Chapter 13 · Test 3
Constrained Optimization
Lagrangians, tangency conditions, and constrained second-order tests.
What you will learn
- Solve a utility-maximization problem
- Recognize the Lagrangian tangency condition
- Minimize cost subject to an output target
Reasoning habits that help
- Cobb-Douglas expenditure shares follow exponents; quantities also depend on prices.
- At an interior consumer optimum, willingness to trade equals the rate at which the market permits trade.
- A binding production requirement can reduce a constrained problem to one variable through substitution.
Where economists use these methods
- Cobb-Douglas demand equations predict how consumers allocate income across goods at given prices.
- The tangency condition characterizes an interior consumer choice where willingness to trade matches market tradeoffs.
- Constrained cost minimization determines a firm's least-cost combination of capital and labor for a target output.