Matthew E. Kahn and Gemini
October 5, 2026.
In standard intermediate microeconomics, a profit-maximizing firm uses an input until marginal revenue product equals marginal factor cost. For a perfectly competitive firm, the output price p is exogenous, so this condition equates the marginal value product of the input to its factor price.
Applying that logic to firm demand for AI tokens raises new issues. The media is filled with stories of leading firms burning through their computing budgets as workers use AI relentlessly without internalizing the opportunity cost of the use of ChatGPT or Claude.
Here I write out the joint optimization decision of a firm choosing which AI model to use and how much to use it. AI firms charge non-linear prices for their tokens.
Suppose four AI models are available (j = 1, 2, 3, 4: specialized reasoning engines, multimodal vision models, lightweight utility models, and frontier models), each with its own nonlinear token-price schedule. The firm solves a discrete-continuous problem: it computes maximized profit from each model at the intensive margin, then selects the model, or portfolio, with the highest profit. Uncertainty about model-specific production functions and about nonlinear token prices is a real barrier to efficient factor use.
Let a perfectly competitive firm produce output with traditional input L and AI tokens. There are four models, indexed by j = 1, 2, 3, 4. Under model j, the firm faces a nonlinear outlay schedule R_j(AI_j), where AI_j is tokens consumed from that model.
Adoption is a two-step problem. First, for each j, the firm solves the intensive-margin problem given production function f_j(AI_j, L) and schedule R_j:
π_j* = max over AI_j and L of [p · f_j(AI_j, L) − wL − R_j(AI_j)].
An interior solution under model j requires that the marginal value product of tokens equal the marginal token price on that schedule:
p · ∂f_j(AI_j*, L_j*) / ∂AI_j = R_j'(AI_j*).
Second, the firm selects the model with the highest maximized profit:
Π* = max of π_j* over j in {1, 2, 3, 4}.
Interesting Point #1; The First Order Conditions are Funky!
Optimization is challenging when firms aren't certain about the marginal benefits and the marginal costs of a choice! In the AI demand case, both sides of this problem are uncertain. The firm does not know f_j for any architecture, so relative productivities are unclear. Token schedules often include volume tiers, context-window scaling, or input-output price asymmetries, so marginal price depends on usage the firm cannot forecast well. Intensive-margin optimality across discrete architectures, followed by global model selection, is much harder than the textbook case.
This fuzzy optimization problem resembles ctricity customers. Electricity demand is derived from appliance use, but customers often do not know how a monthly bill is determined under an increasing-block tariff, what their marginal price for the month is likely to be, or how specific appliance actions map into kilowatt-hours and dollars.
Point #2
Kahn and Wolak ran a randomized field experiment with two California utilities. Homeowners were assigned to an intent-to-treat group or a control group. The treatment group was invited to a short online course covering how the block tariff determines the bill, a typical monthly marginal price, and customized tips linking appliance use to bill dollars.
Using panel data around the intervention, they found that participants reduced average daily consumption. Tier-specific effects went in the expected direction: customers who learned they faced a higher marginal price cut use, while those who learned they faced the lowest block increased use.
Firms choosing among AI models face an analogous gap. Uncertainty over model-specific productivity and over nonlinear token prices pushes them toward rules of thumb rather than intensive-margin optimization and clean model selection.
Three mechanisms can close the gap. Consulting firms can audit workflows, compare the four architectures, estimate task-level production responses, and match models to tasks. Trial and error, through deployment, prompt benchmarking, and internal experiments, reveals empirical gradients across models. Providers of cheaper tokens per unit of effective output have an incentive to show firms when workloads should move off expensive frontier models.
How fast does this happen? Households in Kahn and Wolak (2013) adjusted after a single short course. Firms have much more "skin in the game"!