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Econ-494 · economics · Economics

Agricultural technology adoption constraints

LLM status Open unverified

Statement

Original subject group: Development and poverty

Audit classification: Published research agenda. Metadata and abstract checked. It expressly flags future directions involving credit, insurance and information; detailed full-text agenda was not inspected and the five-part menu is editorial.

Definitions and precise research target

Complete editorial problem. Fix smallholder farmers, a crop technology, and several agricultural seasons. Let $p=(c,r,i,q,m)$ denote a feasible intervention supplying credit, risk coverage, information, verified input quality, and market access. Let $A_{it}(p)$ indicate technology adoption and $\Pi_{it}(p)$ net profits after input, labor, finance, and insurance costs. Define $\tau_\Pi(T,p)=E[\sum_{t=0}^{T}\delta^t\{\Pi_{it}(p)-\Pi_{it}(0)\}]$, where $\delta\in(0,1]$ is a declared discount factor. Estimate adoption, downside risk, and sustained profitability, allowing interactions between constraints. Adoption itself is not evidence of welfare improvement when returns are heterogeneous. A factorial or sequential randomized design should distinguish learning from financial constraints and insurance demand from uninsurable uncertainty. Specify weather support, input reliability, and crop-price responses before extrapolating across seasons or regions. Determine which cost-effective bundles generate continued use after subsidies and advice stop. Account for peer learning and product-market spillovers through an explicit assignment design. The review identifies constraint interactions and future research, while many individual intervention effects are established. The precise policy menu, objective, and multiseason estimand here are an adapted research specification rather than a source theorem.

Definitions and admissible scope. Define the technology by input, training, and usage requirements, and adoption by verified use on a stated share of land. Net profits deduct all input costs, labor opportunity cost, borrowing, insurance premia, and depreciation; gross revenue is not profit. Risk coverage specifies triggers, basis risk, indemnity, and insurer solvency. Information specifies signal accuracy and delivery. The regime includes subsidy withdrawal dates and market access. Weather and prices have a declared joint stochastic law; all outcomes are integrable. Factorial interactions are contrasts such as $E[\Pi(1,1)-\Pi(1,0)-\Pi(0,1)+\Pi(0,0)]$, which establish complementarities of interventions under the design but do not automatically name the underlying behavioral mechanism. Take dates $0,\ldots,T$, $T<\infty$, a fixed crop-season calendar, baseline farmer weights, and a declared intervention menu. Baseline $p=0$ denotes no added bundle, retaining existing access. A downside-risk target is, for example, $\Pr(\sum_t\delta^t\Pi_{it}(p)<0)$, or a stated consumption-shortfall probability; it is separate from $\tau_\Pi$. Sustained adoption means verified use at every prespecified season after support withdrawal. A welfare criterion additionally specifies risk preferences and consumption opportunities. The two-coordinate factorial shorthand $\Pi(1,1)$ holds all other bundle coordinates and coverage fixed. Returns and interaction effects are defined only on the joint design support.

Variants and assumption changes

  1. Credit, insurance, and information (source-motivated): cross the three dimensions in a factorial design and distinguish incomplete learning from insurable production risk and basis risk.
  2. Input quality and scale (editorial): add verified-input certification and regional coverage variation. Compare multiseason utility and adoption after support stops, allowing crop prices, peer information, and supplier behavior to change.

References and source audit

Support and access. Metadata and abstract checked. It expressly flags future directions involving credit, insurance and information; detailed full-text agenda was not inspected and the five-part menu is editorial. Locator: Publisher abstract, final sentence.
  1. Jeremy R. Magruder. 2018. An Assessment of Experimental Evidence on Agricultural Technology Adoption in Developing Countries. Abstract, paragraphs 1–2. https://www.annualreviews.org/content/journals/10.1146/annurev-resource-100517-023202. DOI: https://doi.org/10.1146/annurev-resource-100517-023202.

Integrated refinement: ECON-093

Multiple constraints and heterogeneous agricultural technology adoption

This refinement adopts the additional source conventions (audited:conventions), subject to its local restrictions. Heterogeneous welfare gains and bundle interactions. For a finite supported menu relaxing credit, risk, knowledge and market access, identify $\tau_\pi(z,x)=\mathbb E[\pi_i(z)-\pi_i(0)\mid X_i=x]$ with baseline covariates and an explicit measurement-error model. Fix component versions, intensity, timing, crop seasons and coverage. Factorial assignment can identify arm and interaction means under its interference assumptions; naming a constraint's causal contribution additionally requires credible component interventions. Compare net profits after finance, labor and insurance costs, household utility including risk, and social environmental effects separately. Raising adoption alone need not improve welfare. Report interaction scales and uncertainty, and allow prices, technology supply and peer learning to change under widespread adoption.

