One policy the government could use to reduce differences in wages is to implement a new mininum wage for low earners. This is a wage below which it is illegal to hire workers at, and it must be set above the equilibrium wage rate to have any effect on a labour market.
The diagram above shows the minimum wage successfully raising the wage from W1 to WMIN, which could help to reduce the pay gap between the lowest paid workers, and higher earners.
However, at the higher wage, there are more people (QS) who are willing and able to work, and there are less workers who firms are willing and able to hire. Hence, there is an extension in supply of labour, and a contraction in demand for labour. Therefore, the downside with this policy is that it causes an excess supply of labour at the new wage. This is shown by the difference between QMIN and QS. This would translate to unemployment in the real world. If some workers are now unemployed, this actually increases the pay gap even more so a minimum wage could be an ineffective method of reducing inequality. This is an example of government failure as there are unintended consequences - as the aim was to increase the wage of low earners but unemployment was also caused by the government intervention, causing inequality to worsen.