We develop a N-sector business cycle network model a la Long and Plosser (1983), featuring heterogenous money demand a la Bewley (1980) and Lucas (1980). Despite incomplete markets and a well-defined distribution of real money balances across heterogeneous households, the enriched N-sector network model remains analytically tractable with closed-form solutions up to the aggregate level. Relying on the tractability, we establish several important results: (i) The economy's input-output network linkages become endogenously time-varying over the business cycle—thanks to the influence of the endogenous distribution of money demand on cross-sector allocations of commodities. (ii) Despite flexible prices, money is neither neutral nor superneutral and transitory monetary injections can generate highly persistent effects on sectoral output, thanks to the time-varying distribution of money demand and its effect on input-output coefficients. (iii) Although money injection is distributed equally across households by design, the real effects are asymmetric across production sectors, e.g., the impact of money is strongest on downstream sectors that purchase intermediate goods from the rest of the economy, but weakest on upstream sectors that supply intermediate goods to the other sectors, in sharp contrast to the case of sectoral technology shocks and government spending shocks. Our model also shows that movements in the distribution of money demand could be an important source of the measured labor wedge documented by the business cycle accounting literature.