Supplied source audit for ECON-093

Local [S1], [S2], etc. in this audit and the references immediately below belong to ECON-093, independently of the original entry's reference numbering. [S1] and [S2] directly support multiple constraints and farmer heterogeneity. This conditional bundle-effect formulation is editorial, not a general theorem that relaxing all constraints raises welfare.

References for integrated refinement ECON-093

[S1] Tavneet Suri, Chris Udry, Jenny Aker, Chris Barrett, Laura Falcao Bergquist, Michael Carter, Lorenzo Casaburi, Robert Darko Osei, Douglas Gollin, Vivian Hoffmann, Thomas Jayne, Naureen Karachiwalla, Harounan Kazianga, Jeremy Magruder, Hope Michelson, Meredith Startz, and Emilia Tjernstrom (2024). Agricultural Technology in Africa. VoxDevLit 5(2), March 2024.

Verified locator / source role: Primary publisher page checked for review identity, authors, version and background. The specific published agenda is corroborated in [S2]; the exact formal target is editorial.

https://voxdev.org/voxdevlit/agricultural-technology-africa

[S2] Oliver Hanney / VoxDev (living compilation). Evidence gaps: Key unanswered questions in development economics. Accessed 8 October 2026. The page currently covers 20 topics; the "16-topics URL is a historical slug.

Verified locator / source role: Topic heading: Agricultural Technology in Africa. Supports the broad research agenda; this is not a verbatim quotation or an attribution of the displayed mathematical target.

https://voxdev.org/topic/evidence-gaps-key-unanswered-questions-across-16-topics-development-economics

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.

Common conventions: Additional-source status and mathematical conventions

Of the 100 supplied ECON entries, 65 distinct problems appear here; 32 close matches refine earlier entries, and three duplicate questions map to existing entries. Appendix app:audited-crosswalk lists every destination. The attachment's P/R/S/U distinctions and source audits are retained. Its precise mathematical formalizations are editorial unless the individual audit says otherwise. Candidate subsidy targets ECON-004--006 retain their U flags; the resolved approval-core question ECON-007 updates OP-0202 above. The following supplied conventions govern both this part and the attributed ECON refinements elsewhere in the catalogue, subject to local restrictions.

Parameterized questions. A problem family lists inputs that must be fixed before an instance is evaluated: population, horizon, policies, information, data law, model class and welfare weights. These are required choices, not quantities the citations are assumed to specify. Undefined applications should not be treated as identified estimands.

Indices and integrability. Sets of agents, firms and regions are finite unless a population measure is explicitly used. $i,j$ index units, $r$ regions, $t$ dates and $h$ horizons. $\mathbb E$ and $\Pr$ refer to the declared population and law; $\mathbf1\{A\}$ is an indicator. Every displayed expectation and discounted sum needs existence in the stated domain. Infinite horizons use a discount in $(0,1)$ and a convergence condition; finite horizons may use discount one.

Optimization and existence. A displayed $\max$, $\min$, or $\arg\max$ is conditional on attainment. For finite feasible menus this is immediate; general spaces need continuity and compactness/coercivity or another existence argument. Without attainment, the target is the supremum/infimum and arbitrarily near-optimal feasible choices. $\inf\varnothing=+\infty$. Empty feasibility and an unidentified target are different issues.

Potential outcomes. $Y_i(z)$ is the outcome under a specified intervention, not the observed conditional mean among people choosing $z$. In binary comparisons $\Delta Y_i=Y_i(1)-Y_i(0)$. Specify assignment, treatment versions, compliance, information and observation horizon. Interference is allowed under a full policy vector; compressed exposure notation needs a justified mapping. No interference, consistency and overlap are substantive assumptions, not automatic consequences of notation.

Populations and observation. Fix baseline eligibility and population weights. Conditioning on post-policy employment, survival, relocation or program uptake can change the population being compared. Death is not ordinary loss to follow-up; outcomes truncated by death need a composite convention, joint survival target, or explicitly defined survivor stratum. Fertility-changing interventions need a population functional rather than an unexplained fixed descendant cohort. Measurement and missingness models must be supplied.

