Convex direction of the production possibility frontier

In short, the shape of the PPF is a reflection of "the change in opportunity cost when the allocation of resources is changed," and whether it is outwardly convex is not necessarily a fixed requirement.

Non-convex PPF and Corner Solution: In the case of non-convexity (i.e., inwardly concave), the only contact point that matches the price ratio (slope of the budget constraint line) is the "end point" and the optimal solution is often a corner solution (extreme production of only one good).

Jump due to shape change: When the PPF changes to a convex (bulging outward) shape over time or due to technological innovation, there is a possibility that the optimal solution will be the inner point that is tangent to the budget constraint line (the point where both goods are produced in balance). As a result, the solution suddenly jumps from the "edge" to "near the center," a so-called jump.

This change in the shape (convex or nonconvex) of the PPF may cause the optimal production solution to move significantly from the endpoints to the interior points.

Yes, it can be fully related. In conventional technologies and business models, where the only option was an endpoint (corner solution) due to the non-convex PPF, a disruptive innovation can dramatically change the technological constraints and expand the PPF itself to an outwardly convex form. The optimal solution then jumps from the endpoint to the center (a solution that incorporates both goods and both functions in a balanced manner) at once, fundamentally changing the existing production structure and market - this can be explained consistently with the impact of disruptive innovation.

o1 Pro.icon

There are few well-known studies that directly link the change from non-convex to convex production possibility frontiers (PPF) and the "jump" from corner solutions to interior points of the optimal solution to disruptive innovation. However, there are several theories and studies that provide context and background that may be relevant.

The mechanism of disruptive innovation, as Christensen describes in The Innovator's Dilemma (1997), is that innovation proceeds along a performance axis that is overlooked by existing technology and eventually surpasses the mainstream market, This is the mechanism of disruptive innovation. From the PPF perspective, this can be interpreted as a situation in which the optimal solution "jumps" from an endpoint to an interior point, as a technology that "expands" the conventional non-convex constraints appears.

Schumpeter's concept of "creative destruction" emphasizes the process by which technological innovation replaces (destroys) old modes of production in a single stroke. This is also consistent with the view that the optimal point shifts rapidly as the PPF is largely rewritten.

Theoretical and simulation studies have examined the process of gradual change in the production set (equivalent to PPF) during the process of "search and selection" of technologies, and the process where the mainstream is replaced at once when a certain threshold is crossed. This possibility is also discussed in evolutionary economics.

It is rare to find literature that explicitly models the above as "PPF changes to convex → solution jumps from edge to center → that is disruptive innovation," but when reading the above discussion of creative destruction, disruptive innovation, evolutionary economics, and non-convex production sets together, a theoretical background that points to a similar phenomenon can be found. It is quite conceivable that an approach could be taken to use these studies as a reference to independently explain solution jumps due to "non-convex→convex shape changes" in a destructive innovation framework.

o1 Pro.icon

Excellent. The very perspective of "explaining discontinuous jumps in the optimal solution due to changes in the shape of the PPF as disruptive innovation" is an approach that does not often appear in conventional textbook descriptions of economics (which are mostly convex PPFs and mainly continuous changes).

From an MOT (Management of Technology) perspective, I think it is a very interesting approach to organize market changes brought about by resource allocation and technological evolution in a "PPF" framework, and to visualize how the jump from the endpoint solution to the central solution rewrites the industry structure at once. I look forward to further development of discussions that cross technological innovation and economic theory.

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I'm just going to go with PROCEEDING for now and send it out in English, so I'm good to go.

What was the name of the place (forgotten)?

It was a peer-reviewed international presentation.

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