Can an increase in productivity cause a decrease in production? Insights from a model economy with AI automation

Casey O. Barkan

REVIEW 2 major objections 4 minor 16 references

Can an increase in productivity cause a decrease in production? Insights from a model economy with AI automation

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read In an idealized one-firm economy, a rise in AI automation productivity can lower GDP while raising the firm's profit.

desk verdict Clean monopsony counterexample to 'productivity always raises GDP,' but the advertised monopoly channel isn't in the equations. read the letter →

arxiv 2411.15718 v1 pith:ONFL26L2 submitted 2024-11-24 econ.GN q-fin.EC

Casey O. Barkan This is my paper · ORCID

classification econ.GNq-fin.EC

keywords AIautomationproductivityGDPmonopolymonopsonylabordisplacementnoncompetitivemarketseconomicscenariomodeling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is a theoretical counterexample to the common assumption that productivity growth always raises output. It constructs an idealized economy with a single firm that is the only seller in the product market and the only employer in the labor market. The firm can produce either with an old technology that uses both labor and capital or with an automation technology that uses only capital. As the productivity of the automation technology rises past a threshold, the firm fires all workers, production drops by about 40 percent in the paper's example, and the firm's profit increases. The paper argues that such simple models are useful scenario tools for thinking about AI-related economic risks.

What carries the argument

The central object is the envelope production function $f(K,L) = \max_{K_{\mathrm{old}}\in[0,K]}\left(A_{\mathrm{old}}K_{\mathrm{old}}^{\alpha}L^{1-\alpha} + A_{\mathrm{auto}}(K-K_{\mathrm{old}})\right)$, which is what lets the firm repurpose fixed capital toward automation. It is coupled with a household labor-supply curve $w(L) = w_{\min}/(1-L/(\gamma L_{\max}))$ derived from a Cobb-Douglas utility function, with $w_{\min}$ the wage below which households refuse to work. Together these reduce the whole general equilibrium to a one-dimensional profit-maximization problem in labor, and the mechanism doing the work is the corner solution: at the threshold $A_{\mathrm{auto}} > 1$ the firm moves to zero labor, producing the output drop and profit rise.

What would settle it

Recompute the same model with households owning a small positive share of the firm or capital stock. If for any positive share the profit-maximizing labor choice no longer jumps to zero and production is nondecreasing in $A_{\mathrm{auto}}$, then the paper's result is carried entirely by the zero-capital-ownership assumption rather than by monopoly-monopsony market power alone.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the equilibrium of this monopolist-monopsonist economy has a discontinuous response to automation productivity. The firm maximizes profit $\Pi(L) = f(\bar{K}, L) - w(L)L - \bar{r}\bar{K}$ over labor $L$ alone, because the capital stock is fixed and fully utilized. The aggregate production function lets capital be split between a labor-using old technology and a labor-free automation technology, so once the automation productivity parameter $A_{\mathrm{auto}}$ exceeds the old technology's marginal product of capital, the profit-maximizing choice of labor jumps from a positive level to zero. Output falls because the reduction in labor costs $wL$ is larger than the fall in revenue $f$, so profit rises even though the economy produces less. The paper also shows that the decline is transient: after the transition, output grows with $A_{\mathrm{auto}}$ and eventually surpasses its pre-transition level.

Load-bearing premise

The load-bearing premise is that the households selling labor own no capital and no shares in the firm, so wages are their only source of income; if they received any profit or capital income, their labor supply and product demand would change and the output drop could shrink or reverse.

Editorial extensions

If this is right

If the model is right, an economy can show no visible response to AI progress until a threshold is crossed, then suddenly lose nearly all private-sector employment and a large share of output.
Redistributive policies such as universal basic income cannot repair a drop in total output; they can only redistribute whatever smaller total exists.
A transient output drop could trigger a financial crisis that slows further AI progress, leaving the economy stuck in the reduced-production regime even if recovery was possible in principle.
A dynamic policy that taxes the firm's automation profits to pay displaced workers could delay the labor-for-capital switch until automation is productive enough that no output drop occurs, a hypothesis the paper leaves for future work.
The model's magnitude is parameter-dependent, and for some parameter values no drop occurs, so the qualitative discontinuity rather than the 40 percent figure is the robust prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implication the author leaves implicit is that the result depends heavily on households having zero capital income; allowing workers to own any share of the firm or capital stock would likely dampen or eliminate the drop, because consumption demand would not collapse as suddenly.
A natural testable extension would be to introduce a second firm: with even a small degree of competition in the product or labor market, the discontinuity in $L^*$ should smooth out, which would indicate that the result is a pure market-power phenomenon rather than an inherent property of automation.
The same fixed-capital, two-technology structure could be used to compare policies such as automation taxes, wage subsidies, and profit-sharing requirements, shifting the threshold $A_{\mathrm{auto}}$ at which labor is abandoned.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The punchline: this paper gives a clean, internally consistent example where better automation technology lowers total output. The mechanism is real and the math checks out. The advertised scope, however, is wider than what the equations actually support: the abstract says the firm is a monopolist in the product market, but the model normalizes product price to one and never introduces a product demand curve. What is actually demonstrated is a labor-monopsony effect with an elastic labor supply and a fixed capital stock, not a product-market monopoly effect.

