Chapter 11 · Test 3
Multivariable Calculus
Partial derivatives, total differentials, Hessians, and curvature.
What you will learn
- Evaluate a partial derivative
- Use a total differential
- Calculate a cross-partial derivative
Reasoning habits that help
- A partial derivative changes one input while temporarily holding the other inputs constant.
- The total differential adds the first-order effects of all changing inputs.
- Cross partials measure how one marginal effect changes as another input changes.
Where economists use these methods
- Partial derivatives measure the marginal effect of one economic input while holding the other inputs fixed.
- Total differentials approximate how several simultaneous changes affect output, cost, utility, or equilibrium.
- Cross partials measure complementarity or substitutability and how one variable changes another variable's marginal effect.