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 = -α |
(A2) |
∂ lnηSL ∂ ln(-C ) ∂lnq ----/i_ =---K—ii± +----iι= = -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 wi∂lnwi wi(∂ln pi + ∂lnqi - ∂lnY)
∂ ln Ai ∂ ln Ai ∂ ln Ai
Under the assumption of fixed price, we have:
n nn
wi (∂ ln qi - ∂ ln∑pjqj) ∂∑pjqj ∑pj∂qj
----~ =-----------------j-------= wi (αii--j------) = wi (αii - —--------).
∂lnAi ∂lnAi i ii Y∂lnAi i ii Y∂lnAi
nn
Since ∑ pj∂qj is identical to∑ pjqj∂lnqj , (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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