Most of the debate about AI and labor markets is about jobs. Which ones disappear, which ones emerge, how fast the transition happens, what policy responses are appropriate. These are important questions. But they’re downstream of a more fundamental one that rarely gets asked outside economics departments, and even there, not often enough.
The question is whether the mathematical function we use to describe how economies produce output still works when one of its major inputs can be replaced by capital.
That function is the Cobb-Douglas production function, and for nearly a century it has anchored how economists think about growth, wages, labor’s share of income, and the relationship between investment and output. It looks like this: Y = A · K^α · L^β. Output (Y) is a function of capital (K) and labor (L), scaled by a technology parameter (A) and shaped by exponents (α and β) that determine how much each input contributes to production.
The function has been remarkably durable. It fits historical data well. Its mathematical properties are elegant. And for most of the twentieth century, the empirical regularities it predicted (a stable labor share of income around 60-65%, diminishing returns to capital, constant returns to scale) held up reasonably well against observation.
Three things are now changing simultaneously, and each one challenges a different layer of the model.
The exponent shift
The most visible layer is what’s happening to the exponents. In a standard Cobb-Douglas world where α + β = 1 (constant returns to scale), the exponents represent factor shares: α is capital’s share of national income, β is labor’s share. For decades, these were treated as structural constants. Kaldor listed the stability of factor shares as one of his stylized facts of growth. Textbooks taught it as settled.
It isn’t settled anymore. Labor’s share of income in advanced economies has been declining since roughly the early 2000s, and the trend has accelerated. The causes are debated (globalization, market concentration, automation, measurement issues), but the pattern is clear. β is falling. α is rising. Within the Cobb-Douglas framework, this means capital is capturing a larger share of what the economy produces, and labor a smaller one.
AI intensifies this shift. When a language model performs work that previously required a salaried analyst, the output is now produced by capital (the compute, the model, the infrastructure) rather than labor. The analyst’s contribution to β migrates to α. Do this across enough roles and enough industries, and you don’t get a modest rebalancing. You get a structural rewrite of how income distributes between people who own things and people who do things.
None of this breaks the Cobb-Douglas function mathematically. The exponents can shift and the model still works. But it does break the social contract that was built around their historical values. Entire policy architectures, tax systems, retirement funding, educational investment, wage bargaining frameworks, are calibrated to a world where labor captures roughly two-thirds of output. If that share drops to half, or a third, the policies don’t just need adjustment. They need reconceptualization.
The technology problem
The second layer is subtler and more consequential for the model itself. The A parameter in Cobb-Douglas, total factor productivity, is supposed to represent technology’s contribution to output. In the original formulation, and in the Solow growth model that operationalized it for macroeconomics, A is a Hicks-neutral scalar. It multiplies the entire production function equally. Better technology makes both capital and labor more productive, in the same proportion, without changing the relationship between them.
This is where things get interesting. The Solow residual (the portion of output growth that can’t be explained by increases in capital or labor) is measured as whatever is left over after you account for factor accumulation. It was always a residual in the literal sense: not a direct measurement of technology, but a confession of ignorance about what else drives growth. Abramovitz called it “a measure of our ignorance,” which remains one of the most honest descriptions in economics.
The assumption that this residual is factor-neutral, that technology scales everything equally, was never strongly justified. It was convenient. It made the math tractable. And for most of the twentieth century, when the dominant technologies (electrification, telecommunications, logistics) genuinely did enhance both capital and labor roughly symmetrically, the assumption was close enough to reality that the gap didn’t matter much.
AI is not factor-neutral. It is specifically labor-substituting. A large language model does not make a paralegal more productive in the way that a better telephone made a salesperson more productive. It replaces the paralegal’s cognitive labor with capital-embodied computation. The technology isn’t scaling both inputs. It’s converting one input into the other.
Daron Acemoglu’s work on directed technical change provides the theoretical framework for this. Technology doesn’t arrive neutrally. It’s directed toward the factor it’s designed to augment or replace, shaped by relative prices, profit incentives, and the nature of the innovation itself. When labor is expensive relative to capital, innovation directs itself toward labor substitution. AI is the most powerful labor-substituting technology ever developed, arriving at a moment when the incentive structure overwhelmingly favors exactly that direction.
