Hi Aliburm,
If you derive the whole model of BGG with Bubble, then you will find that equation (A.6) is redundant. Because the firms are making decision of buying and selling capital based on market price S_t, not Q_t. However, we still need Q_t to be derived as the true value, so that’s why we have (A.4) from capital producers which determines Q_t.
Or generally looking, the “Return to stocks and capital” part comparing to BGG is now 2 more variables with three more equations…
Best,
Ethan