Choice at Finite Capacity: The Bounded Agent as an Information Channel and the Recovery of Walrasian Demand

Standard economics assumes the consumer as a flawless calculator who always buys the best basket it can afford. This paper models the shopper instead as a limited information channel: it compresses its world to the detail its attention affords, so its choice is a probability distribution, not a single basket. The textbook consumer returns exactly as the unlimited-attention limit, while at the zero-attention end the shopper falls back on pure habit. The central result is about how this shopper's demand responds to price changes. That pattern of responses is just a rescaling of how the shopper's own choices vary and move together, so it comes out symmetric. And provided the budget really binds, because the shopper wants more than it can afford, raising a good's own price lowers demand for it once buying power is held fixed. So the downward pull comes from the budget and from compression, not from rationality. The framework also covers an artificial agent running a limited-capacity policy. A worked two-good quadratic consumer carries every quantity in closed form.