Identification. A structural model $m\in\mathcal M$ implies observable law $P_m$ and target $\theta(m)$. Identification means \[ P_{m_1}=P_{m_2}\ \Longrightarrow\ \theta(m_1)=\theta(m_2) \quad\text{for all }m_1,m_2\in\mathcal M . \] Without identification, the target is \[ \Theta(P;\mathcal M)=\{\theta(m):m\in\mathcal M,\ P_m=P\}. \] Writing $\theta(P)$ before establishing identification can hide incompatible latent models. Confidence sets additionally need a sampling law, confidence level, asymptotic sequence and uniformity class. Point identification, coverage and informative precision are separate properties.

Mediation. Total effects of randomized assignment are distinct from cross-world natural indirect effects. Belief/effort-channel effects require a meaningful mediator intervention and additional measurement, exclusion or mediation assumptions. Randomization of the initial policy alone does not supply those assumptions. Report bounds or interventional alternatives when the stronger target is unsupported.

Equilibrium. A counterfactual $W(z)$, $p(z)$, or $\mu_t^z$ requires individual optimization, feasibility, government/resource budgets, market clearing and state-transition laws. State equilibrium existence and selection, or report ranges over compatible equilibria. Initial-state integration includes subsequent endogenous transitions; current-state integration must use the policy-dependent distribution. Reduced-form invariance after policy is not assumed.

Welfare accounts. Scores, utility, health, dollars and ecological quantities require explicit conversion before addition. Fees, taxes, subsidies, wages and extortion payments are transfers between parties; distributional weights can make them welfare relevant, but their face value is not automatically a resource loss. State ownership, geographic boundaries, foreign-income weights and fiscal finance. Do not add profits to household welfare already including dividends, or count land capitalization and the underlying benefit twice. A benefit-cost expression must distinguish gross benefits from net welfare and subtract every real cost exactly once.

Derivatives and risk. Log derivatives require positive arguments; local responses require admissible perturbations and specified equilibrium branches. Differentiation under expectations needs regularity/domination, and boundaries may allow only one-sided derivatives. Risk uses a specified law; ambiguity uses a declared nonempty law set on a common history space. Adaptive policies must be nonanticipative. A robust criterion is an editorial choice unless attributed explicitly.

Scope overlaps. Allocation, collective choice, contracts, household bargaining and coordinated policy overlap economics with optimization and game theory. They are retained because they appeared in the original catalogue; no claim of a strictly game-theory-free selection is made.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-494-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-494

Post-subsidy adoption: liquidity survival, insurance, and information

Problem ID: Q16-490. Status: Unresolved; restricted results with complete proofs.

Question and contribution

The target asks which credit, insurance, information, input-quality, and market-access bundles produce profitable adoption that persists after support ends. We analyze a specific obstacle: a technology can have strictly positive mean net profit yet lose adopters after subsidy withdrawal because bad seasons exhaust working capital. We derive the exact persistence probability in a reserve model, show how an explicitly financed insurance contract changes it, and separate the value of information from its effect on adoption rates.

Magruder's review abstract identifies credit, insurance, and information as interacting constraints [magruder]; the VoxDev review emphasizes heterogeneity in returns [agriculture]. Those source passages were inspected. The stochastic-reserve model below is a restricted analytical attempt, not an empirical description or a general claim that more adoption raises welfare.

A working-capital model after withdrawal

A farmer must have wealth at least $k>0$ at the start of a season to pay all required working-capital costs. No loans, subsidies, or advice are available after date zero. A season's incremental net profit relative to a safe outside option is $+d$ with probability $p$ and $-d$ with probability $1-p$, independently over seasons, where $0<d\leq k$. Net profit already deducts inputs, labor opportunity cost, and depreciation; it is not gross sales. Common prices are fixed by an external market, input reliability is known, and there are no peer effects in this benchmark.

The farmer keeps these incremental profits in a reserve account; baseline consumption and any safe income are accounted for outside that account. Initial wealth at subsidy withdrawal is $W_0=k+md$ with integer $m\geq0$. As long as wealth is at least $k$, the farmer follows the adoption rule and updates \[ W_{t+1}=W_t+\Pi_t,\qquad \Pi_t\in\{-d,d\}. \] If wealth falls below $k$, adoption stops permanently and the safe option is used thereafter. This is a specified continuation behavior, consistent with positive expected incremental returns for a risk-neutral farmer with no additional constraint and no superior option; a general risk-averse dynamic optimum is not assumed. Because $d\leq k$, the first failure leaves nonnegative wealth.

