Challenges at Time Warner Memo 1
Reply to: Revenue from STARZ
By: Aaron Canada
Everyone is in business to make a profit, and Time Warner is trying to increase their
profits by increasing the number of people who subscribe to one of their premium cable
tiers, STARZ. They believe their market penetration is too low to maximize their profits
with STARZ. Of course, increasing the number of subscribers would increase profits, but
current customers claim the price is too high. These same customers may decide to add
STARZ to their cable package if the price is decreased. To determine whether or not
decreasing the price will increase profits, Time Warner needs to know how elastic the
demand is for STARZ. The elasticity of demand will be calculated by using data
provided from Region 1.
Own price elasticity of demand: EQx , Px 
%Qxd
%Px
The 3 types of elasticity of demand are (1):
Elastic demand: E Qx , Px  1
Total revenue is inversely related to price when demand is elastic. An increase in price
will decrease total revenue, and a decrease in price will increase total revenue. Elastic
demand is seen in a competitive market. A perfectly competitive market has an elasticity
of ∞ (infinity), so even a small increase in price will take total revenue down to zero.
Gas stations that sell the same quality of product and are close in location can be thought
of as perfectly competitive. If the gas station across the street is 1 cent higher, people are
going to go to the gas station with the lower price.
Inelastic demand: E Qx , Px  1
Total revenue is directly related to price, meaning an increase in price will increase total
revenue, and a decrease in price will decrease total revenue. The classic example of a
perfectly inelastic good, where the elasticity = 0, is insulin. If the price of insulin
increases with all things remaining the same, the same quantity of people will buy
insulin. This will result in an increase of the firm’s total revenue.
Unitary demand: E Qx , Px  1
Unitary demand is the point where the price of a product is set at the optimal level and
total revenue is maximized. All companies should attempt to set their price at a level
where demand is unitary elastic.
The own price elasticity of demand can be used by firms to maximize profits by using a
strategic price. This is valuable in both the short and long term (2).
For our given set of data, the elasticity can be calculated using the formula
Q xd Px
for the price and number of subscribers (4).
EQx , Px 

Px Q x
Factors affecting own price elasticity are substitutes, time, and expenditure share. If
anyone of these variables change, the elasticity can also change. The greater the number
of substitutes, the more elastic demand is. Items tend to be more elastic in the long run,
since more firms enter and more time allows buyers to find substitutes. The larger the
percentage of income that is spent on a good makes it more elastic.
The total revenue test shows the relationship between changes in price, quantity
demanded, and total revenue. Total revenue is the product of price and quantity. When
graphed for a downward sloping demand curve, total revenue has a positive slope where
demand is elastic, peaks where demand is unitary elastic, and has a negative slope where
demand is inelastic. Figure 1 shows this relationship (5).
Figure 1
Figure 2 shows the data the marketing department supplied from Region 1 to be used to
find the price that maximizes total revenue. At a price of $10.50, the demand for one
area equals 881 customers and the total revenue is $9,250. The total revenue is highest at
$11,281.50 with a price of $11.50 in another area. Figure 3 shows each data point plotted
with price on the x-axis and the number of subscribers on the y-axis. Figure 4 shows the
total revenue for each price.
Price
Number of
Subscribers
(Thousands)
Number of
Subscribers
$5.00
$5.50
$6.00
$6.50
$7.00
$7.50
$8.00
$8.50
$9.00
$9.50
$10.00
$10.50
$11.00
$11.50
$12.00
$12.50
$13.00
$13.50
$14.00
$14.50
$15.00
1.493
1.500
0.938
1.224
1.105
0.952
1.205
1.212
1.234
1.104
0.842
0.881
0.872
0.981
0.664
0.848
0.488
0.227
0.249
0.503
0.305
1493
1500
938
1224
1105
952
1205
1212
1234
1104
842
881
872
981
664
848
