Chapter 12 · Test 3
Multivariable Optimization
Stationary points, Hessian tests, and direct variable restrictions.
What you will learn
- Find a multivariable optimum
- Apply the two-variable Hessian test
- Check feasibility of an unconstrained optimum
Reasoning habits that help
- For a strictly concave objective, the stationary point is the unique global maximum.
- The Hessian determinant and the sign of a leading second derivative distinguish local maxima, minima, and saddle points.
- A direct restriction changes the solution only when the unconstrained optimum is infeasible.
Where economists use these methods
- Multivariable optimization chooses combinations of inputs, goods, or policies that maximize an economic objective.
- The Hessian verifies whether a multivariable choice is a local profit or utility maximum, a cost minimum, or a saddle point.
- Feasibility checks ensure theoretical optima respect nonnegative quantities, capacity limits, and other economic constraints.