DemandMang_411A

8/2/2019 DemandMang_411A

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MGMT 411A Spring 2011

Drze, Drolet, Rossi, Sood

Demand Management


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Overview

1. Demand curves

2. The multiplicative/log-linear demand model

3. Price elasticities

4. Demand for groups of items and cross price elasticities

5. Estimating the multiplicative/log-linear demand model

6. Examples of Base Pricing Analysis

7. Appendix: Logarithms and the exponential function

2


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Demand curves

A demand curve or demand function relates the quantity of a good soldto various elements of the marketing mix and other variables influencingconsumer behavior

Both own and the competitors marketing actions will typically affectdemand

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Price

Promotions

Coupon availability

Advertising

Season (spring, fall, Christmas, )

Housing value, ...

sales unitsQ


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Consumer behavior and demand

Where do demand curves come from?

Example: Survey data obtained from full-time MBA students in April 2010

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How much are you willing to pay for oneticket for the Soccer World Cup final2010 (in U.S. dollars)?


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5

1100 10 20 30 40 50 60 70 80 90 100

3000

0

500

1000

1500

2000

2500

Q

Price

Order willingness to pay in descending order and plot against the rank (highestprice first, )

10 students indicated a willingness to pay of $1,000 or higher


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What a demand curve represents

A demand curve shows the distribution of consumers willingness to pay

How does this relate to what they said in micro? The basic microeconomics model emphasizes a model in which consumers

choose a quantity demanded that is continuous (e.g. .5 units!!!) and they adjustdemand downward as price increases.

This is a representative consumer model. Not applicable to most products in themarketplace.

The more general model emphasizes differences heterogeneity inconsumers willingness to pay as a source of downward sloping demand

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Goal: Infer the relationship between unit sales and prices, promotions, and other

variables from the data using regression analysis

To use a statistical tool such as regression analysis we need amathematical formulation of demand

This formulation should be flexible and have a good chance of fitting the demandrelationship present in common data sets

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Modeling demand


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The linear demand model

Formula:

is unit sales, is the price and are parameters

Example:

Effect of a given price changeis the same for high and lowprice points

Is this a desirable property?

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Q = a bP

Q = 40 5 P

Q P

a b

400 5 10 15 20 25 30 35

8

0

1

2

3

4

5

6

7

Q

P

1.4

1.4


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The multiplicative demand model

Formula:

and are parameters

Example:

Effect of a given price changeis larger at low than at highprice points

Consistent with niche andmainstream segments ofconsumers

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Q = A P

Q = 100 P2

A

400 5 10 15 20 25 30 35

8

0

1

2

3

4

5

6

7

Q

P

1.4

1.4


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We can use logarithms to transform the multiplicative demand model:

We will therefore also refer to the multiplicative demand model as thelog-linear demand model both represent the same demand relationship

Purpose of this transformation The parameters and now enter the model linearly model has the form of a linear regression

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Multiplicative demand model = log-linear demand model

Q = AP

og(Q) = log(A) + log(P)

og(Q) = log(A) log(P)

og(Q) = log(P)

log

og(x y) = log(x) + log(y)

log(xa) = a log(x)

Define = log(A)

(L1)

(L3)


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12-4 0 4 8

2.5

-2

-1

0

1

log(Q)

log(P)

400 10 20 30

6

2

3

4

5

Q

P

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Parameter : intercept increase in increases the demandlevel given price

Parameter : slope increase

in makes the demand curvesteeper, i.e. more responsive toprice

A

A

A = 100 A = 150

= 2

= 4

Effect of parameters


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The (own) price elasticity of demand is defined as the percentage changein the quantity demanded relative to a given percentage change in price:

Useful measure of price sensitivity or price response of demand because it doesnot depend on the level of unit sales or prices

The price elasticity is typically negative (why?) Sometimes the absolute value of the price elasticity is reported

Interpretation

Example: Price elasticity is -2.8 A 1% increase in price is associated with a 2.8% decrease in unit sales

Note: The price elasticity can be calculated for any demand curve, notjust the multiplicative demand model

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Price elasticities

price elasticity =%Q

%P=

Q1Q0Q0

P1P0P0


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What does the price elasticity measure?

