Measuring and Testing Advertising-Induced Rotation in the Demand Curve



Appendix B

With price-advertising interaction terms included in equations (2) - (6), the
corresponding own demand elasticities (in absolute values) are

ηiLM (=- (cii +γiAi)( pi Iqi) ), ηiSL(=-(cii+γilnAi)Iqi), ηiDL

(=-(cii+γilnAi)), ηiRM (=-(cii+γidlnAi)Iwi), and ηiAIDS

(=- ((cii +γi ln Ai)Iwi - 1)), respectively. The lnηIlnA term in table 1 is

derived as follows:

(B1)


lnηiLM


ln Ai


∂ηLM
iLM

ηiLMlnAi


pi


LM
ηiLM


piqi


- (cii + γiAi)pi


-ciiqi


qi2lnAi


- ciiln qi +
qiln Ai


γi(qiAi /lnAi - Aiqi /lnAi)


qi2


YiAiqi (dln Ai IdlnA1-dln qi IdlnAi)


qi2


= YiAi - (cii + YiAi )αii
cii + YiA

(B2)


lnηiSL   ln[-(cii +γi ln Ai)]   lnqi


ln Ai


ln Ai


ln Ai


[-(cii +γilnAi)]
(
cii +γilnA)lnAi


-αii


(B3)


lnηiDL


ln Ai


(B4)


lnηiRM


ln Ai


γi


cii +γilnAi


ηiDL
ηiDLln Ai


=(


ηiRM
ηiRMlnAi


-1


RM
ηiRM


-αii,


-1


cii +γi lnAi


-1


RM
ηiRM


(-cii)   γilnAi


ln Ai    ∂ ln Ai


ciiwi


wi2 ln Ai


Yi      and

cii +YilnAi


γi(wi -dlnAiwiIlnAi)


wi2


-ciidlnwi + Yi(1-dlnAdlnwi IdlnA-)


wiln Ai


wi


34




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