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Econ-436 · economics · Economics

Open versus proprietary AI

LLM status Open unverified

Statement

Original subject group: Innovation and AI economics

Audit classification: Background; proposed extension. The 2026 survey metadata and abstract are verified. Full text was unavailable and no exact open-model innovation passage was checked; this causal comparison remains editorial.

Definitions and precise research target

Consider downstream AI startups in prespecified product markets over three years. At baseline, compare two access regimes for models of matched measured capability: $O$, which permits downloading, modification and redistribution under a stated license, and $P$, which provides a priced proprietary service. Compute access and initial support are recorded separately. For market $m$, let $N_m(r)$ be independently validated new-product value under regime $r\in\{O,P\}$, and $C_m(r)$ all real development, adaptation and deployment costs. Define the downstream innovation effect $\tau_N=E[N_m(O)-N_m(P)]$ and net-value effect $\tau_W=E[N_m(O)-C_m(O)-N_m(P)+C_m(P)]$. Expectations concern eligible markets, not all AI development. Clustered rollout, credible licensing changes or another specified design must address endogenous selection into regimes and model-quality differences. Measure knowledge spillovers, entrant survival and incumbent responses, and separately include the upstream developer's future training investment when evaluating a sustained regime. Determine which combinations of appropriability, modification needs and complementary resources make $\tau_W>0$, and whether short-run downstream gains persist once upstream incentives adjust. Existing theories of open and proprietary models support the comparison; this particular empirical target and general-equilibrium extension are proposed specifications.

Definitions, assumptions and mathematical qualifications. The open regime specifies weights access, modification, redistribution and license restrictions; an API is a different treatment even at equal baseline benchmark capability. Initial capability and compute allowance are preregistered baseline attributes. Capability subsequently produced by the regime is an outcome, so conditioning on it may remove part of the causal effect. $N_m(r)$ is monetized validated product value including unsuccessful ventures, and $C_m(r)$ counts resource costs rather than transfers. Define downstream $\tau_W$ separately from system welfare, which additionally includes upstream training costs and benefits. A sustained regime requires an upstream innovation and model-release law and common equilibrium selection.

Variants and assumption changes

  1. Editorial, fixed upstream technology. Compare downloadable models and priced services matched at baseline capability, randomizing compute support separately; estimate the downstream three-year effect.
  2. Editorial, sustained system. Endogenize future upstream training, release decisions and spillovers under the two license regimes. Compare system welfare rather than append upstream spending mechanically to an unchanged downstream forecast.

References and source audit

Checked source. Annual Review of Economics 18 (2026), pp. 417--445, abstract; advance publication 6 May 2026. The abstract surveys AI competition and interacting bottlenecks. Publisher metadata and abstract retrieved; dynamic full text unavailable. https://www.annualreviews.org/content/journals/10.1146/annurev-economics-051624-061832.
  1. Joshua S. Gans. 2026. Market Power in Artificial Intelligence. Annual Review of Economics 18 (2026), pp. 417--445, abstract; advance publication 6 May 2026. https://www.annualreviews.org/content/journals/10.1146/annurev-economics-051624-061832. DOI: https://doi.org/10.1146/annurev-economics-051624-061832.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-436-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-436

AI access regimes: entry distortion, resource costs, and upstream incentives

Problem ID: L17-432. Status: Unresolved. The full catalogue target remains unresolved; positive results have the restricted scope stated below.

Fixed capability is a restricted comparison

The catalogue asks whether access to modifiable downloadable models rather than proprietary services changes validated downstream innovation and net value, at matched baseline capability, and whether gains persist once upstream investment responds. A license label does not fix compute support, adaptation cost, model quality or diffusion. This attempt solves an entry model separating fees from real resource costs and a second model in which upstream incentives reverse a fixed-capability ranking. These are comparative-static examples, not an empirical conclusion about existing AI systems.

There is a unit mass of potential projects with type $\theta$ uniformly distributed on $[0,1]$. A completed project yields validated monetary product value $\theta$. Under regime $r\in\{O,P\}$ it consumes real development and deployment resources $c_r\ge0$ and requires a license or service payment $t_r\ge0$. Project founders receive the product value, pay both costs, and enter if $\theta\ge c_r+t_r$. Failed or non-entered projects have zero realized value in this benchmark. No other spillovers occur. Define $a_r=\min\{1,c_r+t_r\}$, so the entrant mass is $1-a_r$.

For comparability with the canonical downstream net-value target, license payments are transfers rather than real development resources. Actual provider compute use must be included in $c_r$ if it is within the accounting boundary; calling an API payment a transfer does not imply that serving a request is costless. The model treats those resource inputs separately and explicitly.

