From Energy Ceiling to Access Floor

A Feedback Model of AI Compute Scarcity, Price Formation, and Digital Exclusion

Marc Akbar – Fardon Corp – Draft, March 28, 2026

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Abstract

The rapid scaling of artificial intelligence is creating unprecedented demand for computational energy, yet institutional forecasts treat demand growth and supply constraints as independent processes. We propose a coupled dynamical model in which energy scarcity endogenously drives compute prices, which in turn differentially suppress AI adoption across market segments stratified by willingness-to-pay.

We define three user tiers – enterprise, professional, and consumer – each characterised by distinct price elasticities grounded in the ratio of AI-generated value to local wage equivalents. We derive closed-form conditions for the existence of a supply crossover point (where unconstrained demand exceeds supply) and prove that the price feedback mechanism does not eliminate this crossover but delays it while simultaneously generating a monotonically increasing exclusion population: people who would benefit from AI access but are priced out.

We show that under broad parameter ranges consistent with IEA, IMF, and industry projections, the system converges to a regime where energy constraints are resolved not through efficiency or infrastructure expansion, but through market-mediated exclusion of the most price-sensitive users – predominantly in low-GDP economies. The model formalises the mechanism by which an energy crisis transforms into an inequality crisis, and identifies the critical policy parameters (supply acceleration, price convexity, segment elasticity) that determine whether this transformation is reversible.

Keywords: AI energy demand, compute scarcity, digital divide, price feedback, dynamical systems, technology access inequality

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1. Introduction

The deployment of artificial intelligence at scale requires computational infrastructure whose energy appetite is growing faster than any prior technology wave. The International Energy Agency estimates that data centre electricity consumption reached approximately 415 TWh in 2024, growing at 12% annually over the preceding five years, and projects demand between 970 and 1,700 TWh by 2035 depending on efficiency and adoption assumptions [IEA, 2025]. The International Monetary Fund, in its April 2025 World Economic Outlook, warns that sluggish supply responses to this demand could “spur much steeper cost increases that hurt consumers and businesses and possibly curb growth of the AI industry itself” [IMF, 2025a].

A parallel literature documents the widening gap in AI readiness between advanced and developing economies. The IMF’s AI Preparedness Index shows scores of 0.68 for advanced economies versus 0.32 for low-income countries [ISPI, 2025]. The World Economic Forum projects that data centres will consume 945 TWh by 2030, potentially accounting for over 20% of global electricity demand growth [WEF, 2025]. Yet these two bodies of research – energy demand forecasting and digital inclusion analysis – remain largely disconnected.

This paper bridges the gap by constructing a coupled dynamical model in which:

1. AI energy demand grows as a product of population adoption (logistic), per-user compute intensity (exponential), and hardware efficiency (Koomey’s law with physical floor);
2. Energy supply for AI compute grows polynomially, reflecting physical infrastructure constraints;
3. A price signal emerges endogenously from the supply-demand utilisation ratio;
4. Demand is differentially suppressed across market segments with heterogeneous price elasticities, reflecting the ratio of AI-generated value to local economic conditions.

The key contribution is formalising the feedback loop: energy scarcity → price increase → adoption suppression → apparent demand reduction → market “equilibrium” – where “equilibrium” is achieved through exclusion rather than efficiency. We prove conditions under which this exclusion is monotonically increasing and identify the policy levers that determine its magnitude.

1.1 Related work

Energy demand modelling. IEA [2025] provides the most comprehensive scenario-based projection of data centre electricity demand, using three cases (Base, Lift-Off, High Efficiency) but treating demand as exogenous. IMF [2025c] develops a multi-country computable general equilibrium (CGE) model that incorporates price effects but does not segment demand by user willingness-to-pay. De Vries [2023] established the per-query energy footprint of generative AI, providing micro-level calibration data. Epoch AI [2025] models compute-centric growth with feedback loops but focuses on AI capability scaling rather than access.

Jevons paradox in compute. The observation that efficiency gains in computing increase rather than decrease total energy consumption is well-documented. Koomey [2011] established the empirical halving time for energy per computation. The IMF explicitly identifies the Jevons paradox as a structural feature of AI energy dynamics [IMF, 2025d].

Digital divide. The concept of tiered digital exclusion – access divide, usage divide, outcome divide – is established in the literature [Carter et al., 2020, Lutz, 2024]. IMF [2025b] models AI adoption constraints for emerging markets but does not link these to energy-price mechanisms. Acemoglu [2025] argues that capital-intensive AI innovations developed in advanced economies may structurally disadvantage labour-abundant poor countries.

