The complementarity of skills, knowledge, and capital
Modified
Input
Skilled people, accumulated knowledge, and physical or financial capital are complements: weakness in one input can sharply reduce the return to the others. A production function helps distinguish the quantity of an input from the institution's ability to use it productively. AI investment should target the binding constraint rather than assume that more compute, more hiring, or more training is always the answer.
Why Inputs Must Be Studied Together
Many weak strategies begin with a true observation and end with an incomplete prescription.
An organization lacks AI capability, so it hires more specialists. A university appears underproductive, so it receives more funding. A country wants an AI industry, so it buys computing infrastructure. Each action increases an input. None guarantees a productive system.
The missing idea is complementarity. Skilled people need access to usable knowledge and suitable capital. Knowledge becomes productive when people can interpret and adapt it. Capital generates returns when an organization knows what to build and how to operate it.
No input is independently sovereign.
A Three-Capital Production Function
Let output be
where:
- $H$ is human capital: the capability embodied in people;
- $I$ is intellectual capital: theories, methods, data, documentation, routines, and accessible knowledge;
- $P$ is physical and financial capital: compute, laboratories, software, facilities, and funding; and
- $A$ is organizational effectiveness: the rules and coordination that allow the inputs to work together.
This is a Cobb-Douglas representation. It is not a complete empirical description of an economy. It is a disciplined way to ask how several necessary inputs jointly produce output.
Taking logarithms gives
The coefficients are elasticities. Holding other inputs constant, a 1 percent increase in $H$ is associated with an approximate $\alpha$ percent increase in output.
Quantity and Productivity Are Different
The model separates the amount of an input from the effectiveness with which it is used.
A firm may have a large $P$ because it owns expensive computing resources. If the firm cannot choose suitable models, clean its data, or integrate results into decisions, $A$ is low. The investment exists, but its productive effect is weak.
Likewise, an organization may hire many educated people, increasing the apparent quantity of $H$. If roles are poorly matched and initiative is suppressed, effective $H$ remains limited.
Table 1. Complementary inputs in an AI-intensive production system
| Input | High quantity, low effectiveness | High quantity, high effectiveness |
|---|---|---|
| Human capital $H$ | Many credentials, weak task ownership | Independent specialists assigned to suitable problems |
| Intellectual capital $I$ | Large document archive, poor retrieval or adaptation | Shared models, validated data, and cumulative learning |
| Physical capital $P$ | Expensive infrastructure without a use case | Resources selected for a defined computational workload |
| Organization $A$ | Fragmented authority and incentives | Clear interfaces, review, and decision rights |
Counting inputs without examining their productivity can make a weak system appear strong.
The Mathematics of Complementarity
In the Cobb-Douglas model, the marginal product of human capital is
The return to more human capital rises with intellectual and physical capital. The cross-partial derivative is positive:
This is the formal expression of complementarity. Increasing $I$ raises the marginal product of $H$, and increasing $H$ raises the marginal product of $I$.
A researcher with access to better data, literature, and methods can produce more. A knowledge repository becomes more valuable when capable people can interrogate it. The value is created in the interaction.
Bottlenecks and Balanced Investment
Suppose an institution has a fixed budget $B$ and input prices $w_H$, $w_I$, and $w_P$:
The institution chooses the input mix that maximizes output. At an interior optimum,
The last unit of budget should produce the same marginal gain across uses. If one ratio is much larger, that input is underprovided relative to its price.
This condition does not mean equal spending. It means balanced marginal returns.
An AI team with strong models and excellent staff but unreliable data infrastructure may obtain its highest return from data engineering. A team with abundant compute and clean data but weak statistical reasoning may need education or different hiring. A university with capable faculty but no time for research may need workload reform rather than another building.
Why Capital Alone Often Disappoints
Physical investment is visible. It can be announced, photographed, and recorded in a budget. Human and intellectual capital accumulate more slowly and are harder to verify.
This creates a political and managerial bias toward $P$.
Consider two projects:
Read as a diagnostic rather than a second scorecard, the framework becomes clear: Large-model training lab — $H$: Medium; $I$: Low; $P$: Very high; Likely constraint: Model and data knowledge. Applied forecasting unit — $H$: High; $I$: High; $P$: Moderate; Likely constraint: Organizational adoption.
The first project may attract more attention because its capital expenditure is larger. The second may create more value because its inputs are better aligned with a decision.
Under complementarity, adding more of the already abundant input produces diminishing marginal returns:
More hardware cannot indefinitely compensate for missing knowledge.
Intellectual Capital Is More Than Information
Information becomes intellectual capital only when it can be used in a productive process.
A collection of articles is not yet a knowledge system. Neither is a database whose variables lack stable definitions. Intellectual capital includes:
- models that organize observations;
- documented assumptions;
- reusable code and validated data;
- records of failed approaches;
- vocabulary shared across teams;
- access to external scientific communities; and
- procedures for revising inherited knowledge.
This distinction is especially important in AI. General-purpose models can retrieve and recombine information, but they do not automatically supply the local definitions, causal structure, or responsibility required for a decision.
An organization's $I$ improves when knowledge is cumulative and contestable.
