Chapter 1
Markets
Intermediate Microeconomics:
A Tool-Building Approach
Routledge, UK
© 2016 Samiran Banerjee
Market Demand
Market demand:
Qd = f(p)
IDependent
variable
IIndependent
variable
Example: Qd = 120 – 2p
Inverse market demand:
p = g(Qd)
Example: p = 60 – 0.5Qd
Vertical
intercept
Slope
*The function g is the inverse of f.
Adding inverse demands
Suppose the inverse demand on market 1 is
p = 40 – 2Q1d
p
40
20
0
20
Market 1
Qd1
Adding inverse demands
Suppose the inverse demand on market 2 is
p = 30 – Q2d
p
40
30
20
0
Market 1
20
30
Market 2
50
Qd1, Qd2
Adding inverse demands
Graphically, add the two market demands horizontally!
• If p ≥ $30, only consumers in market 1 buy
• If p < $30, consumers in both markets buy
p
40
30
20
Aggregate demand
0
Market 1
20
30
Market 2
50
Qd1, Qd2, Qd
Adding inverse demands
To derive the inverse demand mathematically:
• “Flip” p = 40 – 2Q1d to get Q1d = 20 – 0.5p
• “Flip” p = 30 – Q2d to get Q2d = 30 – p
• Add them: Qd = Q1d + Q2d = 50 – 1.5p
• “Flip” to obtain the inverse aggregate demand:
p = 100/3 – 2Qd/3
“FLIP, FLIP, ADD, and FLIP!”
Market Supply
Suppose the inverse supply is
p = Qs
p
Aggregate supply
40
20
s
0
20
40
Q
Market Equilibrium
• Set the inverse aggregate demand equal to the inverse
supply: 100/3 – 2Qd/3 = Qs
• Since Qd = Qs = Q* in equilibrium, Q* = 20
• Then p*= $20
p
Aggregate supply
40
20
Aggregate demand
0
20
50
Q
Market Stability
• Dynamic story
• What happens if p > p*
• What happens if p < p*
p
Aggregate supply
40
Excess
supply
20
Excess
demand
Aggregate demand
d
0
50
Q
Market Welfare
• Consumer surplus: value to buyer minus price paid
• Producer surplus: price received minus value to seller
p
Aggregate supply
40
Consumer surplus
20
Aggregate demand
Producer surplus
0
50
Q
Demand Determinants
• Income of buyers
◊ increase in demand:
◊ decrease in demand:
• Prices of other goods
◊ increase in demand:
◊ decrease in demand:
• Tastes or preferences of buyers
• Number of buyers
Supply Determinants
• Prices of inputs
• Technology
• Number of sellers
Intervention: Price ceiling
• Set a maximum price below p*
• Smaller of the quantities demanded or supplied is
traded
p
Supply
p*
^p
Excess
demand
Demand
0
^
Q
–
Q* Q
Q
Price ceiling: Welfare
• A = (largest possible) consumer surplus
• B = producer surplus
• C = (smallest possible) deadweight loss
p
Supply
A
C
p*
^p
Excess
demand
B
Demand
0
^
Q
–
Q* Q
Q
Intervention: Price floor
• Set a minimum price above p*
• Smaller of the quantities demanded or supplied is
traded
p
Demand
Excess
supply
_
p
Supply
p*
0
–
Q
Q*
~
Q
Q
Price floor: Welfare
• A = consumer surplus
• B = (largest possible) producer surplus
• C = (smallest possible) deadweight loss
p
Demand
A
Excess
supply
_
p
p*
0
B
Supply
C
–
Q
Q*
~
Q
Q
Intervention: Quota
• Set a maximum quantity below Q*
• The supply curve becomes vertical at the quota
p
Effective
Supply
Supply
~p
p*
Demand
0
~
Q
Q
Q*
Quota: Welfare
• A = consumer surplus
• B = producer surplus
• C = deadweight loss
p
Effective
Supply
A
Supply
~p
p*
B
C
Demand
0
~
Q
Q
Q*
Intervention: Per unit tax
• A per unit tax of t dollars is imposed on sellers
• The new inverse supply is pn = po + t
• Buyers pay pn* to buy one unit
• Sellers receive pn* – t from each sale
p
After-tax
Supply
pn*
t
Original
Supply
po*
pn* – t
Demand
0
Qn*
Qo*
Q
Per unit tax: Welfare
• A = consumer surplus
• B = producer surplus
• T = tax revenue
• C = deadweight loss
p
After-tax
Supply
A
pn*
t
T
po*
Original
Supply
C
pn* – t
B
Demand
0
Qn*
Qo*
Q
Per unit tax: Sellers vs. buyers
On sellers
• New inverse supply is
pn = po + t
• pn* is price paid by buyers
On buyers
• New inverse demand is
pn = po – t
• pn* is price received by sellers
p
p
Original
Demand
After-tax
Supply
A
pn*
t
T
po*
Original
Supply
A
Supply
pn* + t
C
T
po*
C
pn*
pn* – t
B
B
t
Demand
0
Qn*
Qo*
Q
0
Qn*
Qo*
After-tax
Demand
Q
Intervention: Per unit subsidy
• A per unit subsidy of s dollars is given to sellers
• The new inverse supply is pn = po – s
• Buyers pay pn* to buy one unit
• Sellers receive pn* + s from each sale
p
Original
Supply
pn* + s
po*
s
After-subsidy
Supply
pn*
Demand
0
Qo*
Qn*
Q
Per unit subsidy: Welfare
• A = consumer surplus
• B = producer surplus
• Green parallelogram = subsidy payment
• C = deadweight loss
p
Original
Supply
pn* + s
po*
A
s
C
After-subsidy
Supply
pn*
B
Demand
0
Qo*
Qn*
Q
Demand elasticities
Demand elasticities measure how the quantity demanded
of a product changes with different determinants of
demand. In general,
Elasticity =
Percentage change in qty. demanded of x
Percentage change in determinant
“epsilon”
• Own-price elasticity of demand, εxx: determinant = px
• Cross-price elasticity of demand, εxy: determinant = py
• Income elasticity of demand, ηx: determinant = income
“eta”
Own-price elasticity
• Given two points on an inverse market demand:
(Qo, po) and (Qn, pn)
• The percentage change in quantity is
[(Qn – Qo)/Qo] x 100 = (ΔQ/Qo) x 100
• The percentage change in price is
[(pn – po)/po] x 100 = (Δp/po) x 100
ε=
ΔQ
Δp
.
po
Qo
=~
∂Q
∂p
.
po
Qo
Derivative of market demand
at original point*
* For infinitesimal price changes
Own-price elasticity: linear demand
ε@B=
∂Q
∂p
.
po
Qo
FB/FA
ε@B=
OF
p
(Qo, po)
A
OE = FB
B
F
OF
FA
O
E
C
Q
d
Other demand elasticities
• The cross price-elasticity for good x with respect to
the price of y is
εxy =
∂Qx
∂py
.
py
Qx
• The income elasticity for good x is
∂Qx m
.
ηx =
∂m Qx
Supply elasticity
The supply elasticity measures how the quantity supplied
of a product changes with the price of the product.
In general,
εs =
∂Qs
∂p
.
po
Qos