Supply and Demand Models
Chapter 3,4
Laws of Supply and Demand
Supply and Demand Framework
• A description of a market includes the
quantity of goods that are sold in that
market, Q, and the price, P, at which they
are sold.
• Outcomes in the market are a function of
the laws of supply and demand
Law of Demand
•
Ceteris parabis, There is an inverse relationship
between the price of a good and the quantity that
consumers would like to purchase.
Demand Curve Mathematical representation of Law
of Demand
–
–
–
Demand Curve (Geometry)
Demand Function (Algebra)
Demand Schedule (Spreadsheet)
What does
Ceteris Parabis
mean?
Law of Demand
Two Explanations:
1. Substitution Effect – Goods purchased to
satisfy needs but other goods (substitutes)
may also do so. When price rises, consumers
have an incentive to switch goods.
2. Income Effect – Consumers have a limited
budget. When price of a major item goes up,
less money for purchase of all items.
Demand Curve
P
D
P2
P1
Q2
Q1
Q
Demand Functions
• An algebraic equation representing demand
as a function of the price plus consumer
income levels and other factors

Q  Q P, Other Factors
D

• Example:
Q  Dt  Pt
D
t
e

Global Daily Demand Schedule for Oil
2006
P/bbl
60
70
80
90
100
110
120
130
140
150
Q/mil.bbl
83,033.06
81,762.92
80,678.38
79,733.70
78,898.04
78,149.63
77,472.59
76,854.95
76,287.50
75,762.98
Law of Supply:
•
Ceteris parabis, there is a positive relationship
between the price of a good and the quantity
producers bring to the market.
Supply Curve Mathematical representation of Law
of Supply
–
–
–
Supply Curve (Geometry)
Supply Function (Algebra)
Supply Schedule (Spreadsheet)
Law of Supply
Explanation
• Increasing Costs Producers will bring goods to
market only if the price obtained from selling an
extra good will exceed the cost of producing an
extra good. If per unit production costs are rising
in the number of goods produced, higher prices
will be demanded to bring a larger quantity of
goods to market.
Supply Curve
P
S
P2
P1
Q1
Q2
Q
Supply Functions
• An algebraic equation representing supply
as a function of the price plus input costs
and other factors

Q  Q P, Other Factors
S
• Example:

Q  St  Pt
D
t
f

Global Daily Supply Schedule for Oil
2006
P/bbl Q/mil.bbl
60
80,059.86
70
81,303.55
80
82,396.49
90
83,372.72
100
84,255.78
110
85,062.66
120
85,806.03
130
86,495.60
140
87,138.99
150
87,742.26
Equilibrium
• Equilibrium in the competitive market occurs
when the price is set at a level (P*) such that the
amount that consumers want to buy is equal to
the amount that sellers want to sell (Q*).
Excess Supply If P were above equilibrium, sellers
would want to sell more goods than buyers would
want to buy. Competition between sellers would
force prices down.
Excess Demand If P were below equilibrium,
customers would want to buy more goods than
people would want to sell. Competition between
buyers would force prices up.
Competitive Market Equilibrium
P
S
D
1
P*
Q*
Q
Excess Supply
P
S
D
P
P*
Q*
Q
Excess Demand
P
S
D
P*
P
Q*
Q
Market Equilibrium
(Spreadsheet Problem)
At what price and quantity (to closest $10) will the oil
market clear?
P
60
70
80
90
100
110
120
130
140
150
P
Q
80,059.86
81,303.55
82,396.49
83,372.72
84,255.78
85,062.66
85,806.03
86,495.60
87,138.99
87,742.26
60
70
80
90
100
110
120
130
140
150
Q
83,033.06
81,762.92
80,678.38
79,733.70
78,898.04
78,149.63
77,472.59
76,854.95
76,287.50
75,762.98
Market Changes
Shifts in Demand & Supply Curves
To think about commodity prices,
economists first think about the theory
of competitive markets
• Competitive Markets have many buyers and
many sellers who compete without barriers
preventing rivals from entering or leaving
the market.
• Participants in competitive markets are
price takers, agents who behave as if their
own behavior has no effect on market prices.
Shifting Curves/Changing Equilibrium
• Changes in equilibrium result from shifts in
either the demand or supply schedule. We
think of shifts in the curves as changes in
supply or demand that are caused by factors
other than changes in the price of the good.
– Shifts in the demand curve lead to movements
along the supply curve resulting in changes in
prices and quantities that move in the same
direction.
– Shifts in the supply curve lead to movements
along the demand curve resulting in changes in
prices and quantities that move in different
directions.
A Shift in the Demand Curve: A parallel increase in
the demand schedule at every price point.
Price and Quantity Demanded move in same direction
P
S
Shift in the
demand curve
P**
D′
P*
D
Q*
Q**
Q
A Shift in the Supply Curve is a Movement along the
Demand curvePrice and Quantity Supplied Move in opposite Directions
P
S′
D
S
P**
P*
Q** Q*
Q
Equilibrium Effects
• Price system means that shifts in demand
will cause changes in quantity supplied but
also an attenuating change in quantity
demanded.
• Shifts in supply will cause changes in
quantity demanded but also attenuating
change in quantity supplied.
A Shift in the Demand Curve: Equilibrium Effect:
Movement along the supply curve increases quantity supplied;
movement along demand curve ameliorates quantity
demanded.
S
P
P**
Along demand
curve
Along
supply
curve
P*
D′
D
Q*
Q**
Q
A Shift in the Supply Curve: Equilibrium Effect:
Movement along the demand curve reduces quantity
demanded; movement along supply curve ameliorates
quantity supplied.
P
P**
D
S′
Along
supply
curve
S
Along demand
curve
P*
Q** Q*
Q
Price Sensitivity and Equilibrium
Effects
• When supply or demand curve shifts, the
effect will be felt in some combination of
changes in prices and quantities.
• The degree to which changes in either
supply or demand are felt in quantity
changes rather than price changes is
determined by price sensitivity of both
demand and supply.
Algebra of Supply and Demand
• Linear Functions
Demand Curve
Q D  D0  d  P
Supply Curve
Q  S0  s  P
S
Parameters s and d denote the
sensitivity of quantity
demanded or quantity
supplied to price changes.
Linear Functions – Described by Intercept (AS or
AD ) and slope (1/s or 1/d).
P
D0
S
d
P*,Q*
1
1
1
d
s
S0
D
s
Q
• What price sets supply equal to demand?
S0  s  P  D0  d  P
1
1
( s  d ) P D0  S0  P 
 D0 
 S0
sd
sd
• What quantity will be demanded (supplied)
at hat price?
*
1
 1

