Consider the given function:
y = f(x; a) = a2 + x - ax2
where a > 0 is a parameter.
Problem 1. Find the first order condition for a critical point of this function.
Problem 2. Is this a maximum or a minimum or an inflection point?
Problem 3. Solve for x* (a), the maximizer of the function f (x; a) :Also find y* (a), the maxi-
mized value of y as a function of a
Problem 4. Find dx*/da and dy*/da
Problem 5. Now use the FOC from 1 and the implicit function theorem to find
Problem 6. Use the envelope theorem to find dy*/da . Why does this theorem allow you to simplify your calculations with respect to point 4?