Generalized Ozaki cost function¶
In economics the generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura.
Core Idea¶
Generalized Ozaki cost function is treated here as the recurring cross-domain formal modeling identity summarized by this source-grounded definition: In economics the generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura. In economics the generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura. The GO cost function is notable for explicitly considering nonhomothetic technology, where the proportions of inputs can vary as the output changes. This stands in contrast to the standard production model, which assumes homothetic technology.
Scope of Application¶
-
Homothetic- and Nonhomothetic Technology. Commonly used forms of production functions, such as Cobb-Douglas and Constant Elasticity of Substitution (CES) functions exhibit homothticity.
-
Flexible Functional Forms. Widely used examples of FFFs are the transcendental logarithmic (translog) function and the Generalized Leontief (GL) function.
-
The GO function. For a given output y , at time t and a vector of m input prices pi , the generalized-Ozaki (GO) cost function C() is expressed as.
-
The GO function. By applying the Shephard's lemma, we derive the demand function for input i , xi.
-
The GO function. The GO cost function is flexible in the price space, and treats scale effects and technical change in a highly general manner.
Clarity¶
A clear use of Generalized Ozaki cost function names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In economics the generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura.
Manages Complexity¶
Generalized Ozaki cost function compresses multiple cross-domain formal modeling details into a stable diagnostic relation. The source shows both the central mechanism—in essence, under general conditions, a specific technology can be equally effectively represented by both cost and production functions.—and the practical consequence—in a subsequent study, Nakamura attempted to address this issue by employing the Generalized McFadden function.
Abstract Reasoning¶
- Type the carrier. Identify the cross-domain formal modeling entities to which the claim applies.
- State the relation. Use the source-grounded identity: In economics the generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura.
- Check operation and conditions. One advantage of using a cost function rather than a production function is that the demand functions for inputs can be easily derived from the former using Shephard's lemma, whereas this process can become cumbersome with the production function. 4.
Knowledge Transfer¶
Within the home domain. Knowledge about Generalized Ozaki cost function transfers literally when a new case preserves the same carrier type, relation, and recognition test. Commonly used forms of production functions, such as Cobb-Douglas and Constant Elasticity of Substitution (CES) functions exhibit homothticity. Widely used examples of FFFs are the transcendental logarithmic (translog) function and the Generalized Leontief (GL) function. Beyond the home domain. No canonical parent is asserted for Generalized Ozaki cost function.
Relationships to Other Abstractions¶
Current abstraction Generalized Ozaki cost function Domain-specific
Parents (1) — more general patterns this builds on
-
Generalized Ozaki cost function is a kind of Function (Mapping) Prime
The generalized-Ozaki cost function maps production conditions to modeled cost.
Hierarchy path (1) — routes to 1 parentless root
- Generalized Ozaki cost function → Function (Mapping)
Neighborhood in Abstraction Space¶
Generalized Ozaki cost function sits in a moderately populated region (52nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Classical & Trade Economic Theory (20 abstractions)
Nearest neighbors
- Mathematical Modeling — 0.87
- Law of increasing costs — 0.86
- Kenneth Boulding's Evolutionary Perspective — 0.86
- Filling radius — 0.86
- Single Vegetative Obstruction Model — 0.85
Computed from structural-signature embeddings · 2026-10-08