Pumped to the Boundary: AI and the K-Shaped Economy
There is a theorem in optimization that haunts me. It says: when you optimize a linear objective over a convex feasible region, the solution always lies at a vertex -- at a corner, at an extreme point. Never in the balanced interior. Never in the moderate middle. The optimum is always on the boundary.
I keep thinking about this when I look at the economy.
The Shape of Things
The term "K-shaped economy" was coined during the COVID-19 recovery by economist Peter Atwater. Unlike a V-shaped bounce (everyone recovers together) or an L-shaped stagnation (nobody recovers), the K describes a world that splits: one arm rises sharply, the other continues to fall. Same shock, divergent trajectories. Atwater traced the origin not to finances but to confidence -- those who could work from home saw their outlook recover quickly, while those who couldn't watched theirs continue to decline.
The pandemic K was supposed to be temporary. It wasn't. And now AI is sharpening both arms.
The Numbers
The divergence shows up everywhere you look.
Capital flows into a narrowing funnel. Big Tech AI capital expenditure has gone from roughly $107 billion in 2020 to an estimated $650 billion in 2026 -- more than Sweden's GDP.
Big Tech AI Capex ($B)
┌────────────────────────────────────────────────────────────┐
│ ▗▀│
│ ▗▞▘ │ 600
│ ▗▞▘ │
│ ▗▞▘ │
│ ▄▘ │
│ ▗▄▀ │ 400
│ ▄▄▀▘ │
│ ▄▞▀ │
│ ▗▄▞▀ │
│ ▗▄▄▀▀▘ │ 200
│ ▄▄▄▄▄▄▄▄▀▀▀▀▀▀▄▄▄▄▄▄▄▀▀▘ │
│▄▄▄▞▀▀▀▀▀▀ │
└────────────────────────────────────────────────────────────┘
2020 2022 2024 2026
AI now captures over half of all global venture capital, up from about 17% in 2020.
AI Share of Global VC Funding (%)
┌────────────────────────────────────────────────────────────┐
│ ▄▀│ 50
│ ▄▀ │
│ ▄▀ │
│ ▄▀ │
│ ▗▄▀ │
│ ▗▞▘ │
│ ▄▄▀▀▘ │
│ ▗▄▄▀▀ │
│ ▄▄▄▞▀▘ │
│ ▗▄▄▞▀▀▀ │ 25
│ ▗▄▄▄▄▄▀▀▀▀▘ │
│▄▄▄▄▄▄▄▄▄▀▀▀▀▀▀▀▘ │
└────────────────────────────────────────────────────────────┘
2020 2021 2022 2023 2024 2025
Markets concentrate at the top. The Magnificent Seven's share of the S&P 500 nearly tripled from 12% in 2015 to 34.5% in mid-2025. The top ten companies now account for roughly 39% of the index -- exceeding the dot-com peak of 27%. These companies trade at 31x forward earnings; the other 493, at 20x.
Magnificent 7: Share of S&P 500 (%)
┌────────────────────────────────────────────────────────────┐
│ ▄▄▀│
│ ▄▞▀ │
│ ▄▄▞▀▀ │ 30
│ ▞▀ │
│ ▗▀ │
│ ▄▘ │
│ ▄▄▄▄▄ ▞ │
│ ▗▄▀▀ ▀▀▀▀▀▀▄▄▀ │ 20
│ ▄▄▀▘ │
│ ▄▞▀ │
│ ▄▄▄▄▄▞▀▀▀▀ │
│▄▄▄▀▀▀▀▀▀ │
└────────────────────────────────────────────────────────────┘
2015 2020 2025
Productivity splits by sector. Industries heavily exposed to AI saw productivity growth of 27% between 2018 and 2024, up from 7% when measured through 2022 -- a near quadrupling since generative AI arrived (PwC). Meanwhile, manufacturing output has been declining. AI adoption in the information sector runs at 18%; in agriculture and construction, it's below 2%.
The labor market forms a K. AI-related job postings stand at 134% above their February 2020 level. Total job postings? Just 6% above. Workers with AI skills command a 56% wage premium, double what it was a year earlier. The World Economic Forum projects 170 million new AI-adjacent jobs by 2030 -- but also 92 million displaced ones. The catch: "These aren't direct exchanges happening in the same locations with the same individuals."
AI Jobs vs Total Jobs (2020=100)
┌────────────────────────────────────────────────────────────┐
│ ++++│
│ ++++++++ │
│ ++++++ │
│ +++++ │ 200
│ ++++++ │
│ ++++++ │
│ ++++ │
│ ++++ │
│ +++++ │
│ +++++ xxxxxxxxxxxxxxxxxxxx │
│ ++xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx│
│xxxxx │ 100
└────────────────────────────────────────────────────────────┘
2020 2021 2022 2023 2024 2025
++ AI job postings xx Total job postings
Wealth diverges from wages. The top 10% of Americans hold 67% of household wealth; the bottom 50% hold 2.4%. The top 1% own nearly half of all equities. An IMF model predicts that AI adoption could increase the wealth Gini by 7.18 percentage points -- even as it potentially decreases the wage Gini by 1.73 points. More on this paradox later.
