A New Market Theorem for the 21st Century: Dynamic Equilibrium Theorem

This study develops the Dynamic Equilibrium Theorem (DET) approach, which evaluates expectations, sentiment/pessimism affecting demand, and changes in innovation in production capacity within the same analytical framework, rather than treating market equilibrium solely as the equalization of current price and quantity. In the basic model, demand is defined as Q_d(t)=a−bP_t+eE_t−fD_t and supply as Q_s(t)=c+dP_t+gI_t. Here, E_t represents expectations about the future, D_t represents the sentiment/pessimism component that suppresses demand, and I_t represents changes in innovation and production capacity. The distinguishing feature of the model is that these variables are not only used as additional explanatory elements but are defined as state variables that change over time. An analytical equilibrium solution is obtained, and the sensitivity of the equilibrium price and quantity to the relevant state variables is demonstrated through comparative statics. In the numerical examples for gold, agriculture, and the defense industry, all parameters are explicitly specified and equilibrium values are calculated directly from the model equations. These examples are treated as calibrations used to demonstrate how the model operates, rather than as actual market forecasts. The results indicate that expectations increase equilibrium price and quantity, whereas pessimism that suppresses demand reduces both variables. Innovation, by expanding supply in the linear supply function, reduces the equilibrium price and increases the equilibrium quantity. The contribution of the study is to express mechanisms related to expectations, behavioral factors, and innovation together within a single partial-market equilibrium system and to clearly distinguish their marginal effects on equilibrium. The model can be solved in closed form and produces directly testable propositions. However, the results obtained here are results of the theoretical model; the empirical validity of the DET can only be assessed when coefficient estimation, identification, and out-of-sample forecast comparisons are conducted using real data.