Comparative statics

Comparative statics compares equilibrium outcomes under different economic conditions without tracing the adjustment path between them.

Equilibrium: A state in which relevant forces or choices are mutually consistent, so no modeled adjustment is required. Comparative statics takes an equilibrium as its starting point and compares it with another.
Constrained optimization: The process of maximizing or minimizing an objective subject to restrictions on available choices. Many economic equilibria are built from agents’ constrained choices.
Tax incidence: The distribution of an economic tax’s burden among buyers, sellers, workers, or owners of capital. Comparative statics predicts how a tax changes prices, quantities, and who bears its burden.
Comparative dynamics: The analysis of how economic variables evolve over time as conditions or policies change. Unlike comparative statics, it studies paths and timing rather than equilibrium endpoints alone.
Implicit function theorem: A theorem that establishes when an equation implicitly defines one variable as a differentiable function of others. It can show how an equilibrium variable changes locally when a parameter changes.
First-order condition: A condition requiring a differentiable objective’s derivative to vanish at an interior optimum. Differentiating optimality conditions often reveals how choices respond to parameter changes.
Consumer surplus: The difference between what consumers are willing to pay and what they actually pay. A price or income change can be assessed by comparing consumer surplus across equilibria.
Dynamic stochastic general equilibrium model: A macroeconomic model of intertemporal decisions, equilibrium, and random shocks. It represents adjustment over time and uncertainty beyond a static equilibrium comparison.
Total derivative: A derivative that accounts for how a function changes through all variables that depend on the input. It captures indirect as well as direct effects of an economic parameter.
Lagrange multiplier: A quantity measuring the marginal change in an optimized objective when a constraint is relaxed. Its parameter response helps interpret changing constraints in comparative statics.

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