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