The Mathematics of Extremes
What makes the K-shape feel inevitable rather than accidental is that the underlying mathematics predicts it.
Corner Solutions
In constrained optimization, a corner solution is an optimum that sits at the boundary of the feasible set -- where one or more decision variables hit their bounds rather than taking moderate interior values. Corner solutions arise when the tradeoffs encoded in the objective don't balance against the constraints at any interior point. In consumer theory: when the marginal rate of substitution never equals the price ratio within the budget set, the optimum lands at a corner -- all spending on one good, none on another. More generally, in linear programming, the fundamental theorem guarantees that if an optimum exists, it lies at a vertex of the feasible polytope. The interior is never optimal. Not because it's bad, but because moving toward the boundary always improves the objective.
AI steepens the objective. For firms, the "gradient" -- the direction of increasing competitive fitness -- now points sharply toward full AI integration. The returns to partial adoption are modest: McKinsey finds that 88% of organizations use AI in some capacity, but only about 6% see a meaningful impact on earnings. The interior of the feasible region -- partial adoption, hybrid approaches -- is increasingly suboptimal. The solution is at the vertex: either fully AI-native, or not.
Bifurcation
The K-shape has a precise analog in dynamical systems theory. Consider the canonical pitchfork bifurcation:
For , there is a single stable equilibrium at . Everyone clusters in the middle. But when crosses zero -- when a critical threshold is passed -- the single equilibrium becomes unstable, and two new stable equilibria emerge at . The system diverges. Starting from nearly identical conditions, trajectories are pulled toward opposite extremes.
The letter K literally looks like a bifurcation diagram. Think of as AI capability. Below the threshold, one shared economy. Above it, two divergent branches: the AI-complementary and the AI-displaced. And once the bifurcation happens, the middle is no longer a stable place to be. It actively repels.
Preferential Attachment
Early advantages in AI compound in a way that mathematicians call preferential attachment: the more data you have, the better your models; the better your models, the more users; the more users, the more data. This feedback loop follows the same mathematics as the Barabasi-Albert model of network growth, which produces power-law distributions rather than bell curves. A few nodes -- firms, platforms, individuals -- accumulate a disproportionate share of connections, and the distribution has a heavy tail.
The numbers bear this out. Five companies alone (OpenAI, Scale AI, Anthropic, xAI, and others) raised $84 billion in VC funding in 2025 -- 20% of all global venture capital. The distribution of AI returns is not normal. It is Pareto.
The Counterargument: AI as Equalizer
Not all arrows point toward divergence, and intellectual honesty demands taking the counterevidence seriously.
The strongest case for AI as equalizer comes from within-role productivity studies. The Stanford/MIT study by Brynjolfsson, Li, and Raymond found that AI boosted customer service worker productivity by 14% on average -- but the gains were 34% for novice workers and near zero for experienced ones. AI, they argued, "disseminates the potentially tacit knowledge of more able workers." Workers with two months of experience plus AI performed as well as workers with six months without it.
Similarly, AI-augmented job postings requiring a college degree fell 7 percentage points between 2019 and 2024. Open-source models are reducing dependency on proprietary systems. Small business AI adoption has risen to 40%.
But here is the twist that makes the K-shape resilient: wage convergence and wealth divergence can happen simultaneously. Even if AI narrows the gap between novice and expert wages within a given role, the capital returns from AI accrue overwhelmingly to those who own the systems. The IMF's model captures this precisely: AI could decrease the wage Gini by 1.73 points while increasing the wealth Gini by 7.18 points. The within-role leveling is real. The between-class divergence is also real. And the latter dominates.
Pumped to the Boundary
Brookings frames the endgame starkly: rising AI-driven inequality erodes democratic institutions, which lose the capacity to implement redistributive policies, which allows inequality to rise further. A vicious feedback loop -- the societal equivalent of being pumped to the boundary with no restoring force.
The optimization metaphor cuts deep because it suggests this isn't a market failure waiting to be corrected. It's what happens when you optimize. The algorithm doesn't find balance. It finds corners. The solution walks along the boundary, vertex to vertex, always improving the objective, always moving toward a more extreme point. The moderate middle -- the diversified, the balanced -- is provably suboptimal when the gradient is steep enough.
AI is making the gradient very steep.
The question isn't whether the economy will be pushed toward its extreme points. The mathematics is fairly clear on that. The question is whether we design the constraints -- the walls of the feasible region -- so that the corners it finds are ones we can live with.
Data sources: PwC AI Jobs Barometer 2025 (PwC) | McKinsey State of AI 2025 (McKinsey) | AI Adoption and Inequality (IMF) | The Real Winners of the AI Race (SOMO) | AI's Economic Peril to Democracy (Brookings) | The Next Great Divergence (UNDP) | WEF Future of Jobs 2025 (WEF) | Indeed AI Jobs Update (Indeed) | Brynjolfsson, Li, Raymond 2023 (NBER)