Table 1. Decomposition of Advertising’s Effects on the Own-Price Elasticities with Fixed Prices
Model Name |
∣Own - Price Elasticity I ______η______ |
∂ ln ηi / ∂ ln Ai =Rotation effect - Shift effect |
Rotation effect |
Shift effect | |
Without Interaction____________________________________________________________________________________________________________________________________________ | |||||
Linear (A) |
- cii( pi / qi ) |
___________________-αii___________________ |
0 |
αii | |
Semi-log (B) |
_____________- cii / qi_____________ |
___________________-αii___________________ |
0 |
αii | |
Double-log (C) |
______________- cii______________ |
0 |
_________α_________ |
αii | |
Rotterdam (D) |
- cii / w |
Σ^w7αy∙ - αii |
∑ "Л |
αii | |
AIDS (E) |
-(cii / wi-1) |
cii∑wα -αii) i______________________ ___________________cii - wi___________________ |
n cii∑wjα-jj -wiαii i_________________________ _________________________cii - wi_________________________ |
V | |
With interaction________________________________________________________________________________ |
Interaction-related |
Shift-related__________ | |||
Linear (F) |
-( cii + γiAi)( pi / qi ) |
YiAi |
YiAi ( cii + YiAi) |
0 |
αii |
Semi-log (G) |
-( cii + γiln Ai )/ qi |
------Yi--αii |
Yi cii + Yiln Ai |
0 |
αii |
Double-log (H) |
-( cii+ γiln Ai) |
Yi ________________( cii + Yiln Ai)________________ |
Yi ( cii + Yiln Ai) |
αii |
αii |
Rotterdam (I) |
-( cii+ γidln Ai)/ wi |
n ------γ------+ ∑ wiαii - αii in it i * j |
Yi (cii + Yid lnAi ) |
Σ w,αi |
αii |
AIDS (J) |
-((cii + γi lnA1 )/ wi -1) |
n γi + (cii + YilnAi)(∑wjαij -αii) _____________________________i___________________ |
n Yi + Yi lnAi ∑wjαy ___________________i__________ |
n cii Σ wiαii - wiαιι __i_________ |
αii |
____________(cii + Yiln Ai - wi )____________ |
(cii + YilnAi -wi) |
(cii + Yiln Ai - wi ) |
20
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