Demand
The willingness and ability to buy
How does marginal analysis inform simple pricing decisions?
How can the concept of elasticity inform managerial decisions?
How can managers learn about consumer demand?
Professor Spry
University of St. Thomas
•Economics 600
•6:00pm-9:00pm
Today’s agenda
• Demand functions
• Linear Demand Functions and Curves
– Players Theater Example
• Own-Price, Cross-Price, and Income
Elasticities of Demand
• Applications of Demand Estimation
– Forecasting prices of FCC Licenses
– The Demand for Hoosier Lottery Tickets
Motivating Example: Red Lobster
• All you can eat crab dinner –
– For that 2nd and 3rd and … helping,
• What is the marginal cost to customer?
• What is the marginal benefit to customer?
• What is the marginal benefit & cost to Red Lobster?
• What if steak? Fish & chips?
Demand Function for Indiana Lottery Games
The relationship between the quantity demanded of a good or
service and all influencing factors :
Qd = f(X1, X2,X3,X4… Xn)
where Qd is quantity demanded per period and the Xis are the
factors influencing demand
Example:
Demand for Indiana Lottery Tickets
• Q = quantity of Lottery Tickets purchased per period
•X1 = Price per ticket (expected loss)
•X2 = Price of other goods
•X3 = Average income per period
•X4= A binary variable for a state border
•Other variables such as advertising, proximity to riverboat
casinos, seasonal variables
Demand Curve
Definition: A demand curve shows the amount of a
good/service consumer(s) are willing and able to
buy per period at various prices; all else constant
“Plug in” values of other variables, such as income,
prices of substitutes, ect. into the demand function
to obtain the demand curve as a function of the
price of the good only
a 1 
P=a-bQ or Q(P) =    P 
b b 
Modeling demand as a constrained choice problem
The consumer has:
• Desire to maximize
satisfaction from a variety
of purchases
 Tastes & preferences affected
by advertising and other
factors
• A budget constraint for
those purchases
 Affected by income, prices of
goods & services under
consideration
The Logic of Consumer Choice and Demand
Change in a demand factor:
• E.g. lower price of good => change in budget constraint =>
reduces opportunity cost of purchasing this good => purchase
more units
– Movement along a single demand curve
• E.g. increase income => expands budget constraint => buy
more of many goods and services
– Demand curve shifts
• E.g. persuasive advertising => shapes tastes & preferences
=> may sway consumer toward this product without requiring
a price decrease
– Demand curve shifts
Market Demand Function for PTC Tickets
Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I
where P is PTC ticket price, Ps is price of symphony
tickets, Pr is price of nearby restaurant meals, and I is
average per capita income.
•Suppose the variables have the following values:
Ps = $50
Pr = $40
I = $50,000
•Substituting variable values (except for P) into the
equation and rounding:
Q = 400 – 6.6P
P = 60 – 0.15Q
demand curve; or
“(inverse) demand curve”
Graphing the demand curve for PTC
PTC demand curve:
P = 60 – 0.15Q
Think of P as the “Y” variable
Think of Q as the “X” variable
60 is the vertical “Y” intercept
-0.15 is the slope (change in Y/change in X)
How Many Tickets Should PTC Sell:
Using Linear Demand Curve Facts
In general, if
• P = a – bQ (linear)
• TR = aQ – bQ2
• MR = a – 2bQ*
This is an application of the derivative formula.
If f(x)=axb then f’(x)=abxb-1.
Don’t sell as much as possible, maximize your profits!!!!
If it is worth producing, produce until
Marginal Revenue = Marginal Cost!!
Marginal Analysis and Pricing
Q = 400 – 6.6P
P = 60 – 0.15Q
demand curve”
demand curve; or
“(inverse)
TR  PQ  (60  0.15Q)Q  60Q  0.15Q 2
MR  60  (0.15) * 2Q  60  .3Q  0  MC
60
Q
 200
0.3
P  60  0.15Q  60  0.15 * 200  60  30  $30
TR  PQ  $30 * 200  $6,000
Price elasticity of demand
• Measures the sensitivity of quantity
demanded to changes in demand factors
• The price elasticity of demand is given by
(all else constant):
%Q

%P
Does a given (often a 1%) change in the price of
the good lead to a small reduction or a huge,
titanic reduction in the QUANTIY
DEMANDED??
Absolute
Value
Determinants of price elasticity
• Availability of substitutes
• Size of good in consumer budget
• Time period for consumer adjustment
Discuss: a) Southwest Airlines estimates the short-run
price elasticity of business air travel to be 2 and the
long-run elasticity to be 5. Does this seem
reasonable? Explain.
b) Would the market demand for business air travel be
more or less elastic than Southwest’s? Why?
Estimated Price Elasticities
• Prescription drugs (Baye, Maness, Wiggins in Applied Economics
29 (1997))
•
•
•
•
Cardiovascular
Anti-infective
Psychotherapeutic
Anti-ulcer
• Recreation*
1.1
• Clothing*
0.9
• Alcohol & tobacco*0.3
0.4
0.9
0.3
0.7
(short term)
(short term)
(short term)
*Baye, Jansen, Lee, in Applied Economics 24 (1992)
3.5 (long term)
2.9 (long term)
0.9 (long term)
Calculating elasticity from a linear Demand Curve
point price elasticity
 Information requirements
• Demand curve equation:
Q=α-βP, β =Q/P
• Initial price and quantity
• Q
• P
P
 %Q   Q P  
 
