I was going through my notes yesterday and came across something that doesn't entirely make sense. I've been working on it for a while but can't seem to get the answer he got. The problem deals with Bertrand Nash Equilibrium, but is mostly a FOILing problem. Anyway here it is.

=(P-5)x(100-10Pfirm1+5Pfirm2) where P = price

derivative of profit/derivative of price

=(P-5)(-10+5)+(1)(100-10Pfirm1+5Pfirm2)

Here is where I can't figure out why he got what he got.

He got:

150+5Pfirm2-20P=0.

I got:

125-10Pfirm1+5Pfirm2-5p.

Any ideas for the discrepancies?