Substitutability Availability of substitutes Actual or perceived quality differences Awareness of substitutes Cost of finding (or switching to) substitutes

Examples of price elasticity hierarchies:

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Tropicana/Minute Maid orange juice

Private label orange juice

Orange juice

All drinks

All juices

Store level laundry

detergent sales

Market (city) levellaundry detergent sales


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Categorization of price elasticities

Inelastic demand:

Elastic demand:

After a price cut:

Revenue increases for elastic demand

Revenue decreases for inelastic demand

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1 < price elasticity < 0

rice elasticity < 1

Revenue = P Q

Revenue = P Q


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Results of EDLP vs. Hi-Lo Pricing Study (Hoch, Dreze, Purk)

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Price elasticity in the multiplicative demand model

In the multiplicative demand model,

the parameter has simple and straightforward interpretation it is theabsolute value of the price elasticity of demand

The property that one parameter directly measures the price elasticity isvery special and not true for other demand models

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Q = A P


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Use the log-linear representation of the demand model

Change price from to sales will change from tolog(Q) =

log(P)

P0 P1 Q0 Q1

take difference

between equations

= price elasticity

log(Q1) = log(P1)

log(Q0) = log(P0)log(Q1) log(Q0) = [ log(P1)] [ log(P0)]

log(Q1) log(Q0) = [log(Q1) log(Q0)]

log(Q) = log(P)

=

log(Q) log(P)

%Q%P

use logarithmproperty L*


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The multiplicative demand model discussed so far is too simple it doesnot account for the effect of the prices of competing products on demand

We now generalize the multiplicative demand model Allow for the effect of competing product prices

Predict demand for multiple products or groups of products Demand for product in a market with products:

The price coefficients have two subscripts

The first subscript refers to the equation, i.e. demand function for product The second subscript refers to the price of product that influences demand for

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Demand for groups of products

Qi = AiPi11

Pi22

PiKK

i K

i i

k i

ik


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In a market with two products ( ):

Now take the log of each equation (and define ):

The coefficients in these equations are price elasticities, just as in thesimple multiplicative demand model discussed before:

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Q1=

A1P

11

1 P

12

2

Q2 = A2P211

P222

og(Q1) = 1 + 11 log(P1) + 12 log(P2)og(Q2) = 2 + 21 log(P1) + 22 log(P2)

ik =%Qi

%Pk

i = log(Ai)

K = 2


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The coefficient on the price of product in the demand equation forproduct is the own price elasticity of

All other coefficients are cross price elasticities

Why are cross price elasticities typically positive?

Do you expect that cross-price elasticities are typically symmetric,e.g. ?

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Own and cross price elasticities

ik =%Qi%Pk

(> 0)

ii =%Qi%Pi

(< 0)

effect of price of product on demand for

12 = 21

i

i i

k i


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Extent of substitutability

Competing product with high cross price elasticity Competitive price change will have a large impact on the demand for our product Strong competitive effect

Product in our own product line with high price elasticity Cannibalization of own product sales

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What do cross price elasticities measure?


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Estimating the log-linear (multiplicative) demand model

To account for variation in demand that cannot be explained by theproduct prices we need to add an error term to each demand equation:

In the case of two products we have two regression equation, one for eachproduct

is the dependent variable, and are the independent variables, and

General approach Obtain data on sales units and prices Estimate the regression equations to obtain the specific parameters (price

elasticities)

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log(Q1) = 1 + 11 log(P1) + 12 log(P2) + 1

log(Q2) = 2 + 21 log(P1) + 22 log(P2) + 2

log(Qi) yi

log(P1) log(P2) x1 x2


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.2

.4

.6

.8

1

log(P)

9 9.5 10 10.5 11 11.5

log(Q)

Example: Demand for Philadelphia Cream Cheese, 8 oz, at Jewel


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Tellis: The Price Elasticity of Selective Demand: A Meta-Analysis ofEconomic Models of Sales,Journal of Marketing Research.

