SUPPLY AND DEMAND
MODELS
CHAPTER 3,4
VOLATILE OIL PRICES
St. Louis Fed FRED database
PRICES AND PRODUCTION 1976-2013
US$/Barrel
120.00
100.00
80.00
60.00
40.00
20.00
0.00
55000
60000
65000
70000
75000
BP Statistical Review of World Energy
80000
85000
90000
LAWS OF
SUPPLY
AND
DEMAND
SUPPLY AND DEMAND FRAMEWORK
A description of a market includes the
quantity of goods that are sold in that
market, Q, and the price, P, at which
they are sold.
Outcomes in the market are a function
of the laws of supply and demand
LAW OF DEMAND
Ceteris parabis, There is an inverse
relationship between the price of a good
and the quantity that consumers would
like to purchase.
What does Ceteris Parabis mean?
LAW OF DEMAND
Two Explanations:
1. Substitution Effect – Goods purchased
to satisfy needs but other goods
(substitutes) may also do so. When
price rises, consumers have an
incentive to switch goods.
2. Income Effect – Consumers have a
limited budget. When price of a major
item goes up, less money for purchase
of all items.
MATHEMATICAL REPRESENTATIONS
OF LAW OF DEMAND
1. Demand Schedule
(Spreadsheet)
2. Demand Curve (Geometry)
3. Demand Function (Algebra)
GLOBAL DAILY DEMAND SCHEDULE
FOR OIL 2010
P = US$
QD = Thousand barrels daily
P
60
65
70
75
80
85
90
95
100
Q
83,035
82,704
82,398
82,114
81,850
81,602
81,369
81,149
80,941
P
Demand Curve for Oil
103
98
93
88
83
78
73
68
63
58
80,500
81,000
81,500
82,000
82,500
83,000
83,500
Q
GENERAL DEMAND CURVE
P
D
P2
P1
Q2
Q1
Q
LAW OF SUPPLY:
•
Ceteris parabis, there is a positive relationship
between the price of a good and the quantity
producers bring to the market.
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.
MATHEMATICAL REPRESENTATION
OF LAW OF SUPPLY
1. Supply Schedule
(Spreadsheet)
2. Supply Curve (Geometry)
3. Supply Function (Algebra)
GLOBAL DAILY SUPPLY SCHEDULE
FOR OIL
2010
P
60
65
70
75
80
85
90
95
100
Q
81,350
81,611
81,854
82,080
82,292
82,492
82,680
82,860
83,030
SUPPLY CURVE
S
P
P2
P1
Q1
Q2
Q
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
P*
Q*
Q
EXCESS
SUPPLY AT
P
EXCESS
DEMAND AT
P
S
D
Excess Supply
P
Excess
Demand
Creates
Upward Price
Pressure
P
Excess Supply
Creates
Downward Price
Pressure
P*
P
Excess Demand
Q*
Q
MARKET EQUILIBRIUM
(SPREADSHEET PROBLEM)
At what price and quantity (to closest $5) will the oil market clear?
P
60
65
70
75
80
85
90
95
100
QD
83,035
82,704
82,398
82,114
81,850
81,602
81,369
81,149
80,941
QS
81,350
81,611
81,854
82,080
82,292
82,492
82,680
82,860
83,030
SUPPLY & DEMAND
FUNCTIONS
Algebraic equation representing
supply & demand as a function of the
price plus other factors
Q D  Q P, Other Factors

Q  Q P, Other Factors
S




Example:
Linear:
QD = A – B × P
QS = C + D× P

ALGEBRA OF EQUILIBRIUM
Linear Functions
A - B×P = QD = QS = C + D ×P
A - B×P* = C+D×P*
(A-C) = (B+D) ×P*
𝐴−𝐶
𝑃 =
𝐵+𝐷
∗
QS
=
=
𝐴−𝐶
= C+D×
=
𝐵+𝐷
𝐵
𝐷
C×
+A×
𝐵+𝐷
𝐵+𝐷
C+D×P*
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
MARKET CHANGES:
SHIFTS IN DEMAND & SUPPLY
CURVES
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
①
P**
⓪
P*
Excess Demand
D′
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
①
P**
⓪
P*
Excess Demand
Q
Q** Q*
EQUILIBRIUM EFFECTS
Price system means that shifts in demand
will cause accommodating changes in
quantity supplied but also an attenuating
change in quantity demanded.
