The model assumes each person freely produces $V_i = (C_i^{-\rho} + S_i^{-\rho})^{-1/\rho}$. Most knowledge workers face organizational constraints: managers, deadlines, contractual obligations. A more realistic formulation incorporates externally demanded output $D_i$: the effective desire floor becomes $\max(S_i, D_i)$. The desire-constraint result applies primarily to workers with genuine autonomy — freelancers, founders, researchers — not the median employee.
The Desire Model
February 28, 2026
Both capacity-constrained
As AI improves at everything — execution, design, analysis, judgment — the constraint on individual value creation shifts from capability to desire. But abundance depresses prices: you must want more just to maintain what you have. The population splits into those whose ambitions expand, those who run the treadmill, and those who stop running. The gap between them grows without limit.
Each person $i$ has three per-period parameters: baseline value-creation capacity $B_i$ (what you can produce without AI), AI investment $X_i$ (access to and direction of AI capacity — whether hands-on or autonomously deployed), and desired value $S_i$ (how much you actually want to create). AI efficiency $a(t)$ increases over time, augmenting everything: execution, analysis, design, judgment.
$$C_i = aX_i + B_i, \qquad V_i = \bigl(C_i^{\,-\rho} + S_i^{\,-\rho}\bigr)^{-1/\rho}, \quad \rho > 0$$
$C_i$ is total value-creation capacity. $V_i$ is realized value: a smooth CES (constant elasticity of substitution) aggregator that returns the lesser of capacity and desire. The parameter $\rho$ controls the transition sharpness; as $\rho \to \infty$, $V_i \to \min\{C_i, S_i\}$. As AI improves, it lifts capacity across every dimension of production. The question is what happens when capacity surpasses desire.
The crossover occurs at a computable threshold:
$$a_i^* = \max\!\left\{0,\;\frac{S_i - B_i}{X_i}\right\}$$
For $a < a_i^*$: capacity constrains, and better AI increases value created. For $a > a_i^*$: desire constrains, and better AI has diminishing effect — value asymptotically approaches $S_i$. Higher ambition raises the threshold; higher investment lowers it.
For two people both well past their crossover points:
$$C_i \gg S_i,\; C_j \gg S_j \;\implies\; \frac{V_i}{V_j} \;\longrightarrow\; \frac{S_i}{S_j}$$
The value ratio converges to the desire ratio — asymptotically, as capacity dominates. The ability parameters $B_i, B_j$ fade from the expression.
How quickly does ability stop mattering? The marginal return to ability answers directly:
$$\frac{\partial V_i}{\partial B_i} = \left(\frac{V_i}{C_i}\right)^{1+\rho}$$
Always positive, but it decays toward zero as capacity outstrips desire. Not a cliff — a fade. When $C_i \gg S_i$, the ratio $V_i / C_i \approx S_i / C_i \to 0$, so the marginal value of ability vanishes. This depends on AI being good enough at everything: execution, analysis, design, and judgment. If AI handles judgment as well as execution, there is no remaining dimension of production — neither speed nor quality nor taste — where being more able translates into more value.
In practice, $B_i$ itself evolves: AI-assisted learning may raise it, while habitual reliance on AI may erode it through skill atrophy. But this does not rescue ability’s relevance — for large $a$, the $aX_i$ term dominates $B_i$ regardless of which direction $B_i$ moves.
Abundance Depreciation. The model so far is individual-level. But when AI makes everyone more productive, aggregate supply rises and the market price of each unit falls. Define aggregate realized value $\bar{V}(t) = \int V_i \, di$ and the market price, scaled by a base price level $\kappa$:
$$p(t) = \kappa \cdot \bar{V}(t)^{-\delta}, \qquad \delta \in (0,1)$$
Income is price times value: $I_i = p(t) \cdot V_i$. The parameter $\delta$ is the depreciation elasticity — how fast prices fall with abundance. Its severity depends on market structure: software faces near-zero marginal cost (high effective $\delta$), while bespoke services resist commoditization (low $\delta$). Since $p(t)$ is common to everyone, income ratios equal value ratios: $I_i / I_j = V_i / V_j$. Relative inequality depends on the desire model; depreciation affects absolute levels.
This creates a treadmill. For a person with fixed desire $S_i$:
$$I_i(t) = \kappa \cdot S_i \cdot \bar{V}(t)^{-\delta} \;\longrightarrow\; 0$$
As aggregate production grows, those with fixed desire see their income collapse — not stagnate, collapse. To maintain a target income $\bar{I}$, required desire grows as $S_i^{\text{req}}(t) = (\bar{I}/\kappa) \cdot \bar{V}(t)^{\delta}$. You must want more just to stay in place.