Proposition (Entry value and the cost of a pure access fee): For $0\le c_r+t_r\le1$, \[ N_r=\frac{1-a_r^2}{2},\qquad C_r=c_r(1-a_r),\qquad W_r=N_r-C_r. \tag{1} \] If $c_O=c_P=c$, $t_O=0$ and $t_P=t\in[0,1-c]$, then \[ W_O-W_P=\frac{t^2}{2},\qquad N_O-N_P=ct+\frac{t^2}{2}. \tag{2} \]
Proof: An entrant optimally chooses the project exactly when its private payoff $\theta-c_r-t_r$ is nonnegative. Integration over the uniform types gives $N_r=\int_{a_r}^1\theta\,d\theta$ and $C_r=\int_{a_r}^1 c_r\,d\theta$, proving (1). The projects excluded by the fee have types $\theta\in[c,c+t]$. Their total social net value is $\int_c^{c+t}(\theta-c)\,d\theta=t^2/2$, while their total product value is $\int_c^{c+t}\theta\,d\theta=ct+t^2/2$. Fees on the remaining entrants are internal transfers and do not enter this resource calculation. ∎

For $c=0.2,t=0.3$, open access gives $W_O=0.32$, while proprietary access gives $W_P=0.275$, a difference of $0.045=t^2/2$. Subtracting license revenues from system welfare again would incorrectly add a transfer loss. Conversely, if the target is founders' private profits rather than downstream resource net value, those payments belong in the private outcome. The accounting boundary determines which target is being estimated.

Modification and deployment costs can overturn (2). Take $c_O=0.4,t_O=0$ and $c_P=0.1,t_P=0.1$. Then $W_O=0.18$ while $W_P=0.40$. The proprietary service's resource advantage dominates its entry distortion. This example formalizes why an access comparison must hold initial capability and complementary support fixed or report their interactions. The sign cannot be inferred from the permission to modify alone.

Endogenous capability can reverse the short-run ranking

Now consider a separate two-stage technology benchmark. The developer chooses capability $q\ge0$ at real training cost $q^2/(2\kappa)$, $\kappa>0$. Given capability, regime $r$ generates total downstream net benefit $a_rq$ before transfers to the developer. The developer can capture $b_rq$ through a specified payment or appropriability mechanism, with $0\le b_r\le a_r$. Assume these transfers do not change the downstream allocation in this restricted benchmark, and that the developer chooses $q$ to maximize $b_rq-q^2/(2\kappa)$. Fix this same equilibrium rule in both regimes.
Proposition (A capability-matched advantage need not survive investment): The unique equilibrium investment is $q_r=\kappa b_r$, and system welfare is \[ W_r^{\rm sys}=\kappa\left(a_rb_r-\frac{b_r^2}{2}\right). \tag{3} \] It is possible that $a_O>a_P$, so open access is better at every fixed positive capability, while $W_O^{\rm sys}<W_P^{\rm sys}$.
Proof: The strictly concave developer objective has derivative $b_r-q/\kappa$, giving the unique optimum, including zero when $b_r=0$. Total downstream benefit minus training resource cost gives (3); the developer's receipts are not subtracted again because they are transfers. Set $a_O=2,b_O=0.1,a_P=b_P=1$. At fixed $q>0$ open access doubles downstream benefit. Equilibrium system welfare is $0.195\kappa$ under $O$ and $0.5\kappa$ under $P$, proving reversal. ∎

This construction is intentionally different from the entry model: its capture mechanism is nondistortionary by assumption, while the fee in (2) distorts entry. They are not combined into a purported calibrated general equilibrium. Their separate purpose is to exhibit two logically distinct margins that a sustained-regime model must jointly specify. Nothing here establishes that appropriation is necessarily lower under open release; complementary services or other revenue can alter $b_O$.

An experimental contrast with complementary compute

For the fixed-upstream target, randomize eligible market clusters across a $2\times2$ design: access regime $R\in\{O,P\}$ and compute support $G\in\{0,1\}$. Define bounded outcomes $V_m(r,g)=N_m(r,g)-C_m(r,g)$ for every baseline market, including unsuccessful ventures. Assume consistency and no between-cluster spillovers; permit arbitrary within-cluster spillovers. Let $\mu_{rg}={\mathbb{E}}[V_m(r,g)]$.

Randomization identifies all four cell means by the corresponding observed conditional means. The access effect at compute level $g$ is $\mu_{Og}-\mu_{Pg}$. The complementary-resource interaction is \[ I=(\mu_{O1}-\mu_{P1})-(\mu_{O0}-\mu_{P0}). \tag{4} \] A positive $I$ means compute support increases the access advantage on this outcome scale; it is not evidence that compute is the sole mechanism. For independent clusters and known assignment probabilities, inverse-probability cell averages are unbiased. Boundedness gives finite-sample concentration, while shared developer responses across clusters would invalidate the no-between-cluster-interference assumption.

Conditioning on three-year capability or survival after randomization changes the target, because both can be affected by access. A baseline cohort outcome with zero validated value for unsuccessful projects avoids survivor selection, provided real failed-development costs remain in $C$. System welfare additionally requires upstream resource use and innovation responses; one cannot estimate a fixed-capability downstream effect and append an unrelated training-cost difference while keeping downstream capability unchanged.

The solved models establish sign conditions and an explicit reversal. The remaining agenda is to measure validated product value, real costs, spillovers and appropriability, and to identify the sustained innovation law. No empirical sign or welfare magnitude for open versus proprietary AI is claimed.

Completion Estimate

45%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt solves access-fee entry distortions and an endogenous-capability model that reverses fixed-capability rankings, with a factorial compute-support identification design. Measured three-year innovation, real deployment costs, spillovers, appropriation, and sustained upstream release and investment responses remain unidentified.

References

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