Greater equality: rising wage disparities are one of the key drivers of inequality. By putting a plug on both ends of the pay scale we help ensure decent living standards for all and avoid the negative consequences (eg higher crime, poorer public health) of living in a highly unequal society.
The need to tame executive pay: extremely high levels of pay among executives have encouraged risk-taking behaviour (leading to the banking crisis) and have been found to hinder, not aid, the overall productivity of a company.
Tackle over-consumption and debt: as social beings we constantly rate ourselves relative to others. Keeping up with the Joneses in an era of high inequality has led people to take on higher levels of debt and to over-consume at a level they and the planet cannot sustain.
Beyond the costs to society, academic evidence shows that once people earn an annual wage above $80,000 their wellbeing grows by very little. Thus a maximum wage would help both business and society without damaging the wellbeing of the well-off.