Startups, Small Businesses, and Large Companies
One of the reasons I like my Production Function Space (PFS) hypothesis, is that it clarifies a lot of issues that have puzzled me for a while. For example, as part of my work on seed-stage startup investing with RSCM, I have struggled with two questions: (1) what’s the difference between a startup and a small business and (2) why do some large companies have initiatives like venture groups and startup incubators?
To answer these questions, I’m going to have to get a little mathematical. Don’t worry. No derivatives or integrals, but I need to introduce some notation to keep the story straight. First, let’s define production footprint and search area.
A production footprint is the surface that encloses a set of points in PFS.* If A is a production function for basketballs, B is a production function for baseballs, and C is a production function for golfballs, then pf(ABC) looks like this in two dimensions:
We can also talk about the production footprint of a company like Google. pf(Google) is the surface that encloses all the production functions that Google currently uses.
A search area is the surface defined by extending the production footprint outward by the search radius.** Imagine that we wanted to see if making basketballs, baseballs, and golfballs would enable a company to make footballs using production function F, we might want to compute sa(r, ABC). It looks like this in two dimensions:
We can also talk about search areas for a company. sa(r,Google) is the surface enclosing all the points in PFS within r units of Google’s current production footprint. If we write just sa(Google), we mean search area using Google’s actual search radius.
With these two basic concepts in place, I can now easily answer questions (1) and (2). SU stands for startup, SB stands for small business, and LC stands for large company. So what’s the difference between a startup and a small business? Well, when they are founded, a startup doesn’t have any production footprint at all and a small business does. To a first order, pf(SU)=0 and pf(SB)>0. A startup doesn’t know with any precision how it’s going to make stuff. A small business does. Whether it’s a dry cleaner, law office, or liquor distributor, the founders know pretty precisely what they’re going to do and how they’re going to do it. However, startups have a much larger search radius than small businesses. r(SU)>r(SB). Assuming that we can define a search area on a set of production functions the startup could currently implement (but hasn’t yet), I content that also sa(SU)>sa(SB).
This realization was an epiphany for me. Even though the average person thinks of startups and small businesses as similar, they are actually polar opposites. They may both have a few employees working in a small office, but one is widely focused on exploring a huge region of PFS while the other is narrowly focused on implementing production functions within a tiny region of PFS. I also realized that you need to evaluate two things in a startup: (a) its ability to search PFS and (b) the ability to implement a production function once it locates a promising region of PFS. But the magnitude of impact for (a) is at least as big as (b) in the very early stages.
Now on to the issue of large companies. The problem here is search costs. Remember that, in three-dimensional space, volume increases as the cube of distance. In PFS, volume increase as an exponent of distance equal to the dimensionality of PFS. I posit that PFS is high-dimension, so this volume increases very quickly indeed. Now try to visualize the production footprint and search area of a large company. A large company has a lot of production functions in play so pf(LC) is large. But sa(r,LC) increases exponentially from this large volume by a large exponent.
In three dimensions, imagine that pf(LC) is like a hot air balloon. Extending just 10 feet out from the hot air balloon’s surface encompasses a huge volume of additional air. But in high-dimension PFS, the effect is… well… exponentially greater. So a large company has a problem. On the one hand, increasing its search radius is enormously costly. On the other hand, we know that Black Swan shifts in the fabric of PFS will occasionally render a huge volume dramatically less profitable, probably killing companies limited to that volume. So it’s only a matter of time before sa(r,LC) is hit by one of these shifts, for any value of r.
Obviously, there will be some equilibrium value of r where the cost balances the risk, but that also implies there’s an equilibrium value for the expected time-to-live of large companies. Yikes! This explains why the average life expectancy of a Fortune 500 company is measured in decades. Another epiphany.
Internal venture groups and incubators represent a hack that attempts to circumvent this cold, hard calculation. The problem is that it’s difficult to explore a region of PFS without actually trying to implement a production function in that region. Sure, paper analysis and small experiments buy you some visibility, but not very much. Also, in most cases, you don’t get very good information from other firms on their explorations of PFS, unless you observe a massive success or failure, at which point it’s too late to do much about your position. That’s why search costs are so darn high. Enter corporate venture groups and startup incubators.
These initiatives require some capital investment by the large company. But this investment is then multiplied by the monetary capital of other investors as well as the human capital of the entrepreneurs. With careful management, a large company can get almost as much insight into explorations of PFS by these startups as it would from its own direct efforts. Moreover, because startups are willing to explore PFS farther from existing production footprints, the large company actually gets better search coverage of PFS.
This framework answers a key question about such initiatives. To what extent should corporate venture groups and startup incubators restrict the startups they back to those with a “strategic” fit”? If you believe in my PFS hypothesis, the answer is close to zero or perhaps even less than zero (look for startups in areas outside your company’s area of expertise). Otherwise, they’re biasing their searches to the region of PFS that’s close to the region they’re already searching. It doesn’t increase the ability to survive that much. As far as I know, Google is the only company that adopts this approach. I think they’re right and now I think I understand why. Epiphany number three.
* There are some mathematical details here that need to be fleshed out to define this surface. But I don’t think they add to the discussion and my topology is really rusty.
** More mathematical details omitted. The only important one is that the extension outward doesn’t have to be by a constant radius. It can be a function of the point on the pf. In that case, r is a global scaling parameter for the function.