Seven Bakeries · Tereza Vačina

AUTHOR'S NOTE

A bit of the ending at the beginning :D

This is fun tinkering with models... my personal optimistic view is that humanity will survive somehow anyway, and with it a chunk of a functioning economy... maybe turbulent at times, but continuing.

And here's the actual note:

This is a model. Not a prediction, not a forecast... a simplified world in which something can be proven. There will be a few equations here, but I promise each of them comes with a picture, and the picture is a bakery.

One thing about it interests me: most of the debate about AI and work happens on the level of "will it replace people or won't it". This paper asks a completely different and, I think, much more interesting question: even when everyone can see they're driving off a cliff together, why don't they slow down?

Paper: Brett Hemenway Falk (University of Pennsylvania) & Gerry Tsoukalas (Boston University): "The AI Layoff Trap", 1 June 2026 (first version 2 March 2026). SSRN 6448898.

1. THE ASSIGNMENT

I'll start with the abstract, because it's unusually direct:

"If AI displaces human workers faster than the economy can reabsorb
them, it risks eroding the very consumer demand firms depend on. We
show that knowing this is not enough for firms to stop it."

That second sentence is the whole paper. The first sentence isn't new... it's a worry as old as Ricardo and Keynes (you know, those economics guys from the 18th–20th centuries who spent a lot of time on trade, crises, and what the state should do), and the authors admit as much themselves. What's new is the claim that rationality and perfect foresight are not enough to save you. That even if every CEO in the industry could see the cliff precisely, they'd still drive toward it, because slowing down doesn't pay.

That reminds me of the classic collective action problem, most of all the prisoner's dilemma: every individual player behaves rationally with respect to their own incentives, but when everyone does the same, the whole ends up worse. The prisoner's dilemma emerged around 1950 at the RAND Corporation in the experiments of Merrill Flood and Melvin Dresher; the mathematician Albert W. Tucker later gave it its famous two-prisoner formulation. And exactly this paradox is what matters here: the problem isn't that the actors fail to understand something or estimate it badly, but that an individually sensible strategy can be collectively catastrophic.

At one point the authors phrase it so sarcastically that I had to laugh: firms "automate toward unlimited productivity and zero demand". In other words: congratulations, we're producing, with infinite efficiency, things nobody can afford.

2. WHY THIS ISN'T JUST THEORY

This could be waved off as a thought experiment, if the authors hadn't opened with a rather uncomfortable list of facts.

In February 2026, Block laid off almost half of its roughly 10,000 employees. Jack Dorsey said AI had made many of those roles unnecessary, and added:

"within the next year, the majority of companies will reach the same
conclusion"

In 2025, US employers announced more than a million job cuts. AI was explicitly cited as the reason for roughly 55,000 of them, most heavily in tech companies, concentrated in customer support, content moderation and middle management.

Eloundou and colleagues (2024) estimate that about 80% of American workers have a job that includes tasks exposed to large language models.

And two numbers from the demand side that I found most telling: in the first quarter of 2026, business investment overtook consumer spending as the main contributor to US GDP growth. And the personal savings rate fell to 3.6% in March, the lowest since the end of 2022.

The authors don't present this as proof of their model. They present it as the reason to build the model.

3. SEVEN BAKERIES

Now the analogy. Hold on to it, because every single equation follows from it.

There are seven bakeries in a town. Each employs a hundred people. And now the trick the whole thing stands on: the bread in this town is bought mostly by those bakers. The employees of one bakery shop at all seven.

Along comes a technology that can bake bread more cheaply than a human. You are the director of bakery number one. You do the math:

What you gain: on every automated task you save the difference between the wage and the price of the machine. All of it. The saving is yours; you don't share it with anyone.

What you lose: the fired baker stops coming in to shop. But he doesn't stop shopping only at your bakery — he stops at all seven. The lost demand spreads across seven bakeries. You feel one seventh.

That's the entire trap. You pocket the whole saving; of the damage you pay one seventh, about fourteen percent. The rational decision is to automate. And because the same holds for all seven directors, they all automate, the town stops buying bread, and in the end even the owners of the bakeries are worse off than if nobody had moved.

This is the thing that got me most about this paper. It isn't a transfer of money from employees to owners. It's a loss borne by both. The authors put it like this:

"The resulting surplus loss is not a transfer from workers to firm
owners; it is a deadweight loss that harms both."

4. A FORMAL INTERLUDE

Here's the model. It's surprisingly small... and that's deliberate — the authors stripped it to the bone on purpose, so that only one channel is visible.

Setup. The sector has $N \ge 2$ symmetric firms. Each has $L$ jobs. Firm $i$ chooses an automation rate $\alpha_i \in [0,1]$ : tasks $z \in [0, \alpha_i]$ are done by AI at cost $c$ , tasks $z \in (\alpha_i, 1]$ are done by humans at wage $w$ , with $0 \le c \le w$ . Because every automated task displaces one person, $\alpha_i$ is simultaneously the automation rate and the share of workers laid off.

Costs. Integrating each additional task is harder (a convex integration cost):

C_i(\alpha_i) = L \bigl[ \alpha_i c + (1-\alpha_i)\, w \bigr] + \tfrac{k}{2}\, L\, \alpha_i^{2}

Saving per task: $s := w - c$ .

