Non-convexity (economics)¶
An economic setting in which preferences, technologies or feasible sets violate convexity, allowing indivisibilities, increasing returns and multiple or unsupported competitive outcomes.
Core Idea¶
Economic non-convexity occurs when averaging two feasible or preferred alternatives need not yield another feasible or at-least-as-good alternative. Fixed costs, discrete choices or increasing returns create dents and jumps in feasible or preference sets, breaking separating-hyperplane and marginal-price arguments. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of economics. It is violation of convex economic structure that disrupts standard equilibrium and decentralization theorems. That residual remains recognizable when examples, notation, scale, or implementation change, but it disappears if the carrier is mistyped, the condition that the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition fails, a neighboring object is substituted, or notation and topical resemblance replace the constitutive test.
Scope of Application¶
Non-convexity (economics) belongs to economics and is useful where the analyst can specify consumer preference sets, production or budget sets, mixtures of bundles or plans, increasing returns, fixed costs and indivisibilities, prices, competitive equilibrium and welfare claims, then evaluate the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition. The scope is broad within that domain but bounded by the need for the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Non-convexity (economics) can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Non-convexity (economics). Non-convexity (economics) compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: consumer preference sets, production or budget sets, mixtures of bundles or plans, increasing returns, fixed costs and indivisibilities, prices, competitive equilibrium and welfare claims. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of economics because they reuse consumer preference sets, production or budget sets, mixtures of bundles or plans, increasing returns, fixed costs and indivisibilities, prices, competitive equilibrium and welfare claims, Fixed costs, discrete choices or increasing returns create dents and jumps in feasible or preference sets, breaking separating-hyperplane and marginal-price arguments., and type the carrier, state every parameter and convention in the definition, test that the relevant preference upper contour, production or feasible set fails the exact convex-combination closure condition, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Non-convexity (economics) Domain-specific
Parents (1) — more general patterns this builds on
-
Non-convexity (economics) is a kind of Convexity Prime
The proposed strict upward parent is
prime:convexity.
Hierarchy path (1) — routes to 1 parentless root
- Non-convexity (economics) → Convexity → Optimization
Neighborhood in Abstraction Space¶
Non-convexity (economics) sits in a crowded region of the domain-specific corpus (34th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Welfare, Production & Economic Choice (45 abstractions)
Nearest neighbors
- Allocative efficiency — 0.91
- Monotone preferences — 0.90
- Willingness to pay — 0.90
- Subjective theory of value — 0.90
- Applied general equilibrium — 0.90
Computed from structural-signature embeddings · 2026-09-08