### Chapters Four and Five

```CHAPTERS FOUR AND FIVE:
Demand Function – The relation between demand and factors
influencing its level.
Quantity of product X demanded = Qx =
f(Price of X, Prices of Related Goods, Consumer Income, Advertising
Expenditure, etc.)
THE MARKET DEMAND FUNCTION, CONT.
The model:
Qx = a0 + a1Px + a2Pz + a3Y + a4POP + a5i + a6AD + e
The terms a0 , a1 , etc. are the parameters of the model.
This is what we need to estimate.
Estimation of the model:
Q = 100 + -.002Px + .001Pz + .00008Y + .22POP + -800i + .002A
Interpretation of the model:
If the average price increases by \$1, the demand for the product falls
by .002 units
THE DEMAND CURVE
Demand Curve – The relation between price and the quantity
demanded, holding all else constant.
General Form:
P = a – bQ
 Why is this the general form?
Moving from the Demand Function to the Demand Curve.
CONNECTING THE CURVE TO THE FUNCTION
Changes in quantity demanded – movement along a given demand
curve reflecting a change in price and quantity.
Shift in demand – Switch from one demand curve to another following
a change in a non-price determinant of demand
IF AN INDEPENDENT VARIABLE CHANGES, OTHER THAN PRICE OF
THE GOOD, YOU MUST DRAW A NEW DEMAND CURVE!!!
Demand Analysis and Estimation:
Discussion Outline
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Demand Sensitivity Analysis: Elasticity
Price Elasticity of Demand
Cross Price Elasticity of Demand
Income Elasticity of Demand
Demand Sensitivity Analysis:
Elasticity
• Elasticity – The percentage change in a
dependent variable resulting from a 1% change
in an independent variable.
• Elasticity = % change in Y / % change in X
• ELASTICITY IS A RATIO!!!
Percentage Change
Elasticity = Percentage Change in Quantity
(Sales) / Percentage Change in (X)
Percentage change = (X2-X1)/X1
Price Elasticity of Demand
Price Elasticity of Demand (Own-Price):
◦ Measure of the magnitude by which consumers alter the
quantity of some product they purchase in response to a
change in the price of that product.
◦ Responsiveness of the quantity demanded to changes in the
price of the product, holding constant the values of all other
variables in the demand function.
Estimating from the Demand Function.
Estimating from the Demand Curve.
The Point Formula
((Q2-Q1)/Q1) / ((P2-P1)/P1)
Problems:
1.
Order of events dictate outcomes
2.
Does not impose ceteris paribus.
The Arc Formula
((Q2-Q1)/(Avg.Q) / ((P2-P1)/(Avg.P)
Problem:
1.
Does not impose ceteris paribus
The Slope Formula
Elasticity =
%ΔQ / %ΔP = ((Q2-Q1)/Q1) / ((P2-P1)/P1)
◦ Note:
Q2-Q1 = ΔQ
and
P2-P1 = ΔP
◦ Therefore:
Elasticity = ΔQ /Q / ΔP/P
◦ Note:
If you divide by a fraction you multiply by
the reciprocal.
◦ Therefore:
Elasticity = ΔQ /Q * P/ΔP
or
Elasticity = ΔQ / ΔP * P/Q
Where do we get ΔQ / ΔP?
This is the inverse slope of the demand curve, which we can estimate
empirically (via basic econometrics), and therefore we can impose
ceteris paribus.
Interpretation of Price Elasticity
% change in Q > % change in P
◦ (elastic or responsive)
Ep > 1
% change in Q < % change in P
◦ (inelastic or unresponsive)
Ep < 1
% change in Q = % change in P
◦ (unitary elastic)
Ep = 1
Own Price Elasticity and the
Demand Curve
Own-price elasticity = %ΔQ / %ΔP
How does elasticity vary along a linear demand curve?
The upper half of a linear demand curve is elastic.
The lower half of a linear demand curve is inelastic.
BE ABLE TO EXPLAIN WHY!!!
◦ The search for substitutes as price increases
◦ Big number, small number explanation
◦ Calculating elasticity at the midpoint.
Price
Elasticity Along a Demand
Curve
\$10
9
8
7
6
5
4
3
2
1
0
Ed = 
Elasticity declines along demand curve as
we move toward the quantity axis
Ed > 1
Ed = 1
Ed < 1
Ed = 0
1
2
3
4
5
6
7
8
9
10
Quantity
Elasticity and Total Revenue
Connecting Elasticity to Total Revenue
If % change in Q > % change in P
decreasing the price will increase TR
and marginal revenue must be positive.
If % change in Q < % change in P
increasing the price will increase TR
and marginal revenue must be negative.
BE ABLE TO ILLUSTRATE THE RELATIONSHIP
Marginal Revenue
Marginal Revenue - amount of revenue from the last
unit sold.
◦ the rate of change in total revenue
◦ the slope of the total revenue curve.
If demand is downward sloping, then price will exceed
marginal revenue. In other words, the amount of
revenue generated by an additional sale will be less
than the price the firm charges.
Why? To increase quantity the firm will need to lower
the price, not just for the last unit sold, but also for
every unit the firm wishes to sell.
Profit and Elasticity
Profit = Total Revenue - Total Cost
If demand is inelastic (i.e. % change in Q < % change in P) an increase
in price will increase TR.
