Dynamic Adjustments in Environmental Input-Output Models: Incorporating Quantity and Price Traverse Disequilibrium

This paper extends the traditional Leontief Input-Output (I-O) model by introducing a traverse disequilibrium framework that captures simultaneous quantity and price adjustments over time. Unlike standard static I-O models, this approach incorporates continuous-time adjustments in production, prices, and resource utilization. The analysis models how sectors respond to demand fluctuations through inventory accumulation and production adjustments, allowing for temporary imbalances between supply and demand. The model is further extended to include price-setting mechanisms. In this framework, sectors adjust markups in response to cost fluctuations and inventory deviations, and biophysical resource utilisation, leading to physical constraints and cost-push inflation. Calibrated using Brazil's Input-Output matrix and land-use data, the framework is applied to sectoral shocks, including demand surges and price rigidities, to assess their sectoral and macroeconomic impacts. The results highlight the importance of adjustment speeds in shaping economic dynamics, showing that rigid price and quantity settings amplify inventory cycles, while fast quantity adjustments increase output volatility. Sectoral interdependencies create cascading effects, demonstrating how price, and quantity shocks propagate across industries. Additionally, the dependence on environmental services illustrates how pressures on scarce resources feedback into prices and quantities.