In an ink jet printer of the present invention, in order to reduce the manufacturing cost, an inexpensive EEPROM enabling only sequential accesses is applied for storage elements incorporated in a black ink cartridge and a color ink cartridge. The data array of a memory cell included in each of the storage elements mounted on the ink cartridges is determined in such a manner that a second storage area, in which rewritable data, for example, data on remaining quantities of inks in the ink cartridge, are stored, is accessed prior to a first storage area, in which read only data are stored. This configuration enables the rewritable data to be securely written into the second storage area even after a power-off operation. The second storage area has two memory divisions allocated to each ink, that is, a first ink remaining quantity memory division and a second ink remaining quantity memory division. Latest data on the remaining quantity of each ink is alternately written into these two memory divisions. Alternatively, the latest data on the remaining quantity of each ink is written into these two memory divisions in a duplicated manner. Each ink remaining quantity memory division has a write complete flag to determine whether or not a writing operation has been completed normally in the ink remaining quantity memory division. This arrangement enables the remaining quantities of the respective inks to be monitored accurately and continuously.