We develop an economic framework to analyze the optimal pricing and product design of Large Language Models (LLM). Our framework captures several key features of LLMs: variable operational costs of processing input and output tokens; the ability to customize models through fine-tuning; and high-dimensional user heterogeneity in terms of task requirements and error sensitivity. In our model, a monopolistic seller offers multiple versions of LLMs through a menu of products. The optimal pricing structure depends on whether token allocation across tasks is contractible and whether users face scale constraints.

We study how recommendation algorithms affect trade and welfare in markets characterized by algorithmic consumption, such as e-commerce platforms and AI assistants. Our analysis begins with a model of bilateral trade in which a single product is exchanged between a buyer and a seller under uncertainty about product value and seller cost. An algorithm recommends the product based on its price and estimated buyer value, thereby steering purchasing decisions. We characterize the buyer-optimal algorithm and show that it deliberately biases recommendations to amplify buyer price sensitivity, inducing lower seller prices. This optimal algorithm strategically deviates from the ex post optimal rule to exploit price pressure and enhance buyer surplus.

We study information design in games with a continuum of actions such that the payoff of each player is concave in his action. A designer chooses an information structure--a joint distribution of a state and a private signal of each player. The information structure induces a Bayesian game and is evaluated according to the expected designer's payoff under the equilibrium play.