Most of the world’s firms are small, particularly in poor economies. We argue that the existence of indivisibilities of inputs is a key driver of capacity underutilisation in small firms, leading to the endogenous emergence of slack. We present a monopoly model of capacity choice in which one of the inputs is subject to an integer constraint and show how pricing, input choices and investment are non-trivial functions of firm size, with important implications for aggregate economic outcomes in spatial general equilibrium. We validate the model using experimental field data from a large-scale clustered cash transfer RCT in Western Kenya. Building on novel measures of capacity utilisation, we uncover four moments: (1) Slack is larger in small firms, (2) supply curves are highly elastic, particularly where utilization is low, (3) aggregate inflation in response to the fiscal shock is low, (4) there exists some inflation in high-utilisation regions. Our findings can rationalise large multipliers in poor economies.