488
227
249
503
305
Divisional Sales,
Cost of License
General, and
Fees
Administrative Costs
(Thousands)
(Thousands)
$8.210
$8.247
$5.158
$6.729
$6.078
$5.234
$6.629
$6.664
$6.785
$6.071
$4.631
$4.847
$4.796
$5.395
$3.653
$4.666
$2.684
$1.248
$1.371
$2.764
$1.679
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
Elasticity
Total Revenue
0.05
-7.19
3.04
-1.51
-2.41
3.36
0.10
0.32
-2.24
-6.22
0.93
-0.23
2.56
-11.46
5.42
-19.18
-31.04
2.47
14.64
-19.48
$7,465.00
$8,250.00
$5,628.00
$7,956.00
$7,735.00
$7,140.00
$9,640.00
$10,302.00
$11,106.00
$10,488.00
$8,420.00
$9,250.50
$9,592.00
$11,281.50
$7,968.00
$10,600.00
$6,344.00
$3,064.50
$3,486.00
$7,293.50
$4,575.00
Total Profit
-$1,945.00
-$1.30
-$1,197.00
-$0.80
-$730.00
-$0.78
$27.00
$0.02
$457.00
$0.41
$706.00
$0.74
$1,811.00
$1.50
$2,438.00
$2.01
$3,121.00
$2.53
$3,217.00
$2.91
$2,589.00
$3.07
$3,203.50
$3.64
$3,596.00
$4.12
$4,686.50
$4.78
$3,115.00
$4.69
$4,734.00
$5.58
$2,460.00
$5.04
$616.50
$2.72
$915.00
$3.67
$3,329.50
$6.62
$1,696.00
$5.56
Figure 2
Price $
Chart Title
$16.00
$14.00
$12.00
$10.00
$8.00
$6.00
$4.00
$2.00
$0.00
y = -0.0073x + 16.544
Demand for Starz
Linear (Demand for Starz)
0
500
1000
1500
2000
Subscribers
Figure 3
Total Revenue
Total Revenue
$12,000.00
$10,000.00
$8,000.00
$6,000.00
Total Revenue
$4,000.00
$2,000.00
$0.00
0
200
400
600
800
1000
1200
1400
Gain per
subscriber
1600
Subscribers
Figure 4
As can be seen in figure 3, the data is not perfectly linear for region 1. To estimate the
demand function for the given data, a regression analysis is needed. Using the table from
figure 2, the least squares regression line is calculated to be Price=-0.0073Q+16.544.
This can be easily found by adding a trend line to the graphed data or performing the
regression analysis in Microsoft Excel. The summary output for the regression analysis
can be seen in figure 9.
The least square regression line as seen in figure 5 describes the linear relationship
between an independent (X) and dependent (Y) variable. For our Starz example, the
independent variable is price and the dependent variable is the number of subscribers.
The equation for the regression line is Y = a + bX + e, where a and b represent the
smallest sum of squared error between the data points and the line, and e is the error term.
The least square regression line, also known as the “best-fit” line, provides an accurate
prediction and effective means for obtaining predicted values by creating a line that
passes exactly through the center of the data. The strength of the association between the
predicted values and actual values can be determined by the coefficient of determination,
R2. The R2 has statistics between 0 and 1, with values close to 1 (100%) having strong
association between actual and predicted and values close to 0 (0%) having no
association (3).
Figure 5
The significance of the estimated coefficient can also be evaluated using the t-statistic.
This is also available in figure 9. The rule of thumb for a t-statistic is an absolute value
greater than or equal to 2. Also, the p-value can be used to determine significance. A pvalue less than 0.05 is usually considered low enough for a researcher to be confident the
estimated coefficients are statistically significant (1). With a t-statistic of 19.45 and a pvalue of 5.9E-14, we can conclude the estimated coefficients are statistically significant.
Using the least square regression line that was calculated for the data in figure 2, we can
estimate the number of subscribers for each of the given prices. These estimations are
listed in figure 6 and graphed in figure 7. Using the estimated number of subscribers for
each price, the price that will maximize total revenue is $8.50. This is $2.00 less than the
current price of $10.50, but the increase in the quantity demanded more than makes up
for the lower price. The demand elasticity for the price of $8.50 is -1.06, which is not
equal to |1|, but is as close as we can get with using $0.50 price intervals. Figure 8
graphically displays all of the estimated revenues from the various prices, and shows the
total revenue test. This also reinforces the customer feedback that the price of Starz is
too high.
