Calculating the Second Curve

The number that makes a hard problem a market position.

Apr 16, 2026

Article voiceover

0:00

-12:56

Most people working on hard problems, the kind affecting hundreds of millions of people across health, education, financial access, and climate, have calculated the size of the market. The number of people affected, the scale of unmet need, or the Total Addressable Market (TAM) if this were a venture pitch. That calculation is usually large and usually correct.

Almost none have calculated the cost of solving it against what the system is already paying to leave it unsolved. Those are different exercises. The first produces a budget. The second produces a position.

That second number, what it actually takes to deliver a verified unit of change at a price the system will pay, reframes everything. It tells you whether your solution is priced for a charity or for a contract. It tells you whether the economics have crossed. And it is the number that makes your position defensible to a government buyer, a capital allocator, or a serious investor.

This is the Crossover Point: the moment at which solving structurally becomes cheaper than leaving unsolved. Two curves, moving in opposite directions. The organisations that calculate where they cross move while others are still funding the old model.

You have priced the first curve. This edition is about the second.

What is the Crossover Point?

The cost of the solution, its unit economics, is a supply-side question. The Crossover Point calculates the demand-side: what the system pays when the problem stays unsolved, and when the cost of solving drops below that.

A homelessness calculation is the clearest example. Research by Nicholas Pleace for Crisis UK established that the annual cost to public spending of a single person sleeping on the streets is GB£20,128: across emergency services, healthcare, temporary accommodation, and legal processing. The cost of the early intervention that prevents it: GB£1,426. This is a 14-to-1 ratio. The economics were always there. The solution architecture was not.

That ratio is the second curve made visible. Once you know what the system is paying on one side, the cost of solving on the other becomes a procurement decision rather than a philanthropic one.

Both curves are moving. The cost of solving falls as technology deflates and the marginal cost of each additional verified outcome approaches zero. The cost of the status quo rises as the problem compounds and institutional alternatives contract.

Knowing your solution is cheaper than the alternative is the starting point. The calculation is what converts that into a number a government buyer, a capital allocator, or an investor can place next to other options on a spreadsheet. That is what makes the position defensible.

Living Goods: Calculating the second curve in community health

For decades, the institutions with the mandate to solve community health in sub-Saharan Africa had the resources, the political access, and the stated commitment. The results were not proportional. By the early 2000s, child mortality in Uganda remained among the highest in the world. Clinic infrastructure was underfunded and unevenly distributed. Volunteer community health worker programmes operated without supervision structures, without reliable supply chains, and without the data systems that would allow anyone to know what the investment was purchasing.

Health budgets funded activity. They did not buy outcomes.

The hard power approach, involving centralised government systems and large multilateral health programmes, had demonstrated its ceiling. What it could not do was reach the last mile at a cost the system could sustain. That gap was structural, and it was large.

Living Goods entered with a different set of assets: a commercially-trained operating model, community trust built through local health workers known by name in the households they served, and a technology infrastructure that made supervision and verification possible at scale. These are soft power assets. The kind of leverage institutional health systems find hard to replicate, because the trust is earned at the community level and the operating logic runs on local knowledge rather than centralised authority.

The DESC model, meaning Digitally-enabled, Equipped, Supervised, and Compensated community health workers, put those assets inside a measurable architecture. Every element was designed to be verifiable and replicable without depending on the founding team’s presence or the next grant cycle.

The size of the problem, or the TAM, was never the question. Every health ministry knew the scale of the problem; 1.8 billion people globally living in communities where primary healthcare remains inaccessible or ineffective. The second curve, what verified community health coverage would actually cost against what the system was already paying, had never been calculated.

Then Living Goods ran the numbers.

Two gold-standard randomised controlled trials (RCT) in Uganda, in 2013 and 2021, produced consistent results: a 27-28% reduction in under-five mortality at a cost of approximately US$3.09 per person per year for full community health coverage.

The second trial is worth noting separately. The 2013 RCT ran in carefully selected areas under close management. The 2021 trial ran across 13 districts, 500 villages, and over 12,500 households, a far broader and less controlled environment. The 28% mortality reduction held. The model did not depend on optimal conditions to produce its result.

At that point the comparison became unavoidable. This is what a procurement decision looks like in practice: governments placing two numbers side by side, ongoing spending with uncertain outcomes against a defined cost per verified reduction in mortality. County-level contracts in Isiolo and Kisumu in Kenya followed. The model moved from externally funded project to government-contracted public service. Living Goods no longer needed to be in the room for it to operate.

