Hey daveydave.
I've looked at what you've posted and it looks correct to me with how you've differentiated and collected terms. I'm assuming the Rj's and the rest of them are all not related in any way to the Ri's.
I need help with this differentiation. I don't think the answers I'm getting are correct. I'm not sure if I'm differentiating it correctly. For the equation and my working go the link below;
http://i1325.photobucket.com/albums/...ps2da17003.jpg
Hey daveydave.
I've looked at what you've posted and it looks correct to me with how you've differentiated and collected terms. I'm assuming the Rj's and the rest of them are all not related in any way to the Ri's.
I should expain that Ri is firm i's investment and Rj is the other firm's investment. The ki times square root of Ri is the probability that firm i will be successful and kj times square root of Rj is the probability firm j will be successful. Does that make any difference then?
Its two competing firms determining how much to invest in R&D. So Ri and Rj is how much the two firms invest in R&D and ki times square root of Ri is the probability of firm having a successful innovation come from R&D so the probability of success is dependent on the level of investment Ri. Not sure if dependence in that direction makes a difference.
The reason I ask is that if there is any dependency between the two, then your answer will need to involve some extra stuff.
If Rj = f(Ri) then differentiating with respect to Ri will have a huge effect and will be completely different from your answer since you can't treat it as a constant.