42 studies from the marketing and economics literatures 367 price elasticity estimates Most studies are based on time series data, most use brands

Elasticities Average -1.76 Detergents -2.77 Durable goods -2.03

Food -1.65 Toiletries -1.38 Drugs -1.12

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Survey of price elasticity studies


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Summary: Demand Curve Analysis

A demand model mathematically relates the quantity of a good sold tothe marketing mix and other variables influencing consumer behavior

The multiplicative demand model Usually fits the data better than the linear demand model

Easy to generalize for groups of products

Own price and cross price elasticities measure: Substitutability Competition Cannibalization

The log-linear demand model can be estimated as a regression model

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Base-Pricing Analysis

1. Scanner data

2. Base pricing analysis

3. Examples

IRI base pricing analysis

Base pricing analysis: Step by step

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Scanner data

Timeline First scan test at Kroger in Cincinnati in

1972

IRIs InfoScan introduced in 1987

What do scanner data capture?

Sales at the UPC (universal productcode) level

- Honey Nut Cheerios 25.25 oz size Prices and promotions Aggregation levels

- Market (Raleigh-Durham)- Chain/account (Kroger)- Store

Time- Weekly, monthly, ...

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(Some) scanner data sources

IRI InfoScan 34,000+ stores (store census, not sample)

Nielsen

Retail management system (ScanTrack) Scanner (retail audit) data available worldwide

Problem: Wal-Mart no longer shares their POS data (since 2001) Wal-Mart had 14% U.S. grocery market share in 2004

Retailer Data Warehouses -- a new source of power in the channel

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Base pricing analysis

Base price = non-promoted price (everyday shelf price)

Purpose of base pricing analysis Understand competitive influence of prices on sales Adjust / fine-tune base prices

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Case study: Data-driven base pricing

A CPG (consumer packaged goods)manufacturer approaches IRI

Company sells a national brand Product line: 16 oz, 24 oz, and 32 oz bottle

size (32 oz size has recently been added)

Key problems faced by the brand manager Price the different sizes separately or engage

in product line pricing?

Is there cannibalization across product sizes(worry about new 32 oz size)?

Worry about private label (PL) competition is it possible to assess the extent of thecompetitive threat?

Are the current base price points optimal,or should we change our prices?

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Scanner data

Cannibalization?

Cross price elasticities withrespect to other sizes inproduct line

Demand analysis

Price effects / priceelasticities

Private label competition

Cross price elasticities withrespect to private labelproducts

Price simulations

Predict profits from baseprice price changes

Base pricing approach


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Results of base pricing analysis: Elasticities

How responsive is salesvolume to own price changes?

Note

Here, IRI does not reportstandard errors of estimates Always question marketing

consultants about statisticalprecision of results

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-1.5

-1

-0.5

0

16 oz 24 oz 32 oz

Own price elasticity

Note: IRI slides p. 11

-0.95

-1.43

-1.24


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0

0.25

0.5

0.75

1

16 oz 24 oz 32 oz

16 oz 24 oz 32 oz

Influence on demandfor package size:

Cross price elasticity of:

NA NA NA

0.65

0.45

0.32

0.0

0.23

0.72

Is there evidence of cannibalization? Consequence?

Effect on:


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0

0.25

0.5

0.75

1

16 oz 24 oz 32 oz

PL 24 oz PL 32 oz

Influence on demandfor package size:

Cross price elasticity of:

0.0 0.0 0.0 0.0 0.00.07

How severe is the competitive effect of the private label products?

Note: IRI slides p. 13Effect on:


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Base price simulations

Goal: Predict profit for each package size in the product line

Total profit from product line (if we drop the 24 oz pack size):

What we need to conduct base price simulations: Data

- Current base prices across all markets- Retailer margin- Variable cost (per unit or case)

Prediction of unit sales conditional on own and private label prices- Log-linear demand model

profitk = Qk [Pk(1 retail margin) V Ck]

P . . . retail shelf price

V C . . . variable cost

total profit = profit(16 oz) + profit(32 oz)

k


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90 92 94 96 98 100 102 104 106 108 110