Each government contract generates the verification data that makes the next contract faster to close. The marginal cost of each additional verified outcome falls with every cycle. The architecture scales because the Outcome Unit is fixed and the cost is known.

US$3.09. The institutions with the mandate tried for decades. Living Goods calculated the second curve and built from there.

Four questions to run on your own problem

The Crossover Point exists in every field where a structural solution is cheaper than the compounding cost of the status quo. The question is whether you have calculated the second curve. To calculate this, ask:

1. What is the single verifiable unit of change your model produces?

One child covered. One household with formal land tenure. One farmer completing a full input-to-market cycle. If you cannot write it in one sentence with a cost attached, you have a mission with activities. The Outcome Unit is the bridge between ambition and a number a buyer can act on. Without it, the second curve has nothing to anchor to.

2. Has the cost of solving dropped below the cost of leaving it unsolved, and can you prove it?

What is the system currently paying: in health costs, foregone productivity, enforcement, welfare transfers, or lost tax revenue, for each unit that does not reach the desired outcome? Put both numbers in the same sentence. If the cost of the status quo is not materially higher than the cost of your solution, the model, the buyer, or the problem entry point needs reexamining. The second curve exists; the question is whether you have found the right cross-section of it.

3. Which barriers are structural, and which belonged to the institution that last tried?

The constraints that stopped the previous model are not necessarily intrinsic to the problem. Many belong to the institution that attempted it: professional accreditation requirements, centralised data infrastructure, or headquarters sign-offs. When the institution exits, those constraints exit with it. Deploying effort against a constraint that no longer exists is one of the most expensive mistakes a well-designed model makes. The Chokepoint Map, which is the subject of the next edition, is the tool for making that distinction before committing five years to the wrong problem.

4. Would this still work if you removed the founder, the grant, or the relationship that made it possible?

If the answer is no, you have a project. Living Goods passed this test twice. The first RCT ran in selected areas under close management. The second ran across 13 districts, 500 villages, and over 12,500 households. The mortality reduction held at 28%. That is the Voltage Test: does the model keep its result when it moves beyond optimal conditions? When the Kenyan government contracted the DESC model as a funded public service, it passed a third time. The incentive structure, the verification mechanism, and the repayment architecture are embedded in the design, held there by the system rather than by exceptional conditions. A model that depends on its founder to function has not yet calculated the second curve. It has calculated the founder.

What the calculation reveals

If you can answer all four questions with numbers, you have the foundation of a market position. The second curve is calculable, the Crossover Point is behind you, and the work is execution.

If two or three answers are clean and one is not, you know exactly where to direct the next six months. The gap is specific, which means it is closeable.

If the cost of the status quo is lower than the cost of your solution, the economics have not crossed. A different model, a different buyer, or a different entry point may change that. The calculation tells you which. That is more useful than another year of conviction.

There is a fourth outcome the calculation produces, and it is the one most leaders at this stage have not considered. When the Crossover Point is documented and the Outcome Unit is verified, the problem stops being local. The same economics that make the model viable in one market make it contractable in twenty. The cost structure that works in Kisumu works in Kampala, Dhaka, and Nairobi for the same reason: the second curve has a trajectory that does not respect borders. Hard problems at this scale are global by definition. The Global Market Scale can be calculated.

Capital is necessary and rarely sufficient. It cannot buy the trust, the operational knowledge, or the credibility that makes a solution replicable across markets. Those assets are earned inside the problem, over time, at the community level, and they are the ones the system cannot replicate. The organisations that have moved from single-market proof to global architecture have done so by combining a verified, low-cost Outcome Unit with three assets: relationships built at the community level, operational knowledge earned inside the problem, and the credibility that comes from having stayed when institutional alternatives left. These are soft power assets. They are what converts a defensible market position into a global one.

Most leaders at this stage have the ambition to solve a hard problem, the evidence it exists, and, more often than they recognise, and the assets to build a solution at global scale. What tends to be missing is the calculation that makes all three legible to a buyer, a funder, or a partner: the second curve, priced and documented, in a form that produces a decision rather than a conversation.

The Business Case Calculation

The Business Case Calculation is a 90-minute working session. The output is a single page: your Crossover Point, your Outcome Unit, and the three calculations that establish whether your model has a defensible market position. Delivered within 48 hours.

If you are working on a hard problem and the second curve is the calculation you have not yet run, this is where that work begins.

Details here: softpowerindex.lovable.app/work-together

Next edition: the Chokepoint Map; which barriers are structural, which are institutional, and how to tell the difference before committing five years to the wrong problem.

Soft Power, Hard Problems with Sophie Krantz

Discussion about this post

Ready for more?