Before revision:  Since firms are embedded in production networks, these direct shocks to supply and demand will propagate downstream and upstream . We show that existing input-output models which allow for binding demand and supply constraints yield infeasible solutions when applied to pandemic shocksof three major European countries (Germany, Italy, Spain). We then introduce a mathematical optimization procedure which is able to determine best-case feasible market allocations, giving a lower bound on total shock propagation.
After revision:  Since firms are embedded in production networks, these direct shocks to supply and demand will propagate downstream and upstream through production networks. Given the exogenous shocks, we derive a lower bound on total shock propagation.