The pay of CEOs and other top executives has risen disproportionately relative to other earnings. We provide a supply-side explanation based on utility theory using directionally bounded utility functions. As overall income levels have grown, the amount of compensation required to induce top executives to sacrifice a quiet life has risen. We show that directionally bounded utility functions predict a general rise in compensation for stress. More importantly, such utility functions can be used to explain why the CEO pay ratio has risen at an increasing rate, something which other approaches have difficulty explaining.