90 5,672 5,771 5,866 5,957 6,046 6,131 6,213 6,292 6,369 6,443 6,515

92 5,756 5,856 5,952 6,045 6,135 6,221 6,304 6,385 6,462 6,538 6,610

94 5,838 5,939 6,037 6,131 6,222 6,310 6,394 6,476 6,555 6,631 6,705

96 5,918 6,021 6,121 6,216 6,308 6,397 6,482 6,565 6,645 6,722 6,797

98 5,998 6,102 6,203 6,299 6,393 6,482 6,569 6,653 6,734 6,812 6,888

100 6,076 6,181 6,283 6,381 6,476 6,567 6,655 6,740 6,822 6,901 6,978

102 6,152 6,260 6,363 6,462 6,558 6,650 6,739 6,825 6,908 6,988 7,066

104 6,228 6,336 6,441 6,541 6,638 6,732 6,822 6,909 6,993 7,074 7,153

106 6,302 6,412 6,518 6,619 6,718 6,812 6,903 6,992 7,077 7,159 7,239

108 6,376 6,487 6,594 6,697 6,796 6,892 6,984 7,073 7,160 7,243 7,323

110 6,448 6,561 6,668 6,773 6,873 6,970 7,064 7,154 7,241 7,325 7,407

16 oz base price index

24 oz baseprice index

Profits for different 16 oz and 24 oz price combinations

Profits in $1,000


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Note: Corresponds to IRI slides p. 24

Profits highest if both prices are increased by 10% Why not increase prices even further?

- Price constraints acknowledges that statistical reliability of model decreaseswhen proposed prices are very different from prices in the data


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IRI base pricing analysis: Take-aways

IRIs client had very limited access to sales and price data and only alimited understanding of the key pricing issues Competition (private label) Cannibalization Optimality of base prices

Insights to the client Private label competition poses only a very limited threat to the brand There is cannibalization within the product line, but the main offender is not the

new 32 oz size but mainly the 24 oz size

- Consider eliminating 24 oz size to save on costs (packaging, distribution, )

Base price points are sub-optimally low


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Base pricing analysis: Step by step

Goal: Conduct a base pricing analysis for P&Gs Tide laundry

detergent brand

Examine cannibalization within the Tide product line

Examine competitive threat from Wisk Make pricing recommendations

Approach Estimate log-linear demand model using scanner data

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The data contains information from 86 stores in the Dominicks FinerFoods chain in Chicago over a period of up to 300 weeks

File detergent in the R package, PERregress (google CRAN)

store Store id number

week Week

acv ACV (all commodity volume), in $1,000promoflag = 1 if any product in the category was on promotion

q_tide128 Tide 128 oz: unit sales

p_tide128 Tide 128 oz: price ($)

q_tide64 Tide 64 oz: unit sales

p_tide64 Tide 64 oz: price ($)

q_wisk64 Wisk 64 oz: unit sales

p_wisk64 Wisk 64 oz: price ($)


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Calculate: Market shares Summary statistics (mean, median, std. dev.) of prices

Is there sufficient variation in prices to estimate price elasticities?

Step 0: Data inspection


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Step 1: Demand estimation basic model

Dependent variable Straightforward approach: Use as dependent variable However: Stores differ in size and hence sales will differ across stores even if the

product prices are the same

Solution

Use ACV (all commodity volume) is a measure of store size, defined as the storerevenue from all products sold in $ million per year

- Includes the sales of all products (produce, meat, detergents, milk, batteries,etc.), not just the products in the demand model

Add log(ACV) as an independent variable in a multiple regression

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og(Q)


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Remember our goal: Estimate base price elasticities Focus is on the effect of the everyday price, not on the effect of price

promotions

Price promotions are typically associated with sales spikes- More details later

How can we control for the effect of price promotions? Simplest solution: Eliminate observations when at least one product in the

category was promoted

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Calculating Base price elasticities


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Price Elasticity is pretty high (-3.27!!!) No cannabilization!

