About grading: 1.1 Meaning of NDCQ correct +2p, showing correctly that it holds +2p 1.2 Correct first order conditions +2p, all 4 critical points found +3p (if missing some -1p, note affects also 1.3) 1.3 Reductions from full points: -1p if some critical points missing, -1p if Weierstrass theorem not mentioned 2.1 Correct FOCs +2p, finding a solution +4p, note the solution is obtained when only the “first” constraint is binding, Note: also minimum was accepted if in line with the answer to 2.2 2.2 The problem had a typo: minimizer should have been maximizer. In case of considering the minimization there is a unique critical point: (½,1,0,-2,-1), (giving this would give full points, pointing out that the solution of a is not minimizer gives 2p), in case of maximization the problem is concave, which assures that the critical point is a global maximizer (some argument fro the concavity of the objective function was assumed, -1p if missing, also mention of linearity/convexity of constraints was assumed; -1p if missing), (local) optimality by using bordered hessian +2p 2.3 Only envelope theorem +1p 3.1 +2p for correct formulation of the equation for eigenvalues, +1p for each correct eigenvalue 3.2 +2p for each eigenvector, note: -1p is incorrect eigenvalues 3.3 1p if a general solution for a continuous time system was given 3.4 2p if otherwise correct argumentation but condition x_0+y_0=1 ignored