Swappable batteries have been deployed in several services of dockless shared e-scooters. This article provides an economic theory of swappable batteries in the production of a shared e-scooter service (S3). Explicitly modelled are the operations of battery swapping by "juicing tours", as well as the wearing law of the electric batteries depending on the depth of discharge (DoD) that triggers the next swap. In the production model, the daily number of refills and the per-refill swapping cost are key variables as they link the field implementation and the swapping logistics functions to the other production functions of battery inventory, scooter inventory, energy charging, fleet maintenance and commercial. Thus the overall "refill strategy" interplays with the respective inventory policies of batteries and of scooters. The mathematical optimization of the production cost function is addressed in four stages, by optimizing in turn (i) the swapping tours, (ii) the target DoD, (iii) the battery energy capacity (BEC), (iv) the scooter body in terms of lifespan and energy consumption rate. Characteristic equations are established for the optimal per-refill cost, DoD, BEC, scooter lifespan and energy consumption rate. Two sets of specifications, namely Constant Elasticity and Affine Linear, are specified for the battery wearing law, the battery price and the scooter price: under either set the model admits an analytical solution. In a numerical study, it is shown that the S3 cost per unit of fed-in energy is one order of magnitude greater than the out-of-the-grid electricity price.