Plugging (A6) into (B4) yields:
(B5)
n
RM γi+(cii+γidlnAi)(∑wjαij -αii)
d 4 =____________j_______
d ln A ci+γd ln Ai
Finally,
(B6)
∂lnηiAIDS = ∂ηiAIDS
∂lnAi =ηiAIDS∂lnAi
n
Y, ! w - (ci + Y,ln A )(α - ∑ wα) / w
j
( ci+ Yiln A )/ w1-1
n
Yi + (cii +YilnAi)(∑wjαij -αii)
________________________________j_____________________
ci + Yi ln A, - w,
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