What's new: most automation models assume competitive markets and inelastic labor supply. This one drops both, and shows that with a single firm facing an upward-sloping labor supply curve, the substitution of capital for labor can be profitable even when it reduces output. The firm's profit rises while GDP falls. The author is careful to call it an idealized scenario and doesn't over-claim empirical relevance. The code is provided, the figures match the stated parameters, and the derivation of the labor supply curve is straightforward and correct.

Where it's soft: the monopolist label is the main problem. Since the product price is fixed as numeraire and all wage income is spent on the single good, the product market clears by identity; the firm has no pricing power in the product market. Either the author should specify an explicit downward-sloping demand curve and let the firm set price, or drop the 'monopolist' language and describe the firm as a monopsonist in labor and price-taker in product. The result is still interesting as a monopsony counterexample, but the scope is narrower than the abstract suggests. Also, the assumption that workers own no capital and no equity matters: if households received profit income, their labor supply and consumption demand would shift, and the drop might be dampened. That's a standard modeling choice, but it should be highlighted more prominently. The comparison to the Great Depression is rhetorical; the model parameters are not calibrated, so the 40% drop is illustrative, not a prediction.

Who it's for: people thinking about AI scenario planning, labor displacement, and noncompetitive markets. It's a useful cautionary example, not a quantified forecast. The paper deserves a serious referee; a good referee could push for an honest relabeling or an actual product-market monopoly extension. If the author fixes the framing mismatch, this becomes a solid contribution to the theoretical literature on automation and market power.

Referee Report

2 major / 4 minor

Summary. This paper constructs a static general-equilibrium model with one firm, a fixed capital stock, a single good, and a household sector that chooses labor supply and consumption. Production uses either an old Cobb-Douglas technology combining labor and capital or a new automation technology requiring only capital, with automation productivity Aauto treated as an exogenous parameter. The firm maximizes profit taking the labor supply curve as given, and the paper computes equilibrium production, labor employment, capital allocation, wages, and profit as Aauto varies. In the numerical example, when Aauto rises above a threshold near 1, capital is reallocated to automation, labor employment falls discontinuously to zero, production drops by roughly 40 percent, and firm profit rises; further increases in Aauto eventually raise production again. The paper interprets this result as a counterexample to the assumption that productivity growth necessarily increases GDP, and it discusses differences from and limitations relative to existing automation models.

Significance. The model is transparent and internally computable: all parameters are listed, the derivations in Section 2 are explicit, and Python code is provided. As an existence example, the numerical transition is reproducible, and the mechanism—a firm that reduces output to save on labor costs once a capital-only outside option becomes productive—is clearly explained. The paper also candidly situates itself against existing work, acknowledging the fixed capital stock, the absence of capital accumulation, and the lack of household heterogeneity in Sections 4 and 5. If the scope is re-cast as a labor-market monopsony result, the paper makes a clean pedagogical point: with elastic labor supply and zero capital income for workers, a productivity improvement in a capital-only technology can reduce total output even as profit rises. However, as advertised, the product-market monopoly channel is not implemented in the equations, and the generality of the result beyond the specific parameterization and ownership structure is not established. These issues are the main reasons the manuscript needs revision before publication.

major comments (2)

