Specific common spiel

• Concave inequality: f(pa + (1-p)b) >= pf(a) + (1-p)f(b) for p in (0,1)
• Concavity can be shown if hessian is negative definite (positive determinant, negative trace)
• Envelope theorem says we only need to worry about direct effects at the optimum
• Concave problem (concave objective function and convex (linear) constraints) means K-T conditions are necessary and sufficient for a global maxima
• Non-negativity constraints may be neglected if marginal utility tends to infinity as x tends to 0
• If the constraint qualification is satisfied, conditions are necessary
• need to check if K-T solutions are correct by checking alternative constraints / checking if Lagrange multipliers are positive
• a multiplier is a measure of the change in the objective function when the constraint is relaxed
• when f is (strictly) concave, a local maximum or stationary point is a (unique) global maximum
• if a function is not differentiable / C1, we cannot appeal to K-T conditions
• if F is strictly convex, FOCs are necessary and sufficient for a global minimum