Under construction
This repo contains some Python tooling to simplify linear combinations of piecewise linear functions, then finally emit them (and their first derivatives) as Excel formulas.
The motivating application comes from my engagements with very small social enterprise clients, virtually all of which show up with the same story. There's a sole proprietorship or disregarded-entity LLC. It has productive, material operations - often exhaustingly busy operations. But it's fundamentally not big enough to put food on its owner's table. The owner benefits from government support, perhaps paying almost zero in income taxes and getting free healthcare. The owner is steadily liquidating their personal wealth, often obscured by complexities like real estate windfalls, inheritances, family help, grants, increasing debt, or deferred maintenance. And I get a call to apply a couple dozen hours of my expertise to clear up the numbers.
How much will the owner need to grow the enterprise to earn a sustainable living, taking into account that government support will roll off? One must reconcile that it gets easier to make money with scale because fixed costs only have to be paid once, but harder to make money with scale because of the loss of the government support. Capturing these nonlinear behaviors with some precision can be strategically critical. Sometimes, my economic modeling reveals a plausible scale at which the owner both makes a living and stays true to the purpose of their social enterprise. Then the way forward is to push on marketing to grow demand to the needed scale. Other times, there is no such plausible scale. For example, many social enterprises are built around artisanal local production, or they specialize in employing workers from a marginalized community. These operational constraints based on social-purpose considerations could cap out before the social enterprise is financially successful. The way forward in this case, sadly, is either to relinquish the prosocial commitments or shut the enterprise down. That's a fraught consideration for a social entrepreneur, and it demands clarity of mind.
Analyzing prospective business revenue and profit, including scaling of variable costs, requires only four-function arithmetic starting from a decent set of books. Analyzing the owner's burn rate (cost of a lifestyle after tax), starting from personal financial statements, is rather harder. That's due to a need for accounting assumptions (e.g., to capitalize personal fixed assets like a car or house). But it's still routine Excel spreadsheet work.
These two things meet through government support programs that are much more complex, hence not nearly as straightforward.
But government support programs are still usually piecewise linear. In fact, many of them can be written down as linear combinations of translations of Rectified Linear Unit (ReLU) functions - piecewise linear, continuous functions of profit that are constant to the left. If we can express such functions comprehensibly in a general-purpose language like Python and finally emit them as Excel formulas, we can embed the web of Federal and state income taxes, the Earned Income Tax Credit, the Premium Tax Credit, Medicaid, etc., within a spreadsheet analysis that will be accurate enough over a big enough range of scaling to answer the central question.
That's the goal of this repo.