Capital Dominance in the Transition. Depreciation affects absolute income levels. But what determines relative position? Before desire becomes the binding constraint, capital does. While two people both remain capacity-constrained:
$$\frac{V_i}{V_j} = \frac{aX_i + B_i}{aX_j + B_j} \;\xrightarrow{a\to\infty}\; \frac{X_i}{X_j}$$
As $a$ grows, ability washes out. AI investment — not innate ability — determines relative value.
Aspiration Dynamics. Desired value $S_i$ need not be fixed. When capacity exceeds desire, ambitions may expand. Model this with aspiration elasticity $\gamma_i \geq 0$:
$$\dot{S}_i = \gamma_i \cdot (C_i - S_i)^+$$
High $\gamma_i$ means you rapidly discover new ambitions when surplus capacity appears. $\gamma_i = 0$ recovers fixed desire. With linear AI improvement ($a(t) = a_0 + rt$), the steady-state solution is:
$$S_i^*(t) = C_i(t) - \frac{rX_i}{\gamma_i}$$
The aspiration gap $\Delta_i = rX_i / \gamma_i$ is the steady-state distance between capacity and desire. For two aspirational people ($\gamma_i, \gamma_j > 0$):
$$\frac{V_i}{V_j} \;\xrightarrow{a\to\infty}\; \frac{X_i}{X_j}$$
The long-run ratio converges to the capital ratio, not the desire ratio. With endogenous desire, desire is shaped by capacity, so it can’t independently drive the ratio.
Investment Feedback. So far $X_i$ is exogenous. In practice, people who want more invest more in AI — $X_i$ responds to $S_i$. This creates a reinforcing loop: higher desire drives higher AI investment, which raises capacity, which (with $\gamma_i > 0$) raises desire further. The trifurcation amplifies: aspirational people pour resources into expanding capacity, while satiated ones see no reason to invest. Capital heterogeneity becomes endogenous to desire heterogeneity.
Population Trifurcation. Aspiration dynamics, investment feedback, and depreciation interact to split the population into three groups. Aspirational ($\gamma_i > 0$): ambitions expand with capacity; value and income grow. Treadmill runners ($\gamma_i = 0$, income-targeting): desire forced up by falling prices; income maintained at the cost of perpetually raising ambition. Satiated ($\gamma_i = 0$, fixed $S_i$): value plateaus; income collapses toward zero. The gap between the first and third group grows without bound.
Once desire constrains value, inequality in output approximately tracks inequality in desire: $\operatorname{Var}(V) \approx \operatorname{Var}(S)$. But depreciation amplifies the stakes — the same variance in desire produces divergent income trajectories as the treadmill forces some to expand their ambitions and others to fall behind.
Stepping back, the full arc has three phases. In Phase 1 (Ability), capacity $\approx$ baseline ability and value dispersion tracks skill. In Phase 2 (Capital), AI investment dominates and ability washes out. In Phase 3 (Desire + Treadmill), desire binds value and falling prices split the population into aspirational, treadmill, and satiated.
Across all three, ability’s relevance declines monotonically — there is no phase where it recovers. What replaces it is, first, capital, and then desire. What makes Phase 3 distinctive is not just that desire matters, but that standing still is not an option.
Limitations
The model introduces $\gamma_i$ as a psychologically interpretable parameter (openness to expanding goals, growth mindset). No standard instrument measures it. Developing such measures — and establishing their stability and predictive validity — is a precondition for empirically testing the aspiration-dynamics predictions.
The results require $X_i > 0$ for everyone. Current AI pricing creates steep accessibility cliffs. If a significant fraction of people have $X_i = 0$, they remain capacity-constrained regardless of how high $a(t)$ climbs. Solving the access problem is necessary but not sufficient: it changes the driver of inequality from access to desire.
The model captures falling prices through a single depreciation elasticity $\delta$. Real markets are heterogeneous: software faces near-zero marginal cost (high effective $\delta$), while bespoke services resist commoditization (low $\delta$). Winner-take-all dynamics, network effects, and attention scarcity create nonlinearities the power-law form cannot capture.
The capacity function $C_i = aX_i + B_i$ assumes AI lifts production broadly. This holds for digital and knowledge-work output — code, analysis, content, design — but not for land, energy, raw materials, or physical infrastructure. In atom-constrained sectors, capacity is bottlenecked by resources AI cannot conjure. The model’s predictions apply most strongly to the growing share of the economy that is digital, and less to the physical layer where scarcity persists regardless of $a(t)$.
The model assumes people retain the value they create: $I_i = p(t) \cdot V_i$. If AI provision concentrates in a few firms that extract rent $r$, effective income becomes $(1-r) \cdot p(t) \cdot V_i$. Desire still governs relative outcomes among users — higher $S_i$ still means higher $V_i$ — but the monopolist captures a share from everyone. In the extreme ($r \to 1$), the provider-vs-user split dominates the desire-driven split. The affordability cliff worsens: monopoly pricing raises the floor for $X_i$, pushing more people to effective zero.
