ECON1201 Lecture 10: General Equilibrium and Welfare Theorems

Vocabulary practice flashcards covering general equilibrium, Walrasian equilibrium conditions, Edgeworth box concepts, Pareto efficiency, and the First Fundamental Theorem of Welfare Economics.

Partial Equilibrium

A condition where the price clears a single focal market, making the total quantity supplied equal to the total quantity demanded for that good while keeping everything else constant.

General Equilibrium

A condition where prices clear every market simultaneously, meaning that the total quantity supplied equals the total quantity demanded for every single good.

Competitive Equilibrium (Walrasian Equilibrium)

A collection of prices ${p^*_k}_{k=1}^K$ and goods allocations (${x^{i*}}_{i=1}^I$, ${y^{j*}}_{j=1}^J$) such that individual optimization, firm profit maximization, and market clearing are simultaneously satisfied.

Individual Optimization

A condition in competitive equilibrium where, given prices ${p^*_k}_{k=1}^K$, endowment $\omega^i$, ownership $\theta^i$, and productions ${y^j}_{j=1}^J$, every consumer $i$ chooses an allocation $x^{i*}$ such that $x^{i*} \succsim_i x^i$ for all affordable $x^i$ satisfying $p \cdot x^i \le p \cdot \omega^i + \sum_j \theta_{ij} p \cdot y^j$.

Firm Profit Maximization

A condition in competitive equilibrium where, given market prices ${p^*_k}_{k=1}^K$, every firm $j$ selects an optimal production plan $y^{j*}$ such that $p \cdot y^{j*} \ge p \cdot y^j$ for all feasible $y^j$.

Market Clear

A condition in competitive equilibrium where total demand equals total supply for each good $k$, represented mathematically by $\sum_i x^{i*}_k = \sum_i \omega^i_k + \sum_j y^{j*}_k, \forall k$.

Allocative Efficiency

A property of an economy where the allocation of goods maximizes social welfare.

Productive Efficiency

A property of an economy where goods are produced at the lowest possible cost given the available technology.

Feasible Allocation

An allocation ${x^i}_{i=1}^N$ where consumption quantities are nonnegative ($x^i_k \ge 0, \forall i, \forall k$) and resource constraints are satisfied ($\sum_i x^i_k = \sum_i \omega^i_k + \sum_j y^j_k, \forall k$, or $\sum_i x^i_k = \sum_i \omega^i_k, \forall k$ in an exchange economy).

Exchange Economy

An economic setting where production is removed and individuals trade and exchange their initial endowments of goods directly with one another.

Pareto Improvement

A reallocation ${x^{i\prime}}_{i=1}^I$ relative to an allocation ${x^i}_{i=1}^I$ where nobody is worse-off ($\forall i, x^{i\prime} \succsim_i x^i$) and at least somebody is strictly better-off ($\exists i, x^{i\prime} \succ_i x^i$).

Pareto Efficient (Pareto Optimal)

A property of an allocation ${x^i}_{i=1}^I$ if it is feasible and there exists no other feasible allocation ${x^{i\prime}}_{i=1}^I$ that is a Pareto improvement to it.

Contract Curve

The line connecting all Pareto efficient allocations in an Edgeworth Box where consumers have exhausted mutual trade incentives and their indifference curves are tangent ($MRS_{12}^A = MRS_{12}^B$).

The First Fundamental Theorem of Welfare Economics

The theorem establishing that if preferences are rational and locally non-satiated, then any Walrasian equilibrium allocation ${x^{i*}}_{i=1}^I$ is Pareto efficient.