Organizational Capital as the Integration Term
The productivity term $A$ is often treated as a residual. For management, it is a design variable.
We can write
where $C$ is coordination quality, $G$ is governance clarity, $F$ is the quality of feedback, and $R$ is organizational friction.
The expression is illustrative, but it changes the managerial question. Low productivity need not mean that workers are lazy or technology is obsolete. The problem may be that the system prevents the inputs from combining.
Examples include:
- analysts cannot access operational data;
- technical teams cannot speak directly to decision makers;
- errors are punished, so weak assumptions remain hidden;
- procurement selects technology before the task is defined; and
- project knowledge disappears when a contractor leaves.
These are failures of $A$.
A Diagnostic Matrix
Before expanding an AI initiative, an institution can identify its likely bottleneck.
Expressed as a practical comparison rather than another table, the distinctions are clear: Expensive systems remain unused — Likely weak term: $H$ or $A$; Useful diagnostic: Can staff formulate tasks and influence workflows? Skilled staff repeatedly rebuild prior work — Likely weak term: $I$; Useful diagnostic: Are data, code, decisions, and failures documented? Models perform well but decisions do not improve — Likely weak term: $A$; Useful diagnostic: Are incentives and decision rights connected to the output? Teams cannot run necessary experiments — Likely weak term: $P$; Useful diagnostic: Is compute, software, or data access genuinely constrained? More hiring produces little additional output — Likely weak term: $I$ or $A$; Useful diagnostic: Is knowledge cumulative and work well matched?
This matrix discourages a universal remedy. It also makes responsibility more precise.
Implications for Education
An educational institution participates in all four terms.
It develops $H$ through instruction and assessment. It curates $I$ through curriculum, readings, cases, and research. It supplies $P$ through data, software, and computational resources. It shapes $A$ through sequencing, feedback, faculty coordination, and standards.
This is why a school cannot define quality only by admission selectivity or faculty credentials. Its output depends on whether the educational system combines the inputs.
A demanding student with weak guidance can remain directionless. Excellent lecture notes without assessment may become passive information. Large technology budgets without a coherent curriculum may produce demonstrations rather than learning.
The institution's educational production function is also complementary.
Implications for AI Strategy
AI strategy should begin with the production system, not the shopping list.
The relevant sequence is:
- Define the output and decision.
- Identify the capability required.
- inspect the existing knowledge and data base.
- determine the necessary computational and financial resources.
- design the organizational interfaces.
- invest in the term with the highest marginal return.
This approach may lead to more compute, more hiring, or more education. It may also reveal that the main problem is documentation, incentives, or governance.
Complementarity also explains why balanced investment can outperform a larger but one-sided budget. A firm that buys more compute without improving data governance may raise capacity while leaving usable output unchanged. A university that hires technical specialists without coordinating a curriculum may increase expertise while weakening the student’s path through it. The relevant marginal return is conditional: the value of one more unit of capital depends on the current levels of skill, knowledge, and organization. Strategy should therefore identify the weakest complement first, then test whether improving it raises the productivity of assets already in place. The test is empirical: after the constraint is relaxed, the returns to the other inputs should rise as the complementarity model predicts. If they do not, the diagnosis or the assumed production relationship must be reconsidered. Balanced systems create compounding returns; isolated inputs often create expensive evidence of the missing complement. Coordination converts the bundle into output.
SIAI’s current research gives this production logic direct empirical and institutional relevance. From AI Access to Organizational Capability treats workflow integration and governance as fixed costs that determine whether models become productive. Beyond Robot Relations places human–AI relations inside management systems rather than isolated tasks, while Invisible Value explains why data, software, knowledge, and organizational assets are poorly captured by conventional investment measures. The return to any one input depends on the capabilities surrounding it.
Conclusion
Skills, knowledge, and capital generate value together. Their complementarity explains why apparently strong institutions can underperform: they may possess visible inputs without the less visible system that connects them.
The production function is useful because it separates quantities, elasticities, and coordination. It asks not only how much an organization has, but how effectively each input is used and which input limits the return to the others.
In an AI-intensive economy, the winning strategy is rarely to maximize one input. It is to build a balanced system in which skilled people, cumulative knowledge, suitable technology, and organizational judgment reinforce one another.
References
Robert M. Solow, “Technical Change and the Aggregate Production Function”, Review of Economics and Statistics, 1957.
Paul M. Romer, “Endogenous Technological Change”, Journal of Political Economy, 1990.
Nicholas Bloom and John Van Reenen, “Measuring and Explaining Management Practices Across Firms and Countries”, NBER Working Paper 12216, 2006.
Swiss Institute of Artificial Intelligence (2026) ‘From AI Access to Organizational Capability: Pricing the Corporate AI Transition’, SIAI Working Papers, 9 August.
Swiss Institute of Artificial Intelligence (2026) ‘Beyond Robot Relations: Managing, Measuring and Organizing the AI-Dependent Firm’, SIAI Working Papers, 9 August.
Swiss Institute of Artificial Intelligence (2026) ‘Invisible Value: Why AI Intangible Assets Make the Economy Look Smaller Than It Is’, SIAI AI Memo, 22 January.
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