Shifts in supply will cause accommodating
changes in quantity demanded but also
attenuating change in quantity supplied.
EQUILIBRIUM EFFECT: MOVEMENT ALONG THE SUPPLY CURVE
INCREASES QUANTITY SUPPLIED; MOVEMENT ALONG DEMAND
CURVE AMELIORATES QUANTITY DEMANDED.
P
P**
S
Along demand
curve
Along
supply
curve
①
⓪
P*
Excess Demand
D′
D
Q* Q**
Q
EQUILIBRIUM EFFECT: MOVEMENT ALONG THE DEMAND CURVE
REDUCES QUANTITY DEMANDED; MOVEMENT ALONG SUPPLY
CURVE AMELIORATES QUANTITY SUPPLIED.
P
P**
D
Along
supply
curve
S′
①
S
Along demand
curve
⓪
P*
Q** Q*
Q
WHAT SHIFTS THE CURVES?
WHAT SHIFTS THE
WHAT SHIFTS THE
DEMAND CURVE?
SUPPLY CURVE?
1. Price of Related Goods
1. Price of Inputs
2. Income
2. Price of Related Goods
3. Consumer Preferences
3. Technology/Nature
4. Expected Future Prices
4. Expected Future Prices
5. Market Entry
ELASTICITY
AS PRICE
SENSITIVITY
PRICE ELASTICITY: THE % IMPACT ON
QUANTITY DEMANDED/SUPPLIED OF A
1% CHANGE IN PRICE
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.
%𝑋 ≡ 100 ×
[𝑋1 −𝑋0 ]
[𝑋1 +𝑋0 ]
2
P
Rise
in
Price
Q
Drop in
% Rise
Quantity
in
Demanded Price
% Drop in
Quantity
Demanded Elasticity
60 83,035
62.5
82,870
5
332
8.00%
0.40%
0.050
5
306
7.41%
0.37%
0.050
5
284
6.90%
0.34%
0.050
5
265
6.45%
0.32%
0.050
5
248
6.06%
0.30%
0.050
5
233
5.71%
0.29%
0.050
5
220
5.41%
0.27%
0.050
5
208
5.13%
0.26%
0.050
65 82,704
67.5
82,551
70 82,398
72.5
82,256
75 82,114
77.5
81,982
80 81,850
82.5
81,726
85 81,602
87.5
81,485
90 81,369
92.5
81,259
95 81,149
97.5
81,045
100 80,941
DEMAND ELASTICITY
A demand curve is classified as INELASTIC
if the elasticity is between 0 and 1
Unit elasticity (elasticity equal to 1) is
the cutoff point
A demand curve is classified as
ELASTIC if the elasticity is more than 1
PRICES AND REVENUE
Revenue in a market is Revenue = P∙Q
If prices change, revenue will change for two
reasons:
1. Direct Effect of the Price Change (positive)
2. Indirect Effect of the Price Change on Quantity
Demanded (negative)
Rule of Thumb: The percentage change in the
product of two variables is approximately
the sum of the % change in each variable.
PRICE ELASTICITY OF REVENUE
% Revenue  % P  %Q
% Revenue
%Q
 1
 1  elasticity
%P
%P
If demand is elastic, a price rise reduces
revenues
If demand is inelastic, a price rise increases
revenues
INCOME ELASTICITY/ CROSS PRICE ELASTICITY
CHANGING
EQUILIBRIUM
INCOME ELASTICITY
We measure the effect of income on
demand for a good as % effect on
demand of a 1% increase in income,
ceteris parabis.
For normal goods, income elasticity is
positive.
For inferior goods income elasticity is
negative.
LUXURIES VS. NECESSITIES
There are two types of normal goods.
Luxuries take up an increasing share of income as
your income grows.
• Luxuries are income elastic - the income elasticity of
luxuries is greater than 1.
Necessities take up a declining share of income as
your income grows.
