The socially optimal level of capital in a national banking system will exceed the privately optimal level, being the aggregate of individual bank's assessed economic capital, if taxpayers in each national jurisdiction are expected to bear losses which, although unexpected to each bank, are ‘expected' across a portfolio of banks.
This is because the expectation of the socialisation of losses changes the behaviour of banks ex ante. Whether taxpayers should in fact bear losses, given a failure, is a different issue. That is determined by the costs of the bail-out and future costs of moral hazard, including the cost to future taxpayers.