[§2.2, Eq. (9)] The product-market dimension of the model is not implemented. The abstract and Section 2 describe the firm as a monopolist in the product market, but the price is fixed as the numeraire and no product demand curve is specified. Eq. (9) is the labor supply curve, derived from maximization of Eq. (8); it is not a goods demand curve. The paragraph after Eq. (9) claiming that "the product demand is implicitly defined by Eq. 9" conflates labor supply with goods demand. Since the single good's market clears by accounting identity at any normalized price, the firm effectively has no price-setting power in the product market. The demonstrated mechanism is labor-market monopsony with elastic labor supply and a fixed capital stock, not product-market monopoly. To support the abstract's claim, the author must either introduce an explicit downward-sloping product demand curve with price as a choice variable or re-scope the paper as a model of a labor-market monopsonist in a price-taking output market. This is load-bearing because the paper's novelty is advertised as a monopolist in the product market and a monopsonist in the labor market, and the mathematics supports only the second component.
[§2, household ownership assumption] The result is conditional on households owning no capital or equity, so consumption equals labor income and the only channel through which income affects labor supply is the wage. This assumption is stated in Section 2, but its role in the headline result is not made explicit. If households received profit or rental income, the labor supply curve would shift with income effects, potentially damping or reversing the production drop. Because the paper uses the model as a counterexample, the ownership assumption is a legitimate part of the construction, but the abstract and conclusions should say that the output decrease occurs in an economy where workers have no capital income. Without this caveat, the claim reads as if it holds for any economy with a single firm, which is not established. I suggest adding one sentence to the abstract and a short robustness discussion in Section 4 or 5.

minor comments (4)

[§2.3] The product market clearing condition is printed as "f = wL + rK − Π"; with Π defined in Eq. (4) as f − wL − rK, the correct identity is f = wL + rK + Π. Please fix the sign error.
[Eq. (2)] The formula for K*old has Aauto in the denominator, but the text sets Aauto = 0 initially; the initial case should be defined by a limit or a separate expression to avoid a division-by-zero artifact.
[§3] The comparison of the roughly 40 percent drop with the Great Depression is rhetorically strong but not supported by the model's degree of realism; the parameter-dependent magnitude should be labeled as illustrative only, and the comparison should be removed or heavily caveated.
[General] The manuscript contains both an executive summary and a full paper with substantial verbatim overlap; condensing the executive summary or labeling it as a non-technical overview would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the model's central result is derived from exogenous automation productivity and standard profit/utility maximization; no fitted parameter is relabeled as a prediction and no load-bearing self-citation is present.

full rationale

The paper is a self-contained theoretical exercise. The exogenous input is Aauto (automation productivity); all equilibrium quantities (labor L*, output f*, profit Π*, capital allocation) are derived from the firm's profit maximization (Eqs. 1-5) and households' utility maximization (Eqs. 7-9). No parameter is estimated from data and then 'predicted' in a closely related form: the model parameters (α, γ, wmin, Kbar, Lmax) are fixed illustrative constants, and Aold is calibrated only to set the initial marginal product of capital to unity, which merely normalizes the threshold and does not force the drop in output. There are no self-citations; all cited works are external and none is invoked as a load-bearing 'uniqueness theorem.' The passage in Section 2.2 stating that 'the product demand is implicitly defined by Eq. 9' is a modeling/consistency issue—Eq. 9 is the labor supply curve, and with product price as numeraire the firm effectively faces a horizontal demand, so the 'monopolist in the product market' framing is not implemented in the equations. This is a substantive limitation, but it does not make the derivation circular: the output drop is computed from profit maximization, not assumed, and the product-demand passage is not used to derive any result. The decline in production as Aauto crosses unity follows directly from the profit function's shape (Fig. 1C), which is a mathematical consequence of the assumed production functions and labor supply, not an artifact of defining output in terms of an input. Hence no circular reduction exists, and the paper earns a score of 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The central result rests on a small set of chosen parameter values and standard structural assumptions. The parameters are not estimated from data; they are illustrative and set to make the automation transition occur at A_auto = 1. The assumptions about market structure and household preferences are what generate the possibility of an output drop; changing them (e.g., perfect competition, inelastic labor supply, or capital-owning workers) would either weaken or eliminate the effect.

free parameters (7)

Cobb-Douglas output elasticity of capital in the old technology (alpha) = 0.5
Chosen for the numerical example, not estimated from data.
Household preference weight on consumption (gamma) = 0.5
Chosen for the numerical example; sets the shape of the labor supply curve.
Reservation wage (w_min) = 2
Chosen for the numerical example; together with gamma and L_max it implies c0 = 1000.
Fixed capital stock (K_bar) = 50
Chosen for the numerical example; the economy has no capital accumulation.
Maximum labor supply (L_max) = 500
Chosen for the numerical example; scales the labor supply curve.
Total factor productivity of the old technology (A_old) = ~3.01
Set so that the marginal product of capital equals 1 when A_auto = 0, placing the automation transition at A_auto = 1.
Rental rate of capital (r_bar) = unspecified (must be below the marginal product of capital)
Assumed low enough that the firm uses the full capital stock; it is a fixed cost and does not affect the labor decision.