Gap. No existing model chains energy supply constraints through endogenous price formation to quantified, segment-level exclusion. This paper fills that gap.

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2. Model

We define continuous-time functions over a horizon $t\in [0,T]$ where $t=0$ corresponds to the base year (2024) and $T$ is the planning horizon.

2.1 Unconstrained demand

Definition 1 (Unconstrained AI energy demand).

$$D_{\text{raw}}(t)=P\cdot A(t)\cdot I(t)\cdot E(t)\cdot \kappa \text{\hspace{1em}(1)}$$

where:

• $P$ is the global population (treated as approximately constant);
• $A(t)=\frac{L}{1+e^{-k(t-t_0)}}$ is the AI adoption fraction (logistic), with ceiling $L\in (0,1)$, steepness $k>0$, and midpoint $t_0$;
• $I(t)=e^{(r-\epsilon )t}$ is the net per-user compute intensity, where $r>0$ is the gross intensity growth rate and $\epsilon >0$ is the software/model efficiency offset;
• $E(t)=\max \left(E_{\text{floor}},2^{-t/h}\right)$ is the Koomey efficiency factor (energy per FLOP), with halving time $h>0$ and physical floor $E_{\text{floor}}>0$;
• $\kappa >0$ is a calibration constant such that $D_{\text{raw}}(0)$ matches observed baseline demand.

2.2 Energy supply

Definition 2 (AI-allocated energy supply).

$$S(t)=S_0+g\cdot t+a\cdot t^2\text{\hspace{1em}(2)}$$

where $S_0>0$ is baseline supply, $g>0$ is the linear growth rate (annual new capacity), and $a\ge 0$ is the acceleration term reflecting policy-driven buildout (nuclear, renewables, grid expansion).

Remark 1. The polynomial form reflects physical infrastructure constraints: building power plants, transmission lines, and data centres requires permitting, materials, and construction time that cannot be arbitrarily compressed. This is supported by IEA observations that “the broader energy system requires longer lead times” than the technology sector [IEA, 2025].

2.3 Endogenous price formation

Definition 3 (Utilisation ratio and price index). The capacity utilisation ratio is:

$$u(t)=\frac{D_{\text{raw}}(t)}{S(t)}\text{\hspace{1em}(3)}$$

The compute price index is:

$$\pi (t)=1+c\cdot \left(\max \right(0,u(t)-u_0){)}^2\text{\hspace{1em}(4)}$$

where $c>0$ is the price convexity parameter and $u_0\in (0,1)$ is the utilisation threshold below which prices remain at baseline.

Remark 2. The quadratic form captures the empirical observation that electricity markets exhibit convex pricing near capacity constraints. The parameter $c$ reflects market structure: higher values represent oligopolistic or capacity-constrained markets; lower values represent competitive or well-supplied ones.

2.4 Market segmentation and demand suppression

We partition the user population into $n$ segments indexed by $j\in \{1,\dots ,n\}$, each characterised by:

• $w_j$: population share (${\sum }_j{w}_j=1$);
• ${\iota }_j$: relative compute intensity (enterprise users consume more per capita than consumers);
• ${\epsilon }_j$: price elasticity of AI demand.

Definition 4 (Segment retention factor). The fraction of segment $j$’s demand retained under price $\pi (t)$ is:

$${\varphi }_j(t)=\max \left({\varphi }_{\min },1-{\epsilon }_j\cdot (\pi (t)-1)\right)\text{\hspace{1em}(5)}$$

where ${\varphi }_{\min }>0$ is a floor representing irreducible demand (users who will find access regardless of price).

Definition 5 (Price-adjusted demand).

$$D_{\text{adj}}(t)=D_{\text{raw}}(t)\cdot \frac{\sum _{j=1}^n{w}_j\cdot {\iota }_j\cdot {\varphi }_j(t)}{\sum _{j=1}^n{w}_j\cdot {\iota }_j}\text{\hspace{1em}(6)}$$

Definition 6 (Exclusion population).

$$\text{Excl}(t)=P\cdot A(t)\cdot \sum _{j=1}^n{w}_j\cdot (1-{\varphi }_j(t))\text{\hspace{1em}(7)}$$

This counts the number of people who would adopt AI at baseline prices but are priced out.

