Multivariate unconstrained maximization. 22 points. Consider the following maximization problem: max f(x, y; a, b) = ax2 - x + by2 - y x , y (a) Write down the first order conditions for this problem with re- spect to x and y (notice that a and b are parameters, you do not need to maximize with respect to them). 2 points. (b) Solve explicitly for a* and x* that satisfy the first order condi- tions. 3 points.(c) Compute the second order conditions. Under what conditions on a and b is the stationary point that you found in point 2 a maximum? \"Thy (or why not)? 5 points. (d) Assume the conditions on a and b you found above are met. As a comparative statics exercise compute the change in 33* as a varies; that is, compute %. Compute it both directly using the solution you found above and using the general method of the implicit function theorem. These two results should coin- cide! 5 points. (e) We are interested in how the value function f (93* (a, b).y* (a, b); a, b) varies as a, varies. We do it two ways. First, plug in 32* (a, b) and y* (a, b) from the previous steps and then take the derivative with respect to a. Second, use the envelope theorem. You should get the same result! Which method is faster? 5 points. (f) Under what conditions on a and b is the function f concave in a: and 3;? When is it convex in a: and y? 2 points