Put $R_t=(W_t-k)/d$ while adopting and let $\tau$ be the first time $R_t=-1$. Persistent adoption means $\tau=\infty$. For a finite policy horizon $T$, sustained use through seasons $0,\ldots,T$ means $\tau>T$.

Theorem (Exact post-withdrawal persistence): For $0<p<1$, the probability of eventual cessation is \[ \Pr_m(\tau<\infty)= \begin{cases} 1,&p\leq1/2,\\[2mm] \left(\dfrac{1-p}{p}\right)^{m+1},&p>1/2. \end{cases} \] Thus strictly positive mean net profit $d(2p-1)>0$ does not guarantee permanent adoption from any finite reserve. To make eventual cessation probability at most $\varepsilon\in(0,1)$ when $p>1/2$, it is necessary and sufficient that \[ m+1\geq\frac{\log\varepsilon}{\log((1-p)/p)}. \]
Proof: Fix an upper reserve boundary $N>m$ and let $u_j$ be the probability of hitting $-1$ before $N$ from $j$. Absorption in this finite interval is almost sure: from any nonabsorbed state, a run of $N+1$ upward or downward steps reaches a boundary, and this event has probability at least $\min(p,1-p)^{N+1}>0$ in each block. Hence the probability of no absorption over $r$ blocks is at most $(1-c)^r\to0$.

First-step conditioning gives $u_j=pu_{j+1}+(1-p)u_{j-1}$ with $u_{-1}=1,u_N=0$. When $p\ne1/2$, write $r=(1-p)/p$. The solution is \[ u_j=\frac{r^{j+1}-r^{N+1}}{1-r^{N+1}}. \] It satisfies the recurrence and boundaries; uniqueness follows because a difference of two solutions with zero boundary values cannot attain a nonzero positive maximum or negative minimum in the interior of this weighted-average recurrence. When $p=1/2$, the same argument gives $u_j=(N-j)/(N+1)$.

The events of hitting $-1$ before $N$ increase to the event of ever hitting $-1$ as $N\to\infty$: every finite ruin path has a finite maximum, and hence lies in one such event. If $p>1/2$, then $r<1$ and $u_m\to r^{m+1}$. If $p<1/2$, divide numerator and denominator by $r^{N+1}$ to get limit one. The fair case also converges to one. This proves the formula. Taking logarithms of $r^{m+1}\leq\varepsilon$ and dividing by the negative number $\log r$ gives the reserve condition. ∎

At $p=1$ adoption persists with probability one; at $p=0$ it ceases after $m+1$ losses. These boundary cases follow directly. The infinite-horizon result diagnoses persistence risk, but does not replace the finite $T$ in the catalogue's profit estimand.

Proposition (Finite-horizon profit and a recursion): Let $v_t(j)=\Pr_j(\tau>t)$, with $v_0(j)=1$ for $j\geq0$ and $v_t(-1)=0$. Then for $j\geq0$, \[ v_{t+1}(j)=pv_t(j+1)+(1-p)v_t(j-1). \] If nonadoption has incremental profit zero, then for any $T<\infty$ and $\delta\in(0,1]$, \[ {\mathbb{E}}_m\sum_{t=0}^T\delta^t\Pi_t{\mathbf 1}\{\tau>t\} =d(2p-1)\sum_{t=0}^T\delta^t v_t(m). \]
Proof: For the first identity condition on the first reserve step and then use the independent identical future increment law. Starting at $-1$ means adoption has already ceased. For the second, the event $\{\tau>t\}$ is determined by increments before season $t$ and is independent of $\Pi_t$, whose mean is $d(2p-1)$. Factor each expectation and sum finitely many terms. The indexing includes season zero because $\tau>0$ initially. ∎

The formula separates greater conditional returns from longer exposure to the technology. It is an incremental-profit target; consumption risk and household utility still require preferences, other income, and insurance outside this reserve account.

Insurance can secure liquidity, but must itself be funded

Suppose $p>1/2$ and a continuing commercial insurance product is available after temporary public support ends. It pays indemnity $2d$ exactly in the bad state and nothing in the good state, with premium \[ P=2d(1-p)+\ell, \] where $\ell\geq0$ includes administration, capital, and reinsurance charges. There is no basis risk in this specified contract. Each season a solvent outside insurer escrows $2d$ per insured farmer before weather is realized. Premium plus outside shareholder capital funds that escrow; the capital's opportunity cost is included in $\ell$. This is an explicit access assumption, not a conclusion that premiums alone cover every realized claim or correlated weather event.

