Abstract: This paper develops a dynamic production-network model in which monetary non-neutrality emerges under fully flexible prices. Firms finance intermediate-input purchases from current nominal balances, and intermediate goods arrive with heterogeneous lead times across suppliers. A monetary shock then has two distinct effects. The first is miscoordination: because production uses dated input bundles assembled under past nominal conditions, the shock disturbs the composition of usable inputs (within and across firms) and thereby generates a deadweight loss. The second is reallocation: because the incidence of the shock is tilted toward smaller firms, which are disproportionately downstream, the shock redistributes resources along the supply chain. More specifically, positive shocks push resources downstream, negative shocks pull them upstream. This means that under a negative shock, both the miscoordination and the reallocation effect reduce downstream output and therefore GDP. Under a positive shock, reallocation raises GDP while miscoordination reduces it. The money-output relation is therefore sign-asymmetric: negative shocks generate sharp contractions, while positive shocks generate at most mild expansions, and sometimes none. Computational experiments on a reconstructed US production network generate output declines after a monetary contraction that are about three times as large as the increases after a monetary expansion.