Price
Divisional Sales,
Estimated Cost of License
Elasticity of the Total Revenue of the
General, and
Number of
Fees
Estimated Number Estimated Number of
Administrative Costs
Subscribers (Thousands)
of Subscribers
Subscribers
(Thousands)
$5.00
$5.50
$6.00
$6.50
$7.00
$7.50
$8.00
$8.50
$9.00
$9.50
$10.00
$10.50
$11.00
$11.50
$12.00
$12.50
$13.00
$13.50
$14.00
$14.50
$15.00
1581
1513
1444
1376
1307
1239
1171
1102
1034
965
897
828
760
691
623
554
486
417
349
280
212
$8.210
$8.247
$5.158
$6.729
$6.078
$5.234
$6.629
$6.664
$6.785
$6.071
$4.631
$4.847
$4.796
$5.395
$3.653
$4.666
$2.684
$1.248
$1.371
$2.764
$1.679
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
$1.20
-0.50
-0.57
-0.65
-0.73
-0.83
-0.94
-1.06
-1.19
-1.35
-1.53
-1.74
-1.98
-2.28
-2.64
-3.09
-3.67
-4.43
-5.50
-7.09
-9.71
$7,907.40
$8,321.41
$8,666.93
$8,943.95
$9,152.48
$9,292.51
$9,364.05
$9,367.09
$9,301.64
$9,167.68
$8,965.24
$8,694.30
$8,354.86
$7,946.93
$7,470.50
$6,925.57
$6,312.15
$5,630.24
$4,879.83
$4,060.92
$3,173.52
Figure 6
Price $
Chart Title
$16.00
$14.00
$12.00
$10.00
$8.00
$6.00
$4.00
$2.00
$0.00
y = -0.0073x + 16.544
Demand for Starz
Linear (Demand for Starz)
0
500
1000
1500
Subscribers
Figure 7
2000
Gain per
subscriber
$5.00
$5.50
$6.00
$6.50
$7.00
$7.50
$8.00
$8.50
$9.00
$9.50
$10.00
$10.50
$11.00
$11.50
$12.00
$12.50
$13.00
$13.50
$14.00
$14.50
$15.00
Total Revenue
Total Revenue
$10,000.00
$8,000.00
$6,000.00
Total Revenue
$4,000.00
$2,000.00
$0.00
0
500
1000
1500
2000
Subscribers
Figure 8
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.88565798
R Square
0.784390058
Adjusted R Square
0.773042167
Standard Error
1.477994975
Observations
21
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
MS
1 150.9951 150.9951
19 41.50491 2.184469
20
192.5
Coefficients Standard Error t Stat
16.54438917 0.850668 19.4487
-0.007299738 0.000878 -8.31397
F
Significance F
69.1221
9.417E-08
P-value
5.29E-14
9.42E-08
Lower 95%
Upper 95%
Lower 95.0% Upper 95.0%
14.76392003 18.32485831 14.76392003 18.32485831
-0.009137432 -0.005462045 -0.009137432 -0.005462045
Figure 9
Summary:
The pricing manager wanted to know whether the price will yield higher revenues as well
as wanted an estimate of the maximum monthly revenues we can achieve through this
channel.
The price that will yield the maximum revenue is $8.50 and the monthly revenue can be
expected to be $8,694.30. This evaluation of the data should ease the concern that
management had about not being able to fully offset the revenue lost from lower prices
with the additional subscription generated by the lower price.
Questions
1. A firm should increase the price of their product if
a. the demand is unitary elastic
b. the demand is elastic
c. the demand is inelastic
d. the product is a normal good and they want more customers
Answer: c. Increasing the price when the demand is inelastic will lead to higher revenues.
2. Which one of the products below would be considered to have an inelastic demand?
a. Coca-Cola
b. insulin
c. calculators
d. hamburgers
Answer: b. Currently, there are no available substitutes for insulin, so if an individual
needs insulin they would still buy the insulin at different prices.
3. What is the own price elasticity of demand when the demand line is perfectly
horizontal?
a. 0
b. 1
c. -1
d. ∞
Answer: d. A perfectly competitive competition would have a horizontal demand line,
because a change in price would make the quantity demanded zero.
4. If the own price elasticity of a given product equals -1.4, we can conclude that
a. the demand is inelastic
b. the demand curve is downward sloping
c. the demand curve is upward sloping
d. there is not enough information in the question to draw conclusions about demand
Answer: b. A decrease in price and increase in quantity or vise versa would result in a
negative elasticity value and downward sloping demand curve.
5. True or False: The least squared regression line is a method that can be used to
estimate the effects that a dependent variable has on an independent variable.
Answer: False. The least squared regression line is a method that can be used to estimate
the effects an independent variable has on a dependent variable.
6. The coefficient of determination value that represents the strongest association
between actual values and values predicted using least squared regression is
a. -1
b. 0
c. 1
d. 100
Answer: c. The coefficient of determination only has values between 0 and 1, with 1
having the strongest association.
7. Which of the following will cause demand to be more elastic?
a. few competitors
b. cost of good is a small percentage of income
c. long time horizon
d. product differentiation
Answer c. Demand is more elastic in the long run but less elastic if there are fewer
competitors, the good is a small percentage of income, or if the product is unique.
8. True or False: A p-value less than 0.05 is considered low enough to conclude
estimated coefficients are statistically significant.
Answer: True. A p-value less than 0.05 is considered low enough to conclude estimated
coefficients are statistically significant.
References:
1. Baye, Michael. Managerial Economics and Business Strategy. New York. McGrawHill. 6th ed. 2009.
2. Subotnik, Abraham. “Short and Long Run Elasticities in Consumer Demand Theory.”
American Journal of Agricultural Economics. Vol. 56. No. 3. 1974. JSTOR
3. LeBlanc, David C. Statistics: Concepts and Applications for Science. Tichenor. 2007
4. “Price Elasticity of Demand”. Wikipedia. <http://en.wikipedia.org>
5. “Elasticity”. Living Economics. <http://livingeconomics.org>.