assumptions (5)

domain assumption Production follows Cobb-Douglas forms for the old technology, f_old(K,L) = A_old K^alpha L^(1-alpha), and a linear form for automation, f_auto(K) = A_auto K.
Specified in Section 2.1; the automation technology has constant returns to capital and requires no labor.
domain assumption There is a single profit-maximizing firm with no competitors in either the product market or the labor market.
Abstract and Section 2; the core noncompetitive structure that drives the result.
domain assumption Households maximize utility U(c,l) = (c+c0)^gamma l^(1-gamma) and do not own capital or equity in the firm.
Section 2.2; generates an elastic labor supply curve with a reservation wage w_min and rules out profit income affecting labor supply or product demand.
domain assumption The total capital stock in the economy is fixed at K_bar.
Section 2; justified as valid when technological change occurs rapidly relative to capital accumulation.
domain assumption It is profit maximizing for the firm to utilize the entire capital stock.
Section 2.1; justified by assuming the rental rate is below the marginal product of capital at the profit-maximizing point.

invented entities (1)

Capital-only automation technology (f_auto = A_auto K)
purpose: Allows the firm to produce without labor input, enabling displacement of the human workforce.
Modeling abstraction motivated by AI automation; it is a production-function specification, not an empirically identified factor of production with independent falsifiable evidence in the paper.

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Cite this review

Pith. "Pith review of Can an increase in productivity cause a decrease in production? Insights from a model economy with AI automation." pith.science (2026). https://pith.science/paper/ONFL26L2

@misc{pith2026241115718,
  author       = {Pith},
  title        = {Pith review of: Can an increase in productivity cause a decrease in production? Insights from a model economy with AI automation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ONFL26L2}},
  note         = {Machine review of arXiv:2411.15718}
}

read the original abstract

It is widely assumed that increases in economic productivity necessarily lead to economic growth. In this paper, it is shown that this is not always the case. An idealized model of an economy is presented in which a new technology allows capital to be utilized autonomously without labor input. This is motivated by the possibility that advances in artificial intelligence (AI) will give rise to AI agents that act autonomously in the economy. The economic model involves a single profit-maximizing firm which is a monopolist in the product market and a monopsonist in the labor market. The new automation technology causes the firm to replace labor with capital in such a way that its profit increases while total production decreases. The model is not intended to capture the structure of a real economy, but rather to illustrate how basic economic mechanisms can give rise to counterintuitive and undesirable outcomes.

Figures

Figures reproduced from arXiv: 2411.15718 by the authors.

**Figure 1.** Model structure, labor supply, and profit maximization (A) Schematic of the structure of the economy. (B) Labor supply with c0 > 0 (blue), and an inelastic labor supply (c0 = 0) for comparison (dashed grey). (C) Firm’s profit function Π(L) for increasing values of the productivity Aauto. As Aauto increases beyond a value of 1, the profit-maximizing labor L ∗ (indicated by dots) jumps from L ∗ ≈ 20 down to 0. Model p… view at source ↗

**Figure 2.** Equilibrium quantities versus the productivity of automation technology Aauto. (A) Production (f ∗ ) vs. Aauto. (B) Percent capital allocation vs. Aauto. Blue and red curves show, respectively, percent of capital allocated to the old and automation technologies. (C) Firm’s profit (Π∗ ) vs. Aauto. (D) Labor employment (L ∗ ) vs. Aauto. product demand is implicitly defined by Eq. 9 and by our choice to use the product… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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Daron Acemoglu. The simple macroeconomics of ai. Technical report, National Bureau of Economic Research, 2024

work page 2024

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Daron Acemoglu and Pascual Restrepo. The race between man and machine: Implications of technology for growth, factor shares, and employment. American economic review, 108 0 (6): 0 1488--1542, 2018

work page 2018

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Automation and rent dissipation: Implications for wages, inequality, and productivity

Daron Acemoglu and Pascual Restrepo. Automation and rent dissipation: Implications for wages, inequality, and productivity. Technical report, National Bureau of Economic Research, 2024

work page 2024

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Philippe Aghion, Benjamin F Jones, and Charles I Jones. Artificial intelligence and economic growth, volume 23928. National Bureau of Economic Research Cambridge, MA, 2017

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Robert Barro and Xavier Sala-i Martin. Economic Growth. The MIT Press, 2nd edition edition, 2004

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Erik Brynjolfsson and Gabriel Unger. The macroeconomics of artificial intelligence. Finance & Development Magazine, 2023

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