Convex direction of the production possibility frontier
The production possibility frontier is often drawn convex in the direction away from the origin, but isn't that a necessary condition?
In general, textbooks tend to depict PPF as bulging outward from the origin (so-called "convexity outward") to reflect the "increase in opportunity cost. However, this does not mean that PPF is always convex outward. In fact, depending on production technology, economies of scale, and other conditions, PPF may be straight or inward (or inversely, "convex inward").
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.
The optimal solution described in relation to the budget constraint line comes to the edge when it is not convex, but when the PPF changes to convex over time, doesn't it make a jump around the center?
Yes, it is possible.
- 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.
Can we relate that to disruptive innovation?
Disruptive Innovation and the PPF
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.
Are there any existing studies on this?
1.### Disruptive Innovation (Clayton Christensen) . - 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.
2.### Schumpeter's Creative Destruction by Joseph Schumpeter . - 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.
3.### Neo-Schumpeterian and evolutionary economics (e.g., Nelson & Winter, 1982) - 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.
4.### Studies on general nonconvex production sets, economies of scale, etc. . - In the presence of economies of scale (increasing returns) and external economies, the PPF can become non-convex, and it is known that multiple corner solutions can exist path-dependent in such cases. It is theoretically possible to reason that when innovative technology is introduced there, at some point a near-convex shape is achieved and multilateral production becomes possible (see, for example, Arrow (1962) "econometric implications of learning effects" and Romer's endogenous growth theory, which is mentioned in some of his work).
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.
I made this association when I was a working graduate student in MOT.
I don't know what you expect from an AI.
- 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)?
- Shuzo Fujimura, Hirokazu Nishio. Disruptive innovation can occur even if technology progresses gradually. ISPIM Connects Fukuoka. Proceedings of ISPIM Connects Fukuoka: Solving Challenges Through Innovation. 2018. Dec.
- It was a peer-reviewed international presentation.
- T2R2 Tokyo University of Science Research Repository
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