Demand. Workers spend a share $\lambda \in (0,1]$ of their income in this sector, owners nothing (in the base version). A share $\eta \in [0,1]$ of lost wage income comes back — through new employment, transfers, whatever. The rest is gone for the sector. Aggregate spending:

D(\alpha) = A + \lambda w L \Bigl[ N - (1-\eta) \textstyle\sum_j \alpha_j \Bigr]

where $A > 0$ is autonomous demand. The key parameter of the whole paper:

\ell := \lambda(1-\eta)\,w \qquad \text{\footnotesize … demand lost per automated task}

Profit of firm i (after the market clears at price $p = D/(NL)$ ), with $\bar{\alpha}$ as the average automation rate:

\pi_i = \Pi_0 + L \Bigl[ \alpha_i \bigl( s - \tfrac{\ell}{N} \bigr) - \tfrac{k}{2}\, \alpha_i^{2} - \tfrac{\ell}{N} \textstyle\sum_{j \neq i} \alpha_j \Bigr]

Notice the bracket $(s - \ell/N)$ . The whole bakery is in there: the firm takes the entire saving $s$ , but of the demand damage $\ell$ it sees only $\ell/N$ .

Equilibrium (Proposition 1). Define the threshold

N^{*} := \ell/ s = \frac{\lambda(1-\eta)\,w}{w - c}

If $N \le N^{*}$ , nobody automates. If $N > N^{*}$ , then

\begin{aligned} \alpha_{\mathrm{NE}} &= \min\!\left( \tfrac{s - \ell/N}{k},\ 1 \right) && \text{\footnotesize … Nash equilibrium} \\[4pt] \alpha_{\mathrm{CO}} &= \min\!\left( \max\!\left( 0,\ \tfrac{s - \ell}{k} \right),\ 1 \right) && \text{\footnotesize … cooperative optimum} \end{aligned}

and the difference between them, the excess automation wedge, is

\alpha_{\mathrm{NE}} - \alpha_{\mathrm{CO}} = \frac{\ell\,(1 - 1/N)}{k} > 0

The wedge grows with $N$ and with $\ell$ and shrinks with $k$ . That's the point in one equation.

The frictionless limit (Corollary 1). As $k \to 0$ , the game turns into a pure prisoner's dilemma: full automation ( $\alpha_i = 1$ ) is strictly dominant for every firm. And if moreover $s < \ell$ , the cooperative optimum is no automation, the equilibrium profit is $\Pi_0 + L(s - \ell ) < \Pi_0$ , and the total deadweight loss is $N \cdot L \cdot (\ell - s)$ .

The fix (Proposition 5). A Pigouvian tax on each automated task of

\tau^{*} = \ell\,(1 - 1/N)

aligns the equilibrium with the cooperative optimum, because $\alpha_{NE}(\tau) = (s - \tau - \ell/N)/k$ .

End of equations. The rest is reading what they say.

5. THREE THINGS THAT FOLLOW FROM THIS AND ARE COUNTERINTUITIVE

(a) More competition makes it worse. The wedge $\ell (1 - 1/N)/k$ grows with $N$ . A monopolist ( $N = 1$ ) internalizes the externality completely — it automates correctly. The more fragmented the market, the smaller the share of the damage falling on anyone and the less reason anyone has to hold back. As $N \to \infty$ , the wedge approaches $\ell/k$ .

This goes against the standard intuition that competition disciplines firms for the benefit of consumers. Here the consumer and the employee are the same person, and competition works the other way around.

(b) Better AI makes it worse too. Intuition says: once AI is truly productive, not just cheaper, this will solve itself, because output will grow. The authors did the math and it came out the other way. Each firm sees that automating above its competitors' level wins market share, but in the symmetric equilibrium these gains cancel each other out and only the distortion remains.

"This Red Queen effect means that "better" AI, far from mitigating
the externality, amplifies it."

The Red Queen effect comes from Through the Looking-Glass: you have to run as fast as you can just to stay in the same place. Here, all seven bakeries are running.

(c) An agreement won't help. Not even in theory. Here I expected the paper to at least allow a Coasean solution — if the damage is shared, let the firms make a deal. It doesn't allow it, and has a good reason: automation is a strictly dominant strategy. Not "the best response to what the others do" — dominant regardless of anything. So:

"Communication is cheap talk"

Even if everyone agrees that joint restraint would raise everyone's profits, each firm's individually optimal move remains unchanged. No unenforceable agreement holds.

And partial coalitions? Proposition 4: a coalition of $M$ firms out of $N$ chooses $\alpha_M = (s - M\ell/N)/k$ and the residual wedge is $\ell (1 - M/N)/k > 0$ for every $M < N$ . It disappears only at $M = N$ . The classic free rider: non-members enjoy the coalition's restraint without paying for it.

6. WHICH TOOLS WORK (ACCORDING TO THE MODEL)

The authors test six tools against one single question: does it change the marginal incentive to automate? Because if it doesn't, it can be useful in any number of other ways, but it won't fix this particular thing.

