Production Networks, Capital Dynamics, and Heterogeneous Agents

We develop a general equilibrium production network model that spans two periods and incorporates heterogeneous households, firm-specific Cobb-Douglas production technologies, and a time-to-build mechanism for capital formation. Within this dynamic framework, we establish the existence and uniqueness of a competitive equilibrium and provide explicit analytical solutions for key economic variables. In particular, we derive closed-form expressions for the welfare and real interest rate effects of supply-side shocks occurring at different points in time. We calibrate the model using input-output data from the Italian economy, identifying key structural features such as the prominent roles of the real estate, food, and tourism-related sectors. We then extend the calibration to incorporate household heterogeneity by skill level and examine the consequences in terms of welfare and real interest rates of a climate-related productivity shock. This shock is sector-specific, time-dependent, and scaled according to differential exposure to climate risks. Our results show that climate-induced negative supply-side shocks generate disproportionate welfare losses for low-skilled households and induce nontrivial adjustments in real interest rates across sectors.