The ability of the electron localization function to perform a partition of the unit cell volume of crystalline solids into well-defined, disjoint, and space-filling regions enables us to decompose the bulk compressibility into local contributions with a full chemical meaning. This partition has been applied to a set of prototype crystals of the chemical elements of the first three periods of the periodic table, and the equations of state for core, valence, bond, and lone electron pairs have been obtained. Solids are unequivocally classified into two groups according to their response to hydrostatic pressure. Those with sharing electrons (metals and covalent crystals) obey a simple relationship between the average valence electron density and the zero pressure bulk modulus. The stiffness of the closed-shell systems (molecular and ionic solids) is rationalized resorting to the Pauli principle. Overall, the results clearly correlate with chemical intuition: periodic trends are revealed, cores are almost incompressible and do not contribute appreciably to the macroscopic compressibility, and lone pair basins are rather easier to compress than bond basins.