Doesn't work: a tax on capital income. It acts on the level of profit, not on the margin of a single task. The firm still saves $s$ and still sees only $\ell/N$ . (Analogy: you're taxing the race result, not the speed.)

Doesn't work: unconditional basic income. In the model, UBI is an increase in autonomous demand $A$ . Because the employed and the displaced get it alike, it adds a constant to spending, but it doesn't change the marginal income loss from displacement. It raises the floor; it doesn't change the slope. The authors explicitly add that this is a verdict on this model object, not on all forms of UBI... targeted transfers (severance, wage insurance) raise $\eta$ , and that does act on the right margin.

Works partially: requalification and retraining. They raise $\eta$ , and thereby shrink $\ell = \lambda (1 - \eta )w$ . The elegant Corollary 2: the wedge is maximal at $\eta = 0$ , positive for every $\eta < 1$ , zero at $\eta = 1$ and negative at $\eta > 1$ . In other words: if retraining moved people into better-paid roles, firms would automate too little. The authors don't sweep this under the rug — they just add that historical data on displaced workers shows persistent and large earnings losses, which puts most economies firmly in the $\eta < 1$ regime.

Works partially: employee profit-sharing. And the nice Corollary 3: it won't arise voluntarily. A firm loses one crown of retained profits and gains $\lambda/N$ of a crown of demand; because $\lambda/N < 1$ for every $N \ge 2$ , $\epsilon_i = 0$ is the dominant strategy. It has to be mandated to have any effect at all... and even then it doesn't help all that much.

Works: a Pigouvian tax on automation at $\tau^{*} = \ell (1 - 1/N)$ . And it gets a bonus, which is the part I like most: the revenue from that tax can fund retraining, which raises $\eta$ , which lowers $\ell$ , which lowers the required $\tau^{*}$ . A tax that gradually abolishes itself.

7. WHERE I HAVE DOUBTS

I'd be unfair if I sold this as a done deal.

Seven bakeries are not an economy. The model is partial-equilibrium: one sector, symmetric firms, fixed wages in the base version. The authors are aware of this and devote a separate discussion to it: in a smooth general equilibrium, the lost income should be absorbed elsewhere. Their argument for why this doesn't happen for mass-market firms has two parts... consumption saturation at high incomes (the owners' money flows off into the luxury segment, not back into the sector) and the fact that production can't be quickly re-tooled. The second route goes through the interest rate: savings rise, a falling interest rate should bring them back into play as investment — except this fails at the zero bound, and it fails when the income loss is permanent, because then the displaced can't bridge it with debt.

That's an honest defense. But it's a defense, not a result.

The quadratic integration cost is a choice. $(k/2)L\alpha^{2}$ is a standard specification, but it is a specification. The wedge $\ell (1-1/N)/k$ has $k$ in the denominator, so its size hangs on a parameter that is hard to measure in practice.

And one thing in the paper that creaks a little for me. The authors argue that a firm's automation $\alpha_i$ is not contractible — competitors can't see it, can't verify it, and therefore no private agreement holds. That is convincing. But a Pigouvian tax per task needs someone to measure that task. The regulator has an advantage over a competitor (it sees the payroll), but it remains true that a tax on an "automated task" will in practice be a tax on some proxy, most likely on headcount reduction. And proxies can be gamed... outsourcing, reclassifying positions, buying an already-automated supplier. In the model this isn't a problem, because in the model $\alpha$ is observable by the state. In the world, it's a whole implementation topic that's missing there.

8. WHAT I'M TAKING AWAY FROM IT

I won't pretend to know whether this model describes the year 2026. But one thing has stayed with me as a permanently usable lens.

Next time you hear "we laid off a quarter of our people, AI can handle it", that sentence doesn't only contain information about that company. It also contains the information the company didn't include in its decision, because it didn't have to. The $1/N$ share is invisible in every individual balance sheet and perfectly visible in the sum.

And that, after all, is the definition of an externality. We're just used to it with smoke from a chimney, where we're hit by something that has nothing to do with our goods. Here the smoke is our customer.

This is fun tinkering with models... my personal optimistic view is that humanity will survive somehow anyway, and with it a chunk of a functioning economy... maybe turbulent at times, but continuing.

SOURCES

Hemenway Falk, B. & Tsoukalas, G.: The AI Layoff Trap. 1 June 2026 (first version 2 March 2026), SSRN 6448898.

The model's building blocks, which the authors take over: Acemoglu & Restrepo (2018, 2019) — the task-based approach to automation and the reinstatement effect; Murphy, Shleifer & Vishny (1989) and Rosenstein-Rodan (1943) — aggregate demand spillovers; Lucas (1967) — the quadratic adjustment cost; Pigou (1920); Coase (1960); Beraja & Zorzi (2025) — the most closely related mechanism, but through the labor market, not the product market.

The empirical numbers cited in the text come from: Palmer (2026) — Block and Dorsey; Bhaimiya (2025) — announced US job cuts for 2025; Eloundou et al. (2024) — occupational exposure to LLMs; Bureau of Economic Analysis (2026a, 2026b) — the investment share of GDP growth and the personal savings rate.