• Necessities are income inelastic – the income elasticity of
necessities is less than 1
China’s Emerging Middle Class Download
Inferior Goods
RANGE OF INCOME
ELASTICITIES
Normal Goods
0
1
Income Inelastic
(Necessities)
Income Elastic
(Luxury Goods)
CHANGES IN PRICES OF
OTHER GOODS
For any good there are two types of other
goods which are relevant to its demand
1. Substitutes: Those other goods which
can take the place of the good of
interest (bacon vs. ham)
2. Complements: Those other goods
whose use will enhance the value of the
good of interest. (bacon and eggs)
What are substitutes and complements for oil
SUBSTITUTES VS. COMPLEMENTS
A good is defined as a “Substitute” when a
rise in its price leads to a shift out/up in
the demand curve for the good of interest.
A good is defined as a “Complement”
when a rise in its price leads to a shift
in/down in the demand curve for the good
of interest.
CROSS PRICE ELASTICITY
Cross price elasticity is the % effect on
the quantity demanded of a % change in
another price.
• Goods with positive cross-price elasticities are
called substitutes
• Goods with negative cross-price elasticities are
called complements
0
Complements
Substitutes
CROSS PRICE ELASTICITY
We measure the effect of income on
demand for a good as % effect on
demand of a 1% increase in related
price: Ex.D
Q = A - B×P + f × PK
PK = Price of Related Good
For substitutes, cross price elasticity
is positive (f > 0).
For complements , cross price
elasticity is negative (f < 0).
CHAP. 3, 4
COMMODITY
MARKETS
PRICE SENSITIVITY AND
EQUILIBRIUM EFFECTS
When supply or demand curves shift,
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.
WHAT DETERMINES PRICE
ELASTICITY?
AVAILABILITY OF
SUBSTITUTES
A price increase will
lead to a shift away
from the use of a
product and toward
other products.
• Price elasticity will be
stronger if there are
readily available
substitutes for a
good.
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SHARE OF
INCOME
A price increase for
one good reduce
income available for
purchases for all
goods
• Price elasticity will
be stronger if a
good makes up a
big chunk of income.
COMPARISONS OF DEMAND
PRICE ELASTICITIES
Price Elasticities of Other Goods
Salt
Coffee
.1
.25
Tobacco
.45
Movies
.9
Housing
Restaurant Meals
1.2
2.3
Commodities have very inelastic demand.
• Estimate of elasticity of demand for oil in the US is .061
J.C.B. Cooper, OPEC Review, 2003)
ELASTICITIES
EXTREME
P
Perfectly Inelastic
Demand (Insulin)
D
Perfectly Elastic
Demand (Clear Pepsi)
D
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
P1**
S
①
②
P2**
⓪
P*
D2
D1
Q2**
Q1**
Q*
Q
ELASTICITY OF SUPPLY
Elasticity of supply curve depends on
the ability of production sector to
ramp up supply without increasing
the marginal cost of production.
A good that is produced with readily
available factors w/o a need for time
consuming investment will have an
elastic supply curve.
ELASTICITIES:
SUPPLY
P
Perfectly Inelastic Supply
(Van Gogh Paintings)
Perfectly Elastic
Supply (Foot
Massage)
S
Q
S
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
ALGEBRA OF EQUILIBRIUM EFFECTS
If demand or supply elasticities are big, effects of
supply or demand change on equilibrium price will
be small
A
C
P* 

BD BD
1
A  P* 
 A
BD
1
C  P*  
 C
BD
Income Elasticity of Oil
Region
China
Income
Elasticity
0.7
OECD
0.4
ROW
0.6
SOURCE: OECD STUDY
Assume a world
income elasticity
of .5 and an increase
of world income
equal to 5%. Demand
shifts out by 2.5%.
Would oil production
supplied increase by
2.5%?
MARKET EQUILIBRIUM
(SPREADSHEET PROBLEM)
Demand shifts
out by 2.5% at
every price.
At what price and quantity (to closest $5) will the oil market clear?
P
60
65
70
75
80
85
90
95
100
QD
83,035
82,704
82,398
82,114
81,850
81,602
81,369
81,149
80,941
QQDS´
85,111
81,350
84,771
81,611
84,458
81,854
84,167
82,080
83,896
82,292
83,642
82,492
83,403
82,680
83,178
82,860
82,965
83,030
Equilibrium increases by less than 2.5%.
