Measuring and Testing Advertising-Induced Rotation in the Demand Curve



Appendix A

When price-advertising interaction terms are not present in equations (2) - (6), the
own demand elasticities (in absolute values) are
ηiLM (=- cii(pi /qi)),

η (= - Ci / qi ), ηΓ (= - Ci ), η (= - c∙ / ), and n (= - (c« / w -1) ),
respectively. The
lnη / ln A term in table 1 is derived as follows:

(A1)

dlnηLM = dln(-cii) dlnpi + dlnqi =
ln Ai      ∂ ln Ai    ∂ ln A1   ∂ ln Ai      ii,

(A2)

lnηSL   ∂ ln(-C ) lnq

----/i_ =---K—ii± +----= = -α and

lnAi     ∂lnAi    ∂lnAi      ii

(A3)

d ln niDL = d ln(-cJ = 0

ln Ai     ∂ ln Ai

Since the demand elasticities for the Rotterdam and AIDS models include a

budget share, wi /ln Ai is derived beforehand. Note that:

(A4)


(A5)


wi    wilnwi   wi(ln pi + ∂lnqi - ∂lnY)

ln Ai     ln Ai                ln Ai

Under the assumption of fixed price, we have:

n  nn

wi (ln qi - ∂ lnpjqj)          pjqj           ∑pjqj

----~ =-----------------j-------= wi (αii--j------) = wi (αii - —--------).
lnAi              ∂lnAi                i ii    YlnAi       i ii    YlnAi

nn

Since pjqj is identical topjqjlnqj , (A5) leads to:
jj

(A6)    dwi = w (αi - w αi ), or d ln wi = (αii - wα ■ ).

lnAi       i ii j j ij         lnAi        ii j j ij

It follows that:

32



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