Starting from the Ladrón‐de Guevara et al.’s framework, we develop a model with an additional sector for the production of leisure services. By introducing consumption of leisure services as a time‐consuming activity, our model generalizes the standard time allocation problem whereby total available time can be allocated between work, education, free time and leisure activities. We analytically characterize the balanced growth paths of the model, particularly in terms of time allocation and growth. Our comparative analysis of different service economies assumed at equilibrium includes the case of an industrial economy without a service sector and the potential multiple equilibria of such an economy.