Business I / Partial Derivatives
Practice question · Match the pairs

Match each partial-derivative concept to its economic meaning.

  • ∂Q/∂L\partial Q / \partial L
  • ∂Q/∂K\partial Q / \partial K
  • ∂2Q/∂L∂K\partial^2 Q / \partial L \partial K
  • ∇f=0\nabla f = 0
  • Marginal product of capital
  • Whether inputs are complements
  • First-order optimality condition
  • Marginal product of labour
Hints
  1. Each derivative measures a marginal effect of one input.
  2. The mixed partial says how one input changes another's productivity.
Show the answer
  • ∂Q/∂L\partial Q / \partial L → Marginal product of labour
  • ∂Q/∂K\partial Q / \partial K → Marginal product of capital
  • ∂2Q/∂L∂K\partial^2 Q / \partial L \partial K → Whether inputs are complements
  • ∇f=0\nabla f = 0 → First-order optimality condition
Why

Partials give marginal products; cross-partials reveal complementarity; the zero gradient defines optima.

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