PRICE ELASTICITY
AND TIME
ELASTICITY OF DEMAND
SHORT-TERM VS. LONG-TERM
It takes time to find substitutes for goods or
to adjust consumption behavior in response
to a change in prices.
The long-run demand response to a price
rise is larger than the short-run. Price
elasticity of demand is more negative in the
long run than in the short run.
.
OIL DEMAND MUCH MORE
ELASTIC IN LONG RUN THAN
SHORT-RUN
Price Elasticity of Demand
Short-term
Long-term
Germany
0.02
0.27
Japan
0.07
0.36
Korea
0.09
0.18
USA
0.06
0.45
–(J.C.B. Cooper, OPEC Review, 2003)
PRICE ELASTICITY OF SUPPLY
Firms also find it easier to adjust production
in the long-run than the short run. Long-run
price elasticity of supply is typically greater
than short-run
OECD study suggests price elasticity of oil
supply is .04 in short run and .35 in long run.
SPECULATION & SUPPLY
Some commodities have a time
dimension. Producers have a choice
about when to bring goods to market.
If producers believe prices will be
higher in the future, they have an
incentive to delay shipment to the
future.
Note: This won’t work for apples, oranges or other perishable
commodities.
EQUILIBRIUM – PERISHABLE
GOOD
P
S
D
No
speculative
component
PFV
Q*
Q
HOTELLING PRICE
Consider a perfectly storable good, so arbitrageurs could
buy an inventory and decide to bring it to market.
Consider if arbitrageurs expect the price to be greater than
todays price plus interest. Define 1+i as the gross interest
rate. If arbs expect future price, P+1 > (1+i)P, to be larger than
todays price plus interest, then borrowing P, and storing the
good is a way to make profits.
Producers also have an incentive to retain good as long as P
is less than Hotelling price, PH P+1/(1+i)
EQUILIBRIUM – STORABLE GOOD
If Hotelling P
price above
fundamental
price, then
supply
H
P
drains from
market as
demand from
arbs
PFV
increase.
D
S'
D'
S
②
⓪
Q
Q
POLICY
ANALYSIS
PRICE CEILINGS
TAXES
SURPLUS
The demand curve represents how much consumers
are willing to pay for one more unit of a good, if they
have already bought a certain number of goods.
There are diminishing returns to any given product.
As people consume more of that product, the benefit
they get from consuming another one declines, and
they are only willing to pay a lower price.
Difference between the price people are willing to
pay for a good (i.e. the position of the price
schedule) and the actual price is the consumer
surplus (net benefit to the consumer) generated by
that purchase.
P
11
10
10
Surplus generated by buying first good = 6
9
Surplus generated by
buying second good = 5
9
8
8
7
7
6
6
5
5
4
P=3
4
3
3
2
Total consumer surplus is the
sum of surplus of each good
1
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Q
P
11
When prices adjust
continuously, total
consumer surplus is
a triangle created by
price line and
demand curve
10
9
8
7
6
5
P
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Q
PRODUCER SURPLUS
Producers achieve profits whenever they sell an extra goods
at a price above the cost of producing the extra good.
Sum of profits for each good is the total producer surplus,
the area in the triangle below the price line and above the
supply curve.
COMPETITIVE MARKET
Supply and Demand
P
Producer
Surplus
S
P*
Q*
Q
COMPETITIVE EQUILIBRIUM
IS EFFICIENT
Economic efficiency means that there are
no gains to be had at the level of society
from additional trades.
If the price is higher or lower, the sum of
the areas of the consumer & producer
surplus triangles will be less than at the
equilibrium price.
Economic efficiency does not guarantee
that the split of the surplus will coincide
with any notion of fairness.
EFFICIENT EQUILIBRIUM
MARKET
P 12
Consumer
Surplus
10
8
S
6
Producer
Surplus
P*
4
D
2
0
0
2
4
6
8
10
12
Q
PRICE
CONTROLS
In markets for some goods,
government may put a regulatory
cap on the price of a product.