Q  D0  d  P , Q  D0  d  
 D0 
 S0 
sd
sd

s
d
 Q* 
 D0 
 S0
sd
sd
*
*
*
Example
QD  50  5  P
QS  10  5  P  10  5  P  50  5  P
  50  10   10  P  40  10  P  P  4
 QS  10  5   P  4   30
 QD  50  5   P  4   30
Algebra of Equilibrium Effects
• If s or d are big, effects of supply or demand change
on equilibrium price will be small
1
1
P 
 D0 
 S0
sd
sd
*
• Effects of supply or demand changes on equilibrium
quantity will be determined by relative price
sensitivity.
1
1
Q 
 D0 
*
1 d
s
1 s
 S0
d
Steeper (less price sensitive) supply curve means that a demand
shift will have a smaller impact on quantity and bigger impact
.
on price.
S1
P
S2
1
P1**
P2**
P*
2
0
D’
D
Q*
Q1**
Q2**
Q
Steeper (less elastic) demand curve means that a supply shift
will have a smaller impact on quantity and bigger impact on
.
price.
S’
P
S
1
P1**
2
P2**
P*
0
D2
D1
Q1**
Q2**
Q*
Q
Steeper (less price sensitive) supply curve means that a supply
shift will have a bigger impact on quantity and bigger impact
.
on price.
S1
P
S1'
S2
S2'
P*
P2**
P1**
0
2
1
D
Q*Q2**Q1**
Q
Steeper (less price sensitive) demand curve means that a
demand shift will have a bigger impact on quantity and a
.
bigger impact on price.
S’
P
S
P1**
2
P2**
P*
1
0
D2
D2
D1
Q2**
Q*
D1
Q1**
Q
Elasticity as Price Sensitivity
Measuring the Impact of Price on
Quantity Demanded
• A natural way of measuring impact of a price
change is to measure the change in quantity
demanded relative in size to the change in prices.
Q Q
P1  P0
D
1
D
0
Run

 d
Rise
Q Q
Run

s
P1  P0
Rise
S
1
S
0
Economists often prefer elasticity to
slope in real world
•
•
This measure is the inverse of the SLOPE of
the demand curve which is constant when the
demand curve is linear (as often depicted in
textbooks)
Economists typically do not measure the price
impact using slope for 2 reasons.
1. Slope as a measure is not unit free, so price impacts
are not comparable across types of goods or
currency.
2. Empirical demand curves tend not to have constant
slope or constant elasticity, but constant elasticity
functions are a better approximation.
Price Elasticity: The % impact on
quantity demanded of a 1% change in price
%Change in Q
%Change in P
D
elasticity
Demand
%Drop in Q

0
%Increase in P
S
elasticity
Supply
%Increase in Q

0
%Increase in P
Midpoint Method
• If you want to
calculate a %
difference between
two points which is
the same regardless of
which you designate
as the reference point
(denominator), you
can use the average of
the two points as the
reference point.
X1  X 0 

%X 
 X1  X 0 
 2 
Slope and Elasticity of Oil Demand
P
Q
60
70
80
90
100
110
120
130
140
150
%Increase in P
%Decrease in Q
elasticity
83,033.06
15.38%
1.54%
0.10
13.33%
1.34%
0.10
11.76%
1.18%
0.10
10.53%
1.05%
0.10
9.52%
0.95%
0.10
8.70%
0.87%
0.10
8.00%
0.80%
0.10
7.41%
0.74%
0.10
6.90%
0.69%
0.10
81,762.92
80,678.38
79,733.70
78,898.04
78,149.63
77,472.59
76,854.95
76,287.50
75,762.98
Elasticity of Supply in Oil Market
P
Q
60
70
80
90
100
110
120
130
140
150
%Increase in P
%Increase in Q
elasticity
80,059.86
15.38%
1.54%
0.10
13.33%
1.34%
0.10
11.76%
1.18%
0.10
10.53%
1.05%
0.10
9.52%
0.95%
0.10
8.70%
0.87%
0.10
8.00%
0.80%
0.10
7.41%
0.74%
0.10
6.90%
0.69%
0.10
81,303.55
82,396.49
83,372.72
84,255.78
85,062.66
85,806.03
86,495.60
87,138.99
87,742.26
Learning Outcomes
• Solve for equilibrium price and quantities using
graphical supply and demand model or
spreadsheet supply and demand schedules or
simple linear algebra.
• Explain qualitatively the likely consequences for
equilibrium prices and quantities resulting from
exogenous shifts in supply and demand.
• Calculate elasticities using the midpoint method.