      
  
Q
 %P   P Q  
Calculating elasticity
Using a linear demand Curve
• The demand curve facing the Como Park Golf Course is
Qd=100 – 2P
• The current price is $20.00 for a round of golf.
• 60 golfers play Como per day.
• What is the own-price elasticity of demand at Como at a
price of $20.00?

P
20 40
       2  
 0.667
Q
60 60

Calculating elasticity
arc price elasticity
Information requirements:
• Quantity demanded before and after the price
change
• Q1
• Q2
• Price before and after the price change
• P1
• P2
Calculating elasticity
arc price elasticity




Q


 (Q1  Q2 ) 


2


 




P


 ( P1  P2 ) 


2


Example: Housing Sales
• From March to April of 1998, the price of an average
single-family home decreased from $128,200 to
$127,100. Interest rates and income were unchanged.
• Housing sales increase from 4,700,000 to 4,890,000.
Q Q
2 1
Q Q / 2
E D  Elasticity of demand  1 2
P P
2 1
P  P /2
1 2
4.89M  4.70M
190,000
4.89M  4.70M / 2
 
 4,795,000  .0396  4.6
127,100 128,200
1,100
.0086
127,100 128,200/ 2 127,650
Source: WSJ, May 27, 1998




Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
D
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
S2
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
S2
$5
$2
D
100
160
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
S2
$5
$2
D
100
160
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
S2
$5
$2
D
100
160
Q
Total Spending and the Shape of the
Demand Curve: Inelastic Demand
P
S1
S2
$5
A
$2
C
B
100
D
160
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
D
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
S2
$5
D
100
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
S2
$5
$4
D
100
240
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
S2
$5
$4
D
100
240
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
S2
$5
$4
D
100
240
Q
Total Spending and the Shape of the
Demand Curve: Elastic Demand
P
S1
S2
$5
A
$4
D
C
B
100
240
Q
Cross-Price Elasticity
 % Q x 

 xy  

%

P
y 

• Positive if substitutes; negative if complements
• Cross-price elasticity of demand for new car
sales from a change in gas prices = - 0.214
– (McCarthy, in Economic Inquiry 28 (July
1990), pp. 530-43)
– Interpretation?
Income Elasticity of Demand
 % Q 
I  

 % I 
Inferior good:  I <0
Normal good:  >0
I
Luxury good:
>1
I
Examples of income elasticities of demand
• Powerball
0.9
• Daily games
0.68
• Instant games
0.4
Log-Log Demand Functions
Constant Elasticity of Demand
• Assumption
– Constant own-price elasticity of elasticity of
demand and constant income elasticity of demand


Q  P I
ln Q  ln    ln P   ln I
Estimating Demand
Multiple Regression Technique
Information requirements
– Hypothetical demand relationship
Q = a + bP + cPsubst + dI + eAdvert.
– Data
series for Q, P, Psubst , I, Advert.
Estimating Demand
Multiple Regression Technique
• Use statistical program (e.g. Excel) to
estimate parameters using multiple
regression techniques
– a, b, c, d, e
• Assess summary statistics to judge
reliability
Caution: Demand Estimation Problems
• Omission of relevant
variables
– Important demand
variable
• Identification problem
– Price changes may not be
exogenous
– Supply shifts muddy the
water
• Critical issue because
estimates of parameters
can be seriously biased
Demand Estimation in Telecom
CEO of a regional tel. Co. was interested in bidding on licenses for airwaves in
the region that the FCC was licensing off. Purpose was for wireless
communications networks. He read a New York Times article that contained
the following data: price paid per license in 10 different regions (Millions of
dollars), number of licenses sold, quantity of licenses, and regional
population (millions). Given the three logarithmic data series, he clicked the
regression tool button and found the following relation:
Ln P = 2.23 – 1.2 ln Q + 1.25 ln Pop
The estimated equation should give him info on how much he should expect to
bid to buy a license. You can show that with log-linear demand functions
such as this one, the estimated coefficients equal elasticities. Since the
population in the region is 7 percent higher than the average, this means
%change in P
1.25 
7%
or the % change in P = 8.75%.
Thus, the CEO would expect to pay 8.75 % higher in his region. The data
showed the average price to be $70.7 million for a license. So he should
expect to pay $76.9 million.
What type of information would the CEO want to know whether to place a high
degree of confidence in this estimate? Why?
Looking Forward
• Assignment #1 Due Sept. 30, Oct. 4 or 5
– Due at start of class!
• Read Managerial Economics Chapter 5
– Moneyball and the Oakland A’s