CASE STUDY OF SOFT DRINK DEMAND ESTIMATION
Demand can be estimated with experimental data, time-series data, or cross-section data. Sara Lee Corporation generates experimental data in test stores where the effect of an NFL-licensed Caroli Carolina na Panther Pantherss logo logo on Champio Champion n sweats sweatshir hirtt sales sales can be carefu carefull ll examine examined. d. Demand Demand forecasts usuall rel on time-series data. !n contrast, cross-section data is app ear in "able "able #. Soft drin$ consumption in cans per capita per ear is related to six-pac$ price, income per capita, and mean temperature across the %& contiguous in the 'nited States.
"able #
labama ri3ona r$ansas California Colorado Connecticut Delaware Florida 6eorgia !daho !llinois !ndiana !owa 7ansas 7entuc$ Louisiana aine arland assachusetts ichigan innesota ississippi issouri ontan Nebras$a Ne8ada New 9ampshire New :erse
Cans(Capita( *-Pac$ + !ncome )r Price +(Capita /0 0 /.#1 #4 0 #.11 /2 5 #.12 #2 4 /.41 #/ # /./1 ##& /.%1 /# 5 #.11 /% / /./1 /1 4 #.&1 &4 /.21 ##% /.24 #& % /.#1 #0 % /./# #% 2 /.#5 /2 0 /.04 /* 1 #.15 ### /.#1 /# 5 /.## ##% /./1 #0 & /./4 #0 & /.2# /% & #.1& /0 2 #.1% 55 /.2# 15 /./& #** /.#1 #55 /./5 #%2 /.2#
ean "emp. F #2 #5 ## /4 #1 /5 /& #& #% #* /% /0 #* #5 #2 #4 #* /# // /# #& #0 #1 #1 #* /% #& /%
** */ *2 4* 4/ 40 4/ 5/ *% %* 4/ 4/ 40 4* 4* *1 %# 4% %5 %5 %# *4 45 %% %1 %& 24 4%
New exico New )or$ North Carolina North Da$ota ;hio ;$lahoma ;regon Pennsl8ania ashington >est =irginia >isconsin >oming "otal ean
#45 ### 220 *2 #*4 #&% *& #/# #2& /25 14 /2* /// #00 *% /50 55 #%% 15 #0/ 541%
/.#5 /.%2 #.&1 /.22 /./# /.#1 /./4 /.2# /./2 #.12 /.2% /.#1 /.0& /.25 /.2* /.0% /.#1 /.## /.2& /.2# #04.5/
#4 /4 #2 #% // #* #1 /0 /0 #/ #2 #2 #5 #* #* #* /0 #4 #1 #1 &*#
#4&./0&2222
/./0/4
#5.1254
4* %& 41 21 4# &/ 4# 40 40 *4 %4 *0 *1 40 %% 4& %1 44 %* %* /452 42.*0%#*** 5
QUESTION 1
?stimate the demand for soft drin$s using a multiple regression program a8ailable on our computer. ?stimated Demand for soft drin$@ AD B 4#%./*5 /%/.15# Price #.//% !ncome /.12# "emp E%.#/0 r/ B0.*1&
E0.&0% SS?B2&./*#
>here the numbers in parentheses are t-scores.
E-4.4&/
ultiple
Dependent =ariable@ CN ethod@ Least SGuares Sample@ # %& !ncluded obser8ations@ %& =ariable C P
Coefficient 4#%./**1 -/%/.150& #.//%#*% /.12#//& 0.*1&0/% 0.*55%24 2&./*#0& *%%#/.0* -/%0.142* 22.10/2#
Std. ?rror ##2.22#4 %2.4/*/& #.4//*#2 0.5##%4&
t-Statistic %.4255// -4.4&/#*/ 0.&021&1 %.#/00/5
ean dependent 8ar S.D. dependent 8ar $ai$e info criterion Schwar3 criterion 9annan-Auinn criter. Durbin->atson stat
QUESTION 2
!nterpret the coefficients and calculate the price elasticit of soft drin$ demand.
Prob. 0.0000 0.0000 0.%/45 0.000/ #4&./0&2 *5.2*5#1 #0./0*%0 #0.2*/22 #0./*422 #.1&04%2
Ioth temperature and price are statisticall significant with expected signs while income is insignificant in its effect on soft drin$ demand. for the log-linear model J2.#/.
ean P
B#04.5/ ( %& B /./0/4
ean A
B 541% ( %& B #4&./0&2
KA(KP
B -/%/.15
Price elasticit ?D B EKA(KP Eean P(ean A ?D B E-/%/.15 ( E /./0/4 ( #4&./0&2 ?D B E - 2.2& elastic
Interpretation on Price Elasticit! Iased on the calculated price elasticit, the consumption on
soft drin$ is price elastic in nature. "his means that for a #M increase in price will result in more than #M decrease in Guantit demanded for soft drin$s.
"his point elasticit at the mean price and Guantit across the states is in the elastic range, as expected. "hese are mar$et-le8el price elasticities, so no firm beha8iour is directl implied b this estimate. n elastic demand at the mar$et le8el does impl elastic firm-le8el demand at comparable prices, comparable price sensiti8it, and the smaller Guantities facing each firm.
#
"he coefficient for demand for soft drin$ and price of soft drin$ is in8erse relationship.
/ "he Guantit demand for soft drin$ per capita will change in opposite direction as the price of soft drin$ change.
