Neurophysiological experiments indicate that working memory of an object is maintained by the persistent activity of cells in the prefrontal cortex and infero-temporal cortex of the monkey. This paper considers a cortical network model in which this persistent activity appears due to recurrent synaptic interactions. The conditions under which the magnitude of spontaneous and persistent activity are close to one another (as is found empirically) are investigated using a simplified mean-field description in which firing rates in these states are given by the intersections of a straight line with the f-I curve of a single pyramidal cell. The present analysis relates a network phenomenon - persistent activity in a 'working memory' state - to single-cell data which are accessible to experiment. It predicts that, in networks of the cerebral cortex in which persistent activity phenomena are observed, average synaptic inputs in both spontaneous and persistent activity should bring the cells close to firing threshold. Cells should be slightly sub-threshold in spontaneous activity, and slightly supra-threshold in persistent activity. The results are shown to be robust to the inclusion of inhomogeneities that produce wide distributions of firing rates, in both spontaneous and working memory states.