The Mathematics of Disruptive Innovation

In my post How Rent-Seeking Will Kill the Hollywood Studios, I stated that the hollywood studios have implemented a strategy of milking their existing markets instead of trying to capture a new market.

I also mentioned that this business strategy would ultimately kill the hollywood studios.

In this post, I’d like to give a thought experiment to justify why retreating up-market cannot sustain a company when new markets undermine their existing business models.

Suppose we have two companies: Company A and Company B.

Suppose Company A has a customer base of 100,000,000 people and Company B has no customer base.

Suppose that some new technology creates market A of 10,000,000 million new customers and that this market has a growth rate of 10% per year. Also, market A undermines market B at a rate of 5% per year.

Suppose that company A captures 10% of market A per year, and still captures 100% of the diminishing market B.

Suppose that company B captures 90% of market A per year, and does not have any investment in market B.

We can model this situation with the following equations.

Company A = 10^8 * (.95)^year + 10^7 * (1.10)^year * 0.10

Company B = 10^7 * (1.10)^year * 0.90

Simply calculating the results by plugging in the year yields the following results

year Company A Company B
0 101,000,000 9,000,000
1 96,100,000 9,900,000
5 78,988,603 14,494,5900
10 62,467,436 23,343,682
20 42,576,092 60,547,499

I admit that I’ve created a very simple model.

First, we have no exact number of how much a new market can undermine a business besides the fact that it must do so by a value greater than zero: it could be 0.01% or greater than 10%.

Secondly, there are hundreds of variables working together to determine the growth rate of a specific market. That prevents it from being constant over any length of time.

However, the simulation does show the long-term damage caused by bad business strategy. Any decline in a market can severely damage a company over the long run and make it vulnerable to bankruptcy or acquisition.

Ultimately, market forces will punish any company that fights disruption. If a company fights disruption then they can only delay the inevitable by changing the rate of decline.

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