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Stores differ in sales for reasons unrelated to price Consumer demographics Consumer preferences Location

How do we properly control for such store-specific factors? The store identity is a categorical variable We control for categorical variables using dummies

Dummy variables to control for differences across the cross sectionalunits in a data set are called fixed effects

Create store fixed effects and add them to the regression model

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Controlling for Store Differences


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Own price elasticity looks much more reasonable Strong competitive effect from Wisk Note

- Do not report fixed effects unless they serve a specific point

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Goal: Predict the impact on total (product line) profits if we change thecurrent base prices of one or more of our products

We make these predictions using the estimates of the log-linear demandmodel parameters (elasticities)

To predict total profits we need to predict the profit for each productin the product line

variable cost

To predict profits we need to predict demand for each product, , afterthe price change

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Pricing simulations

k

V Ck

Qk

profitk

= Qk [Pk(1 retail margin) V Ck]


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Predicting demand: Some notation

Tide 128 oz is product 1, Tide 64 oz is product 2, and Wisk 64 oz isproduct 3

is the price of one of the products before the change, is the priceafter the change

Correspondingly is demand before the price change, is demandafter the price change

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Pk P

k

Qk Q

k


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Predicting demand: Step A

Change the price of product 1 (Tide 128 oz) by percentage points andthe price of product 2 (Tide 64 oz) by percentage points. The price ofproduct 3, Wisk 64 oz, is unchanged:

Example: If and we increase the price of Tide 128 oz by12% and cut the price of Tide 64 oz by 7%

Evaluate the corresponding log price changes:

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1

2

P

1= (1 + 1) P1

P

2= (1 + 2) P2

P

3= P3

1 = 0.12 2 = 0.07

og(Pk) log(Pk) = log ((1 + k) Pk) log(Pk)

= log(1 + k) + log(Pk) log(Pk)

= log(1 + k)


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Predicting demand: Step B

Evaluate the change in demand corresponding to the price changes foreach product in the product line

Focus on the demand for product 1 (Tide 128 oz)

Write down the log-linear demand equation after and before the pricechange and take the difference:

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log(Q1

) = 1 + 11 log(P

1) + 12 log(P

2) + 13 log(P

3)

log(Q1) = 1 + 11 log(P1) + 12 log(P2) + 13 log(P3)

log(Q1

) log(Q1) = 11 (log(P

1) log(P1)) + 12 (log(P

2) log(P2))

log(Q1

) log(Q1) = 11 log(1 + 1) + 12 log(1 + 2)

logQ1Q1

= 11 log(1 + 1) + 12 log(1 + 2)

log

Q1

Q1

= log

(1 + 1)

11 (1 + 2)

12

Q1

Q1= (1 + 1)

11 (1 + 2)

12

take difference

from previous slide

exp both sides


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Predicting demand: General approach

1. To predict the price effect on demand for product first estimate theparameters of the log-linear demand model,

3. Consider the price changes

5. The ratio of unit sales of product after versus before the price changesis

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i

og(Qi) = i + i1 log(P1) + + iK log(PK) + i

P

k= (1 + k) Pk

Qi

Qi

= (1 + 1)i1

(1 + K)iK

i


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Pricing simulations: Example

Cut the base price of Tide 128 oz by 7% and increase the price of Tide 64oz by 4%

Predicted Tide 128 oz sales ratio after vs before the price changes:

20% increase in Tide 128 oz volume

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Q

Q= (1 0.07)2.414 (1 + 0.04)0.1591 = 1.20


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Average Tide 128 oz unit sales are 55.25 at the week/store level Implies a current annual base volume of 86 52 55.25 = 247,078 units at the

chain (Dominicks) level (86 stores in the chain)

Base volume after price changes: 1.20 247,078 = 296,494

Average Tide 128 oz price is $8.47 $7.88 after the 7% price cut

Tide 128 oz profit after the price changes:

Note: Retail margin at Dominicks = 25% and the per-ounce cost of Tide is 2.7c

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unit sales price retail margin variable cost of

128 oz size

profit(Tide 128 oz) = 296, 494 [7.88 (1 0.25) 128 0.027]


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Goals of a base pricing analysis Understand how the prices of the products in the category influence demand forthe products that we sell

Do the prices of competing products influence our own sales competition? Do the prices of other products in our product line influence our own sales

cannibalization?

Data-driven approach to base pricing Use data on past prices and sales Use regression analysis to estimate a demand model

Use base pricing analysis to predict product line profits

Can we improve pricing? How should we adjust the prices in our product line?

Summary: Base Pricing Analysis

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