Budgetsett

Budgetsett, or budget set in English, is a fundamental concept in consumer theory that describes all bundles of goods a consumer can afford given current prices and income. It represents the feasible set of choices available during a decision period.

Formally, with a price vector p = (p1, ..., pn) where pi > 0 and income m > 0, the budgetsett is B(p, m) = { x ∈ R_+^n : p · x ≤ m }, where p · x = p1 x1 + ... + pn xn and x ≥ 0. The condition p · x ≤ m captures the budget constraint, while x ≥ 0 enforces non-negativity of quantities.

The budget line is the boundary p · x = m; the budgetsett includes all points on or inside that line (within the nonnegative orthant). In the two-good case, the set forms a right-angled triangle with intercepts at m/p1 and m/p2. Increasing income or lowering prices expands the feasible area.

In analysis, the consumer chooses x to maximize a utility function u(x) subject to x ∈ B(p, m). The optimal point typically lies on the budget line where an indifference curve is tangent, under standard assumptions. Changes in prices or income shift the budgetsett, producing substitution and income effects that alter optimal choices.

Notes: Budgetsett is convex and closed when prices are positive and income is nonnegative. The concept extends to more goods and can incorporate additional constraints, such as taxes or quotas, but remains centered on the idea of affordable consumption given resources.