2 Demand for soft drin$ will reduce b /%/.15 when price of soft drin$ change in the opposite direction or in8erse direction. %
"he coefficient for demand for soft drin$ and income and demand for soft drin$ and
mean temperature is positi8el relationship. 4 "he Guantit demand of soft drin$ will change in same direction as the income and mean temperature change. So that, demand for soft drin$ will increase b #.// when income per capita increase, and demand for soft drin$ also will increase b /.12 when mean temperature increase.
QUESTION "
;mit price from the regression eGuation and obser8e the bias introduced into the parameter estimate for income.
Inco#e elasticit
A B 4#%.&1 - /%/.&&P #.//) /.1/" !ncome elasticit, ? B A() x )(A B #.//OE#5.&1(#*0.5* B 0.#% LogA B #.0* - 2.#1LogP 0.//Log) #.##Log" !ncome elasticit, ? B 0.// Interpretation on Inco#e Elasticit! Iased on the calculated income elasticit, a positi8e income elasticit indicates that soft drin$ is a normal goods.
log ADB J 0.#* #.5/ log "?P J 0.#4/ log !NC;?
EJ 0.52
SS? B 0.#25 >hen the independent 8ariable of Price is remo8ed from the eGuation, the <-SGuared 8alue drops from 0.** to 0.%5. "hus the strength of correlation falls under moderate range E0.% to 0.*. "he 8ariables ha8e a low association with the dependent 8ariable as onl %5M in Guantit demanded are explained b the independent 8ariables.
QUESTION $
Now omit both price and temperature from the regression eGuation. Should a mar$eting plan for soft drin$s be designed that relocates most canned drin$ machines into low income neighborhoods >h or wh not
Dependent =ariable@ CN ethod@ Least SGuares Sample@ # %& !ncluded obser8ations@ %& %aria&le C !NC
Coe''icient /4%.4*/1 -4.25#*&2
<-sGuared dHusted <-sGuared S.?. of regression Sum sGuared resid Log li$elihood F-statistic ProbEF-statistic
0.###&%1 0.01/4%/ *%.#5%%0 #&1%%%.2 -/**.&%%* 4.5120#0 0.0/0#*/
St() Error %#.010&/ /./2#
t*Statistic *.#14#/1 -/.%0*&*5
ean dependent 8ar S.D. dependent 8ar $ai$e info criterion Schwar3 criterion 9annan-Auinn criter. Durbin->atson stat
Pro&) 0.0000 0.0/0/
#4&./0&2 *5.2*5#1 ##./0#&* ##./51&2 ##./2#2/ /.2#2%#&
;mitting both price and temperature ields a linear model as follows@ AD B /4%.4*2 4.25/) AD B /4%.* J 4.25 !NC;?
No, a mar$eting plan should not be designed specificall to introduce canned soft drin$ machines into low-income neighborhoods. nd students should not offer the negati8e and significant income parameter estimate abo8e as their reason. "he abo8e regression does N;" call for relocating canned soft drin$ machines awa from low-income neighborhoods. "he regression coefficient on income has been biased downward b the omission of price and temperature enough to ma$e an insignificant factor appear negati8e and significant in its effect on demand. "his illustrates the critical importance of using analtical reasoning and demand theor to correctl specif a regression model.
INCOME 350 300 250 Q 200
Linear (Q)
f(x) = - 5.23x + 254.32 R² = 0.11
150 100 50 0 5
10
15
20
25
30
"he graph abo8e shows the wea$ relationship between !ncome and Auantit Demanded. "hus, the mar$eting plan should not be designed based on the income per capita factor as it does not strongl correlated with the demand of soft drin$ cans. >hether the mar$et the product at low income groups or otherwise, it will not affect the Guantit demanded that much. >e strongl belie8e that the compan should not design their mar$eting plan to relocate most canned drin$ machines into low-income neighbourhood. !n addition, as some 8ariables i.e. price and temperature were remo8ed from the eGuation, it is unwise to rel solel on income factor to design on mar$eting plan as there exists a bias. !nstead of wasting resources in tring to influence a 8ariable that is wea$l related to the dependant 8ariable, the compan should focus on other 8ariables such as pricing as the critical component of their mar$eting plan. Since price is strongl related to Auantit Demanded, the compan can stimulate the demand for their soft drin$ b gi8ing discounts and Qbu one, free oneQ EI;6; promotions. "he Rbest demand specification
PRICE 350 300 250
f(x) = - 311.85x + 845.67 R² = 0.57
200
Q Linear (Q)
150 100 50 0 1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
For Price, the <-sGuared is 0.4*&2 which is within the 0.% to 0.* range. 9ence it has moderatel strong correlation.
INCOME 350 300 250 Q 200
Linear (Q)
f(x) = - 5.23x + 254.32 R² = 0.11
150 100 50 0 5
10
15
20
25
30
For !ncome, the <-sGuared is 0.#01% which is within the range of 0 to 0./. "his indicates a 8er wea$ correlation.
TEMPERATURE 350 300 250
f(x) = 4.91x - 104.03 R² = 0.46 Q
200
Linear (Q)
150 100 50 0 30
40
50
60
70
80
90
For "emperature, the <-sGuared is 0.%444 which is within the range of 0.% to 0.*. 9ence it has moderate strong correlation. Concl+sion! "he best demand specification is to remo8e income per capita from the regression
eGuation as the 8ariable has a low correlation to the eGuation.