If A isn’t neutral, then measuring it as a scalar residual systematically mischaracterizes what technology is doing. The growth attributed to “total factor productivity” is actually a combination of genuine efficiency gains, factor substitution effects, and compositional shifts in what counts as capital versus labor. The single number hides the distributional transformation inside an aggregate that looks benign.
This doesn’t mean A is useless as a concept. It means that treating it as an exogenous, factor-neutral parameter understates the structural change that AI introduces. The technology parameter isn’t just getting bigger. It’s changing what it does.
The functional form problem
The deepest layer is the one that challenges the model itself. Cobb-Douglas is a specific functional form, and it carries a specific assumption: the elasticity of substitution between capital and labor is exactly one. This means that if you double the price of labor relative to capital, firms substitute toward capital at a rate that exactly preserves capital’s and labor’s relative income shares (before any exponent shift). The substitution is smooth, proportional, and bounded.
This is the mathematical property that makes Cobb-Douglas produce stable factor shares. It’s also the property that may be least defensible in an AI-transformed economy.
The more general form is the CES (constant elasticity of substitution) production function, where the elasticity of substitution, σ, is a free parameter rather than fixed at one. When σ = 1, CES collapses to Cobb-Douglas. When σ > 1, capital and labor are gross substitutes: it’s easy to replace one with the other, and increases in capital accumulation drive labor’s share down without limit. When σ < 1, they’re complements: more capital actually increases the return to labor.
The question is empirical, and the answer matters enormously. If σ > 1, then the substitution of AI-capital for labor doesn’t reach a natural equilibrium. It accelerates. Each increment of AI capability makes the next increment of labor substitution easier and more profitable. Labor’s share doesn’t stabilize at some lower level. It trends toward zero, constrained only by the tasks that capital genuinely cannot perform.
Historical estimates of σ are contested, but most land somewhere between 0.5 and 1.5, with the majority below 1. If those estimates are correct, capital and labor are complements, and AI-driven capital accumulation should eventually increase labor’s returns, not decrease them. This is the optimistic case, and it has serious empirical support from previous waves of automation.
But there’s a question of whether historical estimates of σ remain valid when the nature of capital changes qualitatively. Previous automation substituted for physical labor: muscles, repetitive motion, routine operations. The tasks that remained, the ones requiring cognition, judgment, creativity, and interpersonal skill, were deeply complementary with the new capital. More machines meant more need for the people who designed, managed, and directed them.
AI substitutes for cognitive labor. The residual tasks, the ones AI can’t yet perform, may not be complementary with AI-capital in the same way that cognitive work was complementary with physical-automation capital. If that complementarity breaks down, then σ shifts upward, potentially above 1, and the historical relationship between capital accumulation and labor returns reverses.
This is the deepest version of the production function problem. Not that the exponents are shifting (they are, but the model can accommodate that). Not that the technology parameter isn’t neutral (it isn’t, but you can extend the model to handle directedness). The deepest problem is that the functional form itself, the mathematical relationship between capital and labor, may be changing in a way that the model cannot represent by adjusting its parameters. If the elasticity of substitution is itself a function of the type of capital deployed, then no fixed-σ model, not even CES, fully captures the dynamics.
Where this leaves us
I want to be honest about what this analysis does and doesn’t establish. It doesn’t predict mass unemployment. It doesn’t prove that labor’s share will collapse. It doesn’t resolve the empirical question of whether σ is above or below 1 in an AI-augmented economy.
What it interrogates is something narrower but, I think, more important: the analytical framework that most economists use to think about growth and distribution was built for a world where technology was factor-neutral and the substitutability of capital for labor was bounded. Neither assumption may hold in the near future. And if neither holds, then the framework’s predictions about wages, income distribution, and the returns to human capital don’t fail in the sense of being slightly off. They fail in the sense of potentially pointing in the wrong direction.
The function itself is more resilient than the society built around its historical calibration. Cobb-Douglas will continue to fit aggregate data tolerably well, because aggregate data smooths over the distributional shifts occurring under the surface. The production function problem is not that the math breaks. It’s that the math keeps working while the world it describes reorganizes underneath it.
That gap, between a model that still fits and a reality that has structurally changed, is where the interesting questions live. And they’re questions that economics, as currently practiced, is not well equipped to answer, because the answers require engaging with the possibility that the model’s parameters aren’t just shifting. Just maybe, the model’s assumptions are dissolving.