A soft budget constraint arises when a government is unable to commit to not ‘bailout’ a public hospital if the public hospital exhausts its budget before the end of the budget period. It is shown that if the political costs of a ‘bailout’ are relatively small, then the public hospital exhausts the welfare‐maximising budget before the end of the budget period and a ‘bailout’ occurs. In anticipation, the government offers a budget to the public hospital that may be greater than or less than the welfare‐maximising budget. In either case, the public hospital treats ‘too many’ elective patients before the ‘bailout’ and ‘too few’ after. The introduction of a private hospital reduces the size of any ‘bailout’ and increases welfare. Copyright © 2015 John Wiley & Sons, Ltd.