Market Limits and Infinite Dimensional Compression

Genius may have its limitations, but stupidity is not thus handicapped.
Elbert Green Hubbard

The International Cost Estimating and Analysis Association (ICEAA) recently held its annual Professional Development & Training Workshop in Minneapolis, Minnesota. This event, a cornerstone of professional development for our members, was a remarkable success. I submitted a paper to it, and it won the award for best paper overall.

Market Dimensional Expansion, Collapse, Costs, and Viability” delved into several crucial yet under-explored areas. Dimensional expansion and collapse are vital to comprehending market evolution. In it, I unveiled a groundbreaking method to compress standard 3D Cartesian Coordinate Systems into as many as 16 dimensions. Theoretically, there is no upper limit to the number of dimensions that can be depicted using these methods. Equally significant was the exploration of multiple views on Demand Frontiers.

In (D), I plotted the ten-year demand figures for 95 Western Bloc business aircraft, with the horizontal axis for their quantities and the prices on the vertical. Several crucial limitations become evident when one does that.

An Outer Demand Frontier reflects the market’s saturation threshold. Any model attempting to exceed this line will find that the market has exhausted its buyers. One can drop one’s price and gain more sales, but this line is very steep and will soon intersect any Learning Curve associated with the aircraft model that forms it. Note that none of the planes in the study vastly exceeded this limit.

The Lower Demand Frontier reveals a market’s margin limitation. There are planes priced below this line but fall into the General Aviation category. They are not for business travel due to the stricter regulations by which Business Aircraft abide.

Inner Demand Frontiers are efficiency-limited. Planes to the left of this line are either 1) reconfigured airliners (where the main airliner line keeps the learning going), 2) ramping up production, 3) winding down their line, or 4) underwritten by governments. In this case, all Textron planes are going extinct, as the company gave up building these aircraft types. The Dassault planes benefited from a large subsidy from the French government, and Piaggio got the same treatment from the Italian state.

The Upper Demand Frontier is the limit that took down the Aerion AS2, as it attempted to go far beyond it. In a different market, this made the B-2 bomber stop at 21 units rather than the 132 vehicles the USAF sought.

In sum, it pays to know where your contest’s boundaries lie. In markets, as in competitive games, there are boundaries. In business, your buyers form those boundaries. Knowing what your buyers can and can’t afford is critical to developing a product with a chance for success.


In (A), I hold a 2D Demand Plane in one hand, and a 3D Value Space in the other. The paper I gave using this concept won the awards in (B), allowing me to speak to 450 People (C). Among other things, my paper addressed markets’ Demand Frontiers (D).