Hawaii, which often has
the highest gasoline
prices in the nation, has
already gone beyond
talk: Lawmakers have
mandated a moving cap
on the wholesale price of
gasoline - that is, the
price as it leaves in-state
refineries
So far, the most extreme effort has
come from Hawaii, which this week
will cap the wholesale price of
gasoline at $2.74 a gallon,
including taxes. The cap itself
would be indexed to average
wholesale prices in other parts of
the United States. According to
wire reports, for consumers this
would mean retail prices of about
$2.86 a gallon in Honolulu.
GOVT IMPOSES PRICE CEILING
Firms reduce output
P 12 Remaining Consumer Surplus
10
Total Surplus Deadweight
Loss
8
Willingness to Pay
6

P*
4
S
Ceiling

2
D
0
Q* 4
Remaining Producer Surplus
0
2
6
8
10
12
Q
EFFECTS OF PRICE
CONTROLS
Direct
• Shortages will occur
Indirect
• Black markets will develop
• Investment in production capacity of goods may
decrease
• Quality of product or service will drop.
• Non-price rationing (allocating goods to friends or
long-time customers) will develop.
TAXES: THE GOVERNMENT CAN COLLECT PART OF THE
SURPLUS FOR ITSELF BY IMPOSING TAXES ON
SUPPLIERS. A PER UNIT TAX INCREASES THE MARGINAL
COST OF PROVIDING A GOOD WHICH LEADS TO A
PARALLEL UPWARD SHIFT IN THE DEMAND CURVE.
PRICE GOES UP, QUANTITY DOWN.
Remaining Consumer Surplus
12
P
Revenue =
Unit
10
S
Tax x Q*
Tax
8

P**

6
Deadweight
Loss
P*
4
D
2
0
Q* 4
Remaining Producer Surplus
0
2
6
8
10
12
Q
Government collects part of surplus as revenue but also reduces societies
total surplus by reducing the amount produced and sold
ELASTICITY AND
DEADWEIGHT LOSS
The more elastic are the supply curve or the demand curve,
the more quantity traded will be affected by a tax.
The greater is the change in quantity traded, the greater will
be the deadweight loss.
PART OF THE REVENUE COMES FROM PREVIOUS
CONSUMER SURPLUS AND PART OF THE REVENUE
COMES FROM PRODUCER SURPLUS.
P 12
Revenue from
consumer
10
S
8
6
P*
4
Revenue from
producer
2
D
0
0
2
4
6
8
10
12
Q
REDUCE THE MARGINAL BENEFIT OF EACH EXTRA
GOOD AND CAUSE A PARALLEL DOWNWARD SHIFT
IN DEMAND CURVE. THIS LEADS TO DROP IN
PRICES AND A DROP IN OUTPUT.
Notice the deadweight loss and tax incidence are identical to the
case with a producer tax.
P 12
S
Revenue
10
8
P*
6
Deadweight
4
Loss
P***
Unit
Tax
2
D
0
0
2
Q*
4
6
8
10
12
Q
TAX INCIDENCE:
ACTUAL VS. STATUATORY
The incidence of a tax describes the allocation of
the surplus loss to producers vs. consumers.
The actual impact of a tax on producers and
consumers is not determined by whom law directly
imposes the tax on.
Actual incidence depends on the relative elasticity
of supply and demand.
• If demand is inelastic, consumers will not cut back on
consumption and will pay higher prices and pay for much of
the tax.
• If supply is inelastic, sellers will not drop production much and
merely charge a lower price absorbing much of the tax.
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 and calculate
quantitatively, the likely consequences for
equilibrium prices and quantities resulting
from exogenous shifts in supply and demand.
Calculate elasticities using the midpoint
method.
LEARNING OUTCOMES
Distinguish substitutes/complements,
luxuries/necessities/inferior goods.
Identify the impact of demand & supply
elasticity on price and quantity volatility in
the short and long run.
Identify the impact of expectations of the
future on current prices.
LEARNING OUTCOMES
Students should be able to
Calculate the price elasticity of supply and demand
from a supply schedule.
Calculate the revenue effect of a price change given
elasticity.
Explain the determinants of the deadweight loss of
taxes and the incidence