Kuhn-Tucker (KKT) Conditions
Optimization with inequality constraints: complementary slackness and corner solutions.
Definition
The generalization of Lagrange to INEQUALITY constraints: stationarity plus complementary slackness, either a constraint binds or its multipliermultiplierThe amount total output changes per dollar of initial spending change, powered by respending: 1/(1−MPC) in the simplest case. is zero.
Key equation
λᵢ ≥ 0, gᵢ(x) ≤ 0, λᵢ·gᵢ(x) = 0
The intuition
Complementary slackness is just economics: a resource you don't fully use has a zero shadow price. KKT handles corner solutions the plain Lagrangian misses, buying zero of a good, producing at capacity.
Exam tip
Enumerate the binding/slack cases systematically; most KKT marks are lost by skipping the case analysis.
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