Here are are the lessons I've learned after 5 years of running a non-profit, illustrated in a simple formula:
X(scale + innovation + implementation + luck) = social change, where X = money
Here are those lessons put another way: the math of social change should be algebraic but rather resembles a calculus problem
Why So Hard?
Let's consider the non-profit paradigm. Non-profit begs for money from individuals, foundations, corporations and government. Money dribbles in. Money is predominantly spent on programs, because funders don't like their donations to go toward "overhead" (read that: infrastructure, personnel, marketing, etc.). Programs result in some good stories that touch the hearstrings of funders. Money dribbles in again. Rinse and repeat.
Notice that scale and social impact were left out of that equation. Now consider the for-profit paradigm. For-profit pitches the investment opportunity to investors. For-profit knows how much it need to become profitable. Investors evaluate for-profit for profit potential. For-profit makes necessary investments: it probably loses money for several years as it builds up back-end systems, refines the business model, markets its products and services and grows its market share. For-profit seeks new investment as needed. Some for-profits return profit to investors; others go under. Those that are profitable continue to grow and either go public or are purchased by a larger company.
Notice that social impact is left out of the equation.