Working Paper（24-018E）Non-exponential growth theory

To explain the observed stability in real GDP growth, existing endogenous growth theories proposed models in which the quantity, quality or variety of the final output increases exponentially in the long run. However, such exponential increases typically require a knife-edge degree of externality, which is not supported by microlevel observations. This paper presents a new theory of long-term growth where a constant number of new goods are introduced per unit of time and focuses on the movement of prices and quantities after introduction. We show that if the quality-adjusted prices and quantities of individual goods follow a typical pattern of product lifecycle, then the long-term rate of real GDP growth, as measured by the SNA statistics, becomes positive without exponential growth in the quantity, quality or variety of final outputs. We develop a prototype model and extensions and show that the conditions for positive real GDP growth are less restrictive than typical knife-edge assumptions. We also show that the long-term real GDP growth rate in the non-exponential model is closely related to the rate of increase in the money-metric utility.

Revised October 6, 2025

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