Stability of price and quantity to a long-run equilibrium: a dynamic Leontief model with bounded rationality

The notorious 'dual stability' paradox is stated as follows: in a closed dynamic Leontief model, when the quantity system is relatively stable, its corresponding price system will be unstable, and vice versa. This paradox arises from the neoclassical assumptions of full utilization of capacity and perfect foresight, which have caused serious complications in the dynamic Leontief model. In this study, we aim to construct a dynamic input-output model within an evolutionary framework, departing from neoclassical assumptions. Two new assumptions are introduced: incomplete utilization of capital stocks and bounded rationality in decision-making. Our findings reveal that the 'dual stability' paradox of the quantity and price systems can be addressed by including these two assumptions, and some special conditions are proposed for the stability properties in both the systems. Furthermore, we prove that the distance between the time paths and equilibrium position converges to a constant, which is related to the initial position.