2.5 Three-segment parameterisation

For concreteness, we define three segments reflecting the economic structure of AI adoption:

Table 1: Segment parameterisation

Segment	Description	$w_j$	${\iota }_j$	${\epsilon }_j$
Enterprise	High-value users (finance, pharma, tech)	0.08	5.0	Low
Professional	SMBs, knowledge workers	0.27	1.0	Medium
Consumer	General public, low-GDP economies	0.65	0.3	High

The economic intuition for the elasticity ordering is as follows. Enterprise users evaluate AI against the value it creates relative to the cost of the human task it replaces: a trading algorithm generating large alpha can absorb a 10x price increase. Consumer users in low-GDP economies face a binding constraint: when monthly AI subscription costs exceed a meaningful fraction of disposable income, adoption drops to near zero.

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3. Analytical Results

Proposition 1 (Existence of unconstrained crossover). If $r-\epsilon >0$ (net intensity growth is positive) and $E_{\text{floor}}>0$, then for sufficiently large $L$ and $k$, there exists a finite $t^{\ast }>0$ such that $D_{\text{raw}}(t^{\ast })=S(t^{\ast })$ and $D_{\text{raw}}(t)>S(t)$ for all $t>t^{\ast }$.

Proof. For large $t$, $A(t)\to L$ (constant), $I(t)=e^{(r-\epsilon )t}$ (exponential), and $E(t)\to E_{\text{floor}}$ (constant). Thus $D_{\text{raw}}(t)\sim P\cdot L\cdot E_{\text{floor}}\cdot \kappa \cdot e^{(r-\epsilon )t}$, which grows exponentially. Meanwhile $S(t)=S_0+gt+a{t}^2$ grows polynomially. Since exponential growth dominates polynomial growth, $D_{\text{raw}}(t)/S(t)\to \infty$, guaranteeing a crossover. $\square$

Proposition 2 (Price feedback delays but does not prevent crossover). If the conditions of Proposition 1 hold, then there exists $t^{\ast \ast }\ge t^{\ast }$ such that $D_{\text{adj}}(t^{\ast \ast })=S(t^{\ast \ast })$, with $t^{\ast \ast }>t^{\ast }$ strictly when $c>0$ and ${\max }_j{\epsilon }_j>0$.

Proof. The price-adjusted demand satisfies $D_{\text{adj}}(t)\le D_{\text{raw}}(t)$ for all $t$, with equality when $\pi (t)=1$. As $t\to \infty$, the utilisation ratio $u(t)\to \infty$, driving $\pi (t)\to \infty$. However, the retention factors are bounded below by ${\varphi }_{\min }>0$, so:

$$D_{\text{adj}}(t)\ge D_{\text{raw}}(t)\cdot \frac{{\sum }_j{w}_j{\iota }_j{\varphi }_{\min }}{{\sum }_j{w}_j{\iota }_j}=D_{\text{raw}}(t)\cdot {\varphi }_{\min }\text{\hspace{1em}(8)}$$

Since $D_{\text{raw}}(t)\cdot {\varphi }_{\min }$ still grows exponentially while $S(t)$ grows polynomially, $D_{\text{adj}}$ eventually exceeds $S$. The delay $t^{\ast \ast }-t^{\ast }$ is strictly positive because $D_{\text{adj}}(t^{\ast })<D_{\text{raw}}(t^{\ast })=S(t^{\ast })$ when the price mechanism is active at $t^{\ast }$. $\square$

Proposition 3 (Monotonic exclusion growth). If $D_{\text{raw}}(t)$ is monotonically increasing for $t>t_1$ and $S(t)$ grows sub-exponentially, then $\text{Excl}(t)$ is eventually monotonically increasing.

Proof. For $t$ sufficiently large, $u(t)=D_{\text{raw}}(t)/S(t)$ is increasing (exponential over polynomial), so $\pi (t)$ is increasing, which means ${\varphi }_j(t)$ is decreasing for all $j$. Since $A(t)$ is increasing (logistic, pre-ceiling), both factors of $\text{Excl}(t)=P\cdot A(t)\cdot {\sum }_j{w}_j(1-{\varphi }_j(t))$ are increasing, hence $\text{Excl}(t)$ is increasing. $\square$

Corollary 1 (Inequality transformation). Under the conditions of Propositions 2 and 3, the system exhibits a regime where $D_{\text{adj}}(t)\approx S(t)$ (apparent market clearing) while $\text{Excl}(t)$ grows without bound. That is, the market appears to solve the energy constraint while the exclusion population grows. The energy crisis is not resolved – it is transformed into an access inequality crisis.

