Optimal Pricing with Advertising
Given how the problem is set up, I think they want you to take A as given when you choose price.  If that is the case, then you can find the comparative static $\partial P / \partial A$

We can think of p in the Foc as being a function of all the other parameters: $A\alpha-2A\beta P(A,\alpha,\beta,c)-A\beta c=0$

Now differentiate this wrt A: $\alpha-2\beta P(A,\alpha,\beta,c) -2A\beta (\partial P / \partial A)-\beta c=0$

Now you can solve for $\partial P / \partial A$