Discounting at Finite Capacity: Micro-Founding Geometric Discounting: and the Compressed Euler Equation

Why do people value the present over the future? Economics assumes this impatience without explaining it. This paper derives it from one idea: people process information at a limited rate. To plan for a future payoff you must keep pace with the novelty in your income, and spreading limited attention across the horizons ahead produces a steady discount on the future, one that steepens with both how much novelty the income generates and how costly attention is. Impatience is thus the price of a novel future met by a finite mind, and it disappears when the world is predictable or attention is unlimited. The same idea recasts present bias, the pull toward the near term, as a novelty rate not yet learned, and explains why consumption reacts only gradually and smoothly to income surprises. The account concerns what generates discounting and what the data can pin down, not forecasting, and rests on a reproducible numerical illustration, not an empirical test.