Because Q falls (law of demand), so too will Total Cost
Why? Total Cost (which we will discuss later) is an increasing
function of output. The more you produce, the higher your total cost.
Consequently, if demand is inelastic, a firm can raise its price and
increase its profits.
Summarizing Demand
The Law of Demand - Quantity demanded rises as price falls, ceteris
paribus. Quantity demanded falls as price rises, ceteris paribus
◦ The Law of Demand is based upon Gossen’s First and Second Laws.
◦ The Law of Demand gives us the Demand Curve
◦ Via own-price elasticity, we move from the demand curve to total revenue.
Total Revenue = Price * Quantity
◦ Without own-price elasticity we do not know how changes in price and
quantity will impact total revenue.
◦ The variation in total revenue gives us the concept of marginal revenue.
Optimal Pricing Policy
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MR = P [1 + 1/EP]
Be able to show why this relationship
exists.
To maximize profits: MR = MC
MC = P [1+1/EP]
P = MC / [1 + 1/EP]
Lerner Index
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Lerner Index (Measure of Inequality)
L = (p - MC)/p
Lerner Index is bound between (0,1)
Closer to 1 the more pricing power the firm has.
NOTE: Mark-up power reflects monopoly
power.
The Lerner Index
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Own Price Elasticity is Always Negative.
MR = P[1 – 1/EP] and therefore
MC = P[1 – 1/EP] or
MC = P - P/EPor
P – MC = P/ EP or
[P-MC]/P = 1/EP
PUNCHLINE: If elasticity increases, markup will decline. If the product becomes less
elastic, mark-up will increase.
Determinants of Price Elasticity
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The extent the good is considered a necessity.
Proportion of income spent on the product
Time
Availability of substitutes
HINT: The fourth determinant encompasses the
first three.
PUNCHLINE: The key to establishing market
power is the elimination of substitutes in the
minds of consumers.
WHAT IMPACT DOES ADVERTISING HAVE ON
ELATICITY?
• Substitutes – products for which a price increase for
one leads to an increase in demand for the other.
• NOTE: Two goods are substitutes only if the consumer
behavior indicates this relationship.
• Complements – products for which a price increase
for one leads to a decrease in demand for the other.
Cross Price Elasticity of Demand
Substitutes vs. Complements
• Responsiveness of demand for one product to
changes in the price of another.
• Calculating from the Demand Function
• Note: We already know if two goods are
substitutes or complements from the demand
function. We do not know the magnitude of the
relationship without calculating elasticity.
Cross- Price Elasticity
• Normal Goods – products for which demand is
positively related to income.
• Inferior Goods – products for which demand is
negatively related to income.
• Note: What is normal or inferior can vary across time
and geographic distance.
Income Elasticity
Normal vs. Inferior Goods
• Responsiveness of demand to changes in income.
• Calculating from the Demand Function
• Note: We already know if two goods are normal or
inferior from the demand function. We do not know
the magnitude of the relationship without calculating
elasticity.
Income Elasticity
• Counter-cyclical goods – inferior goods
• During recessions demand will increase.
• During expansion demand will decrease.
• Non-cyclical normal goods – income elasticity is less
than 1.
• Cyclical normal goods – superior goods – luxury
goods – income elasticity is greater than 1.
Cycle
• Interest Rate Elasticity
• Weather Elasticity
• Any factor that can be included
in a demand function can be
analyzed in terms of elasticity.
Product
Tobacco products
Electicity (household)
Health Services
Nodurable toys
Movies/motion pictures
Beer
Wine
University tuition
Price elasticity
Short Run Long Run
0.46
1.89
0.13
1.89
0.20
0.92
0.30
1.02
0.87
3.67
0.56
1.39
0.68
0.84
0.52
—
Income elasticity
Product
Short Run Long Run
Motion pictures
0.81
3.41
Foreign travel
0.24
3.09
Tobacco products
0.21
0.86
Furniture
2.60
0.53
Jewelry and watches
1.00
1.64
Hard liquor
—
2.50
Private university tuition
—
1.10
Commodities
Beef in response to price change in pork
Beef in response to price change in chicken
U.S. automobiles in response to price changes
in European and Asian automobiles
European automobiles in response to price
changes in U.S. and Asian automobiles
Beer in response to changes in wine
Hard liquor in response to price changes in
beer
Cross-Price
Elasticity
0.11
0.02
0.28
0.61
0.23
- 0.11
Linear Functional Form
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Y = β0 + β1 X1 + β2 X2 + ε
Slope = β1
Impact of X1 on Y is independent of the
quantity of X2.
Elasticity = β1 * [X1/ Y]
Double-Log Functional Form
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What if you wished to estimate the following
model?
Y = β0 X1 β1 X2β2
To make this linear in the parameters
InY = β0 + β1 InX1 + β2 InX2 + ε
Slope = β1 = ΔlnY / ΔlnX1 = [ΔY / Y] / [ΔX1 / X1]
What is this? The elasticity, which is constant
across the sample.
What is the slope in a double log functional form?
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Slope = β1 * (Y/X) =
[ΔY / Y] / [ΔX1 / X1] * (Y/X) =
ΔY / ΔX
Impact of X1 on Y depends upon the quantity
of X2
In other words, the slope of X1 varies across the
sample.
Why would this be a realistic property?
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