This paper deals with the implications of factor demand linkages for monetary policy design. We develop a dynamic general equilibrium model with two sectors that produce durable and non-durable goods, respectively. Part of the output produced in each sector is used as an intermediate input of production in both sectors, according to an input-output matrix calibrated on the US economy. As shown in a number of recent contributions, this roundabout technology allows us to reconcile standard two-sector New Keynesian models with the empirical evidence showing co-movement between durable and non-durable spending in response to a monetary policy shock. A main result of our monetary policy analysis is that strategic complementarities generated by factor demand linkages amplify social welfare loss. As the degree of interconnection between sectors increases, the cost of misperceiving the correct production technology of each sector can rise substantially. In addition, the transmission of different sources of exogenous perturbation is altered, compared to what is commonly observed in standard two-sector models without factor demand linkages. In this respect, the role of the relative price of non-durable goods is crucial, as this does not only influence the user cost of durables through the conventional demand channel, but also affects in opposite directions the real marginal cost of production in either sector through the intermediate input channel.