
Q S P 1 P 1 .3
E 
S
 S   S  E S  40   26
P Q slope Q 2

b. The share of a tax borne by consumers and producers is:

ES
Share born by consumer  
26
 0.8 or 80%
ES  ED 26  6.5

ED 6.5
Share born by producer    0.20 or 20%
ES  ED 26  6.5
 In-text
figure it out

c. If there is a tax of $0.15 per bottle, buyers pay 80%, or $0.12

per bottle(0.15×0.80), and sellers pay 20%, or $0.03 per
bottle (0.15×0.2)

Initial Equilibrium Price = $1.30

‒ Price buyer now pays = $1.30 + 0.12
𝑷𝒃 = $𝟏. 𝟒𝟐

‒ Price seller now receives = $1.30 − 0.03

𝑷𝒔 = $𝟏. 𝟐𝟕
 Additional
figure it out

The supply and demand for soda in a market is represented by

QD = 12 – 8P
QS = 50P – 60
Where Q is in millions of bottles per year and P is dollars per bottle,
The current equilibrium price is $1.17, and 2.62 million bottles are
sold per year.

Answer the following questions:

a. Calculate the price elasticity of demand and the price elasticity
of supply at the current equilibrium
b. Calculate the share of a tax that will be borne by consumers and
the share borne by producers
c. If a tax of $0.10 per bottle is created, what do buyers now pay
for a bottle? What will sellers receive?
 Additional
figure it out

a. The elasticity of demand and supply are

 Q D
P 1 P E D  8 
1.17
 3.75
ED   D  D 
P Q slope Q 2.62
 Q S
P 1 P E S  50 
1.17
ES   S  S   22.33
P Q slope Q 2.62

b. The proportion of a tax borne by buyers and sellers is:

ES 22.33
Share born by consumer    0.856 or 85.6%
ES  ED 22.33  3.75
ED 3.75
Share born by producer    0.144 or 14.4%
ES  ED 22.33  3.75
 Additional
figure it out

c. If there is a tax of $0.10 per bottle, buyers pay 85.6%, or

$0.0856 per bottle(0.10×0.856), and sellers pay 14.4%, or
$0.0144 per bottle (0.10×0.144)

Initial Equilibrium Price = $1.17

‒ Price buyer now pays = $1.17 + 0.0856
𝑷𝒃 = $𝟏. 𝟐𝟐𝟓𝟔

‒ Price seller now receives = $1.17 − 0.0144

𝑷𝒔 = $𝟏. 𝟏𝟓𝟓𝟔
 In-text
figure it out

Consider the supply and demand for ethanol in small town below,
QD = 9,000 – 1,000P
QS = 2,000P – 3,000
Where Q measures gallons per day and P represents the price per
gallon.
The current equilibrium price is $4, and 5,000 gallons per day;
suppose the government wants to create a subsidy of $0.375 per
gallon to encourage the use of ethanol
Answer the following questions:
a. What will happen to the price buyers pay per gallon, the price
sellers receiver per gallon, and the number of gallons consumed
per day?
b. How much will this subsidy cost the government?
 In-text
figure it out

a. The first step is determining how the subsidy affects prices

Pb  subsidy  PS
The price the seller receives is larger than the price paid by the buyers
because of the subsidy,
PS  Pb  0.375

Supply and demand are given by

Q D  9,000  1,000 Pb , Q S  2,000 Ps  3,000

Substituting in for PS
Q S  2,000( Pb  0.375)  3,000  2,000 Pb  2,250
Equating the new supply and original demand, and solving for Pb

2,000 Pb  2,250  9,000  1,000 Pb  Pb  $3.75

 In-text
figure it out

The new producer price is given by

PS  Pb  0.375  PS  $4.125

To estimate the quantity of ethanol sold after the subsidy we can plug
Pb into the demand equation or PS into the supply equation

Q D  9,000  1,000(3.75)  Q D  5, 250 gallons

Q S  2,000(4.125)  3,000  Q S  5, 250 gallons
So, the price paid by consumers has decreased by about $.25 per
gallon to $3.75, the price received by the seller has increased by
about $.125 per gallon to $4.125, and the number gallons of ethanol
sold per day has increased by 250 gallons to 5,250.

b. How much did this cost the government?

Cost  subsidy  Q  $0.375  (5, 250)  $1,968.75per day
 Additional
figure it out

For years the government has subsidized higher education through

grants; consider the demand and supply for college credit hours at a
local private liberal arts college
QD = 8,000 – 500P
QS = 1,000P – 2,500
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 subsidizes credit hours
at a rate of $200 per hour
Answer the following questions:
a. What will happen to the price paid by students, the price received
by the college, and the number of credit hours completed?
b. What is the cost of the subsidy to the government?
 Additional
figure it out

a. The first step is determining how the subsidy affects prices

Pb  subsidy  PS
In this problem,
Pb  2  PS
Supply and demand are given by

Q D  8, 000  500 Pb ; Q S  1, 000PS  2,500

Substituting in for PS
Q S  1, 000  Pb  2   2,500  1, 000 Pb  500
Equating supply and demand, and solving for Pb
8, 000  500 Pb  1, 000 Pb  500  Pb  $566.7
 Additional
figure it out

The new producer price is given by

Pb  200  PS  PS  $766.7
To estimate the credit hours taken after the subsidy we can plug Pb
into the demand equation or PS into the supply equation
Q D  8,000  500(5.667)  Q D  5,166.50
Q S  1,000(7.667)  2,500  Q S  5,166.50 (rounding )

So, the price paid by consumers has decreased by about $133, the
price received by the college has increased by about $67, and the
number of credit hours consumed has increased by about 667

b. How much did this cost the government?

Cost  subsidy  Q  $200  667  $133, 400