Cross-demand creates links between goods which cause demand-driven cross-price dependencies. We construct a theoretical model to analyze their role in propagating microeconomic price shocks to the CPI inflation rate and examine their empirical relevance using spatial econometric techniques. The results highlight the importance of complementarity and substitution properties between goods in exacerbating or mitigating price shocks. This contrasts with the propagation through the production network. Most importantly, demand-driven cross-price dependencies determine the impact of producer prices on the CPI inflation rate.