3.1 Sensitivity and critical parameters

The delay $\Delta t=t^{\ast \ast }-t^{\ast }$ and the exclusion trajectory $\text{Excl}(t)$ are functions of the following critical parameters:

• Supply acceleration $a$: increasing $a$ extends $\Delta t$ and reduces exclusion. This parameter captures nuclear buildout, renewables scaling, and grid policy.
• Net intensity growth $(r-\epsilon )$: the Jevons paradox is encoded here. If efficiency gains ($\epsilon$) keep pace with intensity growth ($r$), the crossover can be pushed arbitrarily far. Empirically, $r>\epsilon$ has held for every prior computing wave.
• Consumer elasticity ${\epsilon }_{\text{con}}$: the higher this value, the faster consumers are excluded. It is structurally higher in low-GDP economies where AI value-to-wage ratios are lower.
• Price convexity $c$: reflects market structure. Oligopolistic compute markets (few hyperscalers) produce higher $c$, accelerating exclusion.

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4. Discussion

4.1 Relationship to existing projections

Our model nests the IEA scenarios as special cases. The IEA Base Case corresponds to moderate $(r-\epsilon )$ with no price feedback ($c=0$). The Lift-Off Case corresponds to high adoption steepness $k$ and high $r$. The High Efficiency Case corresponds to large $\epsilon$. Our contribution is showing what happens between these scenarios when the market responds endogenously.

The IMF’s finding that electricity prices could rise by 10% by 2030 under constrained supply [IMF, 2025c] is consistent with our model at moderate utilisation ($u\approx 0.7$) and low convexity ($c\approx 3$). Our framework extends this by disaggregating the impact of that price increase across user segments.

4.2 The ROI constraint as a natural exclusion mechanism

The maximum sustainable price per user in segment $j$ is bounded by:

$${\pi }_{\max ,j}\propto \frac{{\text{AI productivity gain}}_j\times {\text{local wage}}_j}{{\text{switching cost}}_j}\text{\hspace{1em}(9)}$$

For enterprise users in high-GDP economies, this bound is high (AI replaces expensive knowledge work). For consumers in low-GDP economies, the bound is structurally low: wages are lower, so the absolute value of AI-augmented productivity is lower, even if the relative gain is comparable. This creates an inherent asymmetry that no amount of model efficiency improvement can fully resolve – it is a function of economic structure, not technology.

4.3 Policy implications

The model identifies four intervention points:

1. Supply acceleration ($a$): the most direct lever. Nuclear renaissance, modular reactors, and dedicated AI energy infrastructure push the crossover further out.
2. Price regulation: capping $c$ through competition policy or subsidised compute tiers for developing economies.
3. Efficiency investment: increasing $\epsilon$ to approach $r$. This is the current industry focus (smaller models, quantisation, distillation) but faces diminishing returns.
4. Edge compute and local inference: structurally lowering ${\iota }_{\text{con}}$ by moving inference to local devices, reducing dependence on centralised, energy-intensive data centres. This changes the demand function itself rather than suppressing it through price.

4.4 Limitations and Path B

This paper presents a theoretical framework (Path A). Key limitations include:

• Parameter values are illustrative, not empirically calibrated. A follow-up paper (Path B) will anchor each parameter to published data sources: IEA for supply/demand baselines, IMF for price elasticities, World Bank for GDP-segmented willingness-to-pay, and Epoch AI for compute scaling trends.
• The model assumes a global market; in practice, energy and compute markets are regional, with significant variation in grid capacity, pricing, and policy.
• We do not model the second-order effect where exclusion from AI widens the economic gap, further reducing willingness-to-pay – a reinforcing feedback loop that would accelerate exclusion.
• The price formation mechanism is stylised. Real compute pricing involves contracts, spot markets, reserved capacity, and vertical integration that introduce nonlinearities beyond our quadratic approximation.

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5. Conclusion

We have shown that under broad conditions – positive net intensity growth, sub-exponential supply expansion, and heterogeneous price elasticity – the market response to AI energy scarcity does not eliminate the underlying constraint but transforms it. Energy scarcity becomes access scarcity. The system converges to a regime where supply and price-adjusted demand appear balanced, but this balance is achieved by pricing out the most economically vulnerable users.

This is not a failure of the market mechanism; it is the market mechanism working as designed: allocating scarce resources to the highest-value uses. The question is whether societies accept the consequence – a world where AI access, and the economic advantages it confers, is stratified by ability to pay for energy-intensive computation.

The model identifies concrete policy parameters that determine the severity of this outcome. Supply acceleration, price regulation, and the development of energy-efficient edge inference are not merely technical objectives – they are the variables that determine whether AI becomes a tool for broad-based productivity growth or a mechanism for deepening global inequality.

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