The premium is paid at the beginning of each season. Insured use therefore requires $W_t\geq k+P$. Input returns and indemnities arrive after payment. The resulting net reserve increment in either state is \[ g=d-2d(1-p)-\ell=d(2p-1)-\ell. \]

Theorem (A fully funded persistence condition): If $g\geq0$ and $W_0\geq k+P$, then insured adoption remains affordable in every season on every weather path under the stated contract. If $W_0<k+P$, the same insurance cannot initiate adoption without an additional liquidity source even when its long-run net gain is positive. The required initial liquidity top-up is exactly $[k+P-W_0]_+$ in this model.
Proof: The bad state gives increment $-d+2d-P=d-P=g$ and the good state gives $d-P=g$ as well. Hence $W_t=W_0+tg\geq W_0\geq k+P$, proving affordability by induction. Conversely, initial input and premium payments require exactly $k+P$ before any harvest return or indemnity, so wealth below it cannot finance the first season. A top-up equal to the displayed shortfall meets the requirement exactly; any smaller amount fails. Insurer escrow guarantees that the promised indemnity is available in every state. ∎

The theorem explains a complementarity between risk coverage and temporary liquidity, but the top-up is a transfer that has to be charged to the program budget. Replacing it by a loan requires specifying repayment and interest, which can destroy the nonnegative increment $g$. Continued insurance is a market service paid by the farmer, not an unrecorded continuing public subsidy. Basis risk, price shocks, or an unfinanced insurer return the possibility of negative increments. A farmer with sufficiently large reserves may rationally prefer the higher expected profit of uninsured use when $\ell>0$; persistence alone is not the welfare objective.

Information may improve profits while lowering adoption

Let a farmer's uncertain type be $\theta$, with integrable mean incremental profit $\mu(\theta)$ under a feasible technology. There is no liquidity constraint in this separate one-decision benchmark. The farmer is risk neutral and can choose the safe option with gain zero. An information signal $Z$ is generated by a specified law, and information is free for the following comparison.
Proposition (Value of information and adoption are distinct): Expected optimized profit weakly increases from $\max\{0,{\mathbb{E}}\mu(\theta)\}$ to ${\mathbb{E}}\max\{0,{\mathbb{E}}[\mu(\theta)\mid Z]\}$ after observing $Z$. Adoption probability can strictly decrease while this value strictly increases.
Proof: The maximum function $x\mapsto\max(0,x)$ is convex, so Jensen's inequality conditional on no signal gives the value inequality. Equivalently, the informed farmer can always ignore the signal and reproduce the old decision. For strict reduction in adoption, take equally likely types with means $2$ and $-1$. Without information the mean is $1/2>0$, so adoption is certain and expected gain is $1/2$. A perfectly revealing signal induces adoption only in the good type, with probability $1/2$ and expected gain one. Both assertions follow. ∎

Information costs must be subtracted in a cost-effectiveness calculation. With incomplete insurance, a signal may change posterior downside risk as well as its mean, so the risk-neutral result does not substitute for household expected utility. Experimentation can also reveal type only after a costly initial adoption; a dynamic learning policy must then value and finance that experiment explicitly.

Identification and remaining policy task

Random assignment over supported bundles identifies each arm's multiseason profit and downside risk. It also identifies the indicator of sustained use under the complete assignment design, provided the original baseline farmers are tracked and measurement is correct. Under cluster randomization with within-cluster spillovers, these are cluster-regime outcomes; conditional means among adopters are selected outcomes. A factorial interaction is a difference of supported arm means, not proof that it isolates a unique latent liquidity or learning mechanism.

The reserve model identifies a precise mechanism that a field design can test: withdrawal-date reserves and the distribution of net bad-season losses jointly predict persistence, while the commercial premium creates an additional initial financing threshold. Estimating farmer heterogeneity in $p,d,k$, basis risk, input quality, crop-price responses, and endogenous consumption is still necessary. No welfare-optimal credit--insurance--information bundle or general scale equilibrium has been established. The full target remains unresolved.

Completion Estimate

40%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt solves post-withdrawal reserve persistence and finite-horizon profit, establishes funded-insurance liquidity conditions, and separates information value from adoption rates. The full bundle comparison still needs heterogeneous risk preferences, credible channel interventions, input-quality and